pam_rule_generation_example.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rule Generation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook we will showcase the efficiency of PAM for rule generation.\n",
    "\n",
    "We will follow the procedure described in Section 3.4 for the applicaiton of rule generation.\n",
    "\n",
    "The process is simple:\n",
    "1. First download the **YAGO3-10** dataset. The .tsv with the triples is expected to be in folder in the same directory as this notebook with the name \"data\".\n",
    "2. Create the **lossless** $1$-hop PAM  and the **k-hop** PAMs $P^k$ which hold the corresponding paths.\n",
    "3. Find paths $Path^k$ that may imply a head relation $r_H$ through a simple check: $P[A,B] = r_H$ and $P^k[A,B] = Path^k \\neq 0$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initial imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import tqdm\n",
    "import time\n",
    "import string\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from itertools import permutations, product\n",
    "from pam_creation import create_pam_matrices\n",
    "from utils import load_data, get_primefactors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loading the data\n",
    "\n",
    "We simply read the collection of triples in a dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total: 735915 triples in train + eval!)\n",
      "In train: 732556\n",
      "In valid: 3359\n",
      "In test: 3390\n",
      "# of unique rels: 36 \t | # of unique nodes: 122780\n",
      "Total time: 0.91459 secs (0.02 mins)\n"
     ]
    }
   ],
   "source": [
    "path_to_files = './data/YAGO3-10'\n",
    "project = \"YAGO3-10\"\n",
    "\n",
    "\n",
    "time_s = time.time()\n",
    "_, df_train, _, _, _ = load_data(path_to_files, project)\n",
    "\n",
    "unique_rels = sorted(list(df_train['rel'].unique()))\n",
    "unique_nodes = sorted(set(df_train['head'].values.tolist() + df_train['tail'].values.tolist()))\n",
    "print(f'# of unique rels: {len(unique_rels)} \\t | # of unique nodes: {len(unique_nodes)}')\n",
    "\n",
    "\n",
    "time_prev = time.time()\n",
    "time_needed = time_prev - time_s\n",
    "print(f'Total time: {time_needed:.5f} secs ({time_needed/60:.2f} mins)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>head</th>\n",
       "      <th>rel</th>\n",
       "      <th>tail</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Chatou</td>\n",
       "      <td>isLocatedIn</td>\n",
       "      <td>France</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toni_Kuivasto</td>\n",
       "      <td>isAffiliatedTo</td>\n",
       "      <td>Helsingin_Jalkapalloklubi</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Albrecht_Dürer</td>\n",
       "      <td>diedIn</td>\n",
       "      <td>Nuremberg</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Edwin_Holliday</td>\n",
       "      <td>isAffiliatedTo</td>\n",
       "      <td>Hereford_United_F.C.</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>William_Hopper</td>\n",
       "      <td>actedIn</td>\n",
       "      <td>The_Bad_Seed_(1956_film)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             head             rel                       tail\n",
       "0          Chatou     isLocatedIn                     France\n",
       "1   Toni_Kuivasto  isAffiliatedTo  Helsingin_Jalkapalloklubi\n",
       "2  Albrecht_Dürer          diedIn                  Nuremberg\n",
       "3  Edwin_Holliday  isAffiliatedTo       Hereford_United_F.C.\n",
       "4  William_Hopper         actedIn   The_Bad_Seed_(1956_film)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create the $1$-hop **lossless** PAM and its powers.\n",
    "\n",
    "Here we limit $k=3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# of unique rels: 36 \t | # of unique nodes: 122780\n",
      "(122780, 122780) Sparsity: 100.00 %\n",
      "Sparsity 2-hop: 99.97 %\n",
      "Sparsity 3-hop: 99.84 %\n"
     ]
    }
   ],
   "source": [
    "max_k = 3\n",
    "pam_1hop_lossless, pam_powers, node2id, rel2id = create_pam_matrices(df_train, \n",
    "                                                                     max_order=max_k, \n",
    "                                                                     spacing_strategy='step_100', \n",
    "                                                                     use_log=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate possible rules\n",
    "\n",
    "The procedure is as follows:\n",
    "1. We first find all pairs of $(i,j)$ for which $P[i,j] = r_H = \\neq 0 $.\n",
    "2. Then we keep track of all the different values for these $(i,j)$,that $P^k[i,j] =  Path^k = \\neq 0$.\n",
    "3. We aggregate all of these rules in a DataFrame, keeping also frequencies and other characteristics of the rules (e.g. support, confidence etc.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1-hop rules\n",
    "\n",
    "Rules that have only one atom in the body.\n",
    "E.g. $knows(A,B)->friend(A,B)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_2379803/3213398325.py:9: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
      "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
      "  for index_nonzero, body_rel in tqdm.tqdm_notebook(enumerate(head_rels.flatten()), total=len(head_rels)):\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c4bcdfeff5214b17b43341ad4295edba",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/725199 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total # rules: 104\n",
      "Total time: 0.00000 secs (0.00 mins)\n"
     ]
    }
   ],
   "source": [
    "all_rules = []\n",
    "cur_power = pam_1hop_lossless\n",
    "rows, cols = pam_1hop_lossless.nonzero()\n",
    "head_rels = np.array(pam_1hop_lossless[rows,cols]).flatten()\n",
    "cur_rules = []\n",
    "\n",
    "time_s = time.time()\n",
    "\n",
    "# Iterate over all non-zero # P[i,j]\n",
    "for index_nonzero, body_rel in tqdm.tqdm_notebook(enumerate(head_rels.flatten()), total=len(head_rels)):\n",
    "    head_rels_cur = get_primefactors(body_rel)\n",
    "    if len(head_rels_cur) > 1 :\n",
    "        # Subrelation rules\n",
    "        for comb in permutations(head_rels_cur, 2):\n",
    "            if comb[0] in rel2id.values():\n",
    "                cur_rules.append(\n",
    "                    {\n",
    "                        'head_rel':comb[0], \n",
    "                        \"body\":comb[1], \n",
    "                        \"hop\":1, \n",
    "                        'type':'same_cell',\n",
    "                        'row': rows[index_nonzero],\n",
    "                        'col': cols[index_nonzero]\n",
    "                     }\n",
    "                )\n",
    "\n",
    "# Keep all rules\n",
    "df_rules = pd.DataFrame(cur_rules)\n",
    "# Aggregate the patterns by their body value\n",
    "grouped_by_head_and_body = df_rules.groupby([\"head_rel\", 'type'])['body'].value_counts().to_dict()\n",
    "# Calculate the support of the heads\n",
    "head_support = df_rules['head_rel'].value_counts().to_dict()\n",
    "\n",
    "\n",
    "\n",
    "all_bodies = []\n",
    "for value in cur_power.data:\n",
    "    all_bodies.extend(get_primefactors(value))\n",
    "# Calculate the support of the bodies\n",
    "body_support = pd.Series(all_bodies).value_counts().to_dict()\n",
    "\n",
    "for key in grouped_by_head_and_body:\n",
    "    head_rel, type_, body_rel  = key\n",
    "    all_rules.append({\n",
    "        \"head_rel\": head_rel, \n",
    "        'body':body_rel, \n",
    "        'head_body_count':grouped_by_head_and_body[key], \n",
    "        'body_count':body_support[body_rel],\n",
    "        'head_count':head_support[head_rel],\n",
    "        'hop':1, \n",
    "        'type':type_})\n",
    "\n",
    "print(f'Total # rules: {len(all_rules)}')\n",
    "\n",
    "time_prev = time.time()\n",
    "time_needed = time_s - time_s\n",
    "print(f'Total time: {time_needed:.5f} secs ({time_needed/60:.2f} mins)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## $k-$hop rules\n",
    "\n",
    "Rules of the form:\n",
    "$r1(A,B) \\wedge r2(B,C) \\wedge ... rk(Y,Z) - > r_H(A,Z)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2-hop level rules: 4320\n",
      "3-hop level rules: 24015\n",
      "Total # rules: 28439\n",
      "Total time: 1.64373 secs (0.03 mins)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>head_rel</th>\n",
       "      <th>body</th>\n",
       "      <th>head_body_count</th>\n",
       "      <th>body_count</th>\n",
       "      <th>head_count</th>\n",
       "      <th>hop</th>\n",
       "      <th>type</th>\n",
       "      <th>conf</th>\n",
       "      <th>head_coverage</th>\n",
       "      <th>score</th>\n",
       "      <th>body_head_str</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>2851</td>\n",
       "      <td>1049</td>\n",
       "      <td>992</td>\n",
       "      <td>2566</td>\n",
       "      <td>1587</td>\n",
       "      <td>1</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>3.865939e-01</td>\n",
       "      <td>0.625079</td>\n",
       "      <td>4.777269e-01</td>\n",
       "      <td>1049_2851</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9902</th>\n",
       "      <td>1049</td>\n",
       "      <td>25500143730021451</td>\n",
       "      <td>619</td>\n",
       "      <td>731</td>\n",
       "      <td>2339</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>8.467852e-01</td>\n",
       "      <td>0.264643</td>\n",
       "      <td>4.032573e-01</td>\n",
       "      <td>25500143730021451_1049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1180</th>\n",
       "      <td>2221</td>\n",
       "      <td>2556371</td>\n",
       "      <td>718</td>\n",
       "      <td>2335</td>\n",
       "      <td>1252</td>\n",
       "      <td>2</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>3.074946e-01</td>\n",
       "      <td>0.573482</td>\n",
       "      <td>4.003345e-01</td>\n",
       "      <td>2556371_2221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21132</th>\n",
       "      <td>2953</td>\n",
       "      <td>11743094698</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>1.000000e+00</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>4.000000e-01</td>\n",
       "      <td>11743094698_2953</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>865</th>\n",
       "      <td>1361</td>\n",
       "      <td>1566511</td>\n",
       "      <td>1391</td>\n",
       "      <td>2230</td>\n",
       "      <td>5155</td>\n",
       "      <td>2</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>6.237668e-01</td>\n",
       "      <td>0.269835</td>\n",
       "      <td>3.767095e-01</td>\n",
       "      <td>1566511_1361</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7918</th>\n",
       "      <td>839</td>\n",
       "      <td>8068178897</td>\n",
       "      <td>3</td>\n",
       "      <td>3101484</td>\n",
       "      <td>4737</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>9.672789e-07</td>\n",
       "      <td>0.000633</td>\n",
       "      <td>1.931608e-06</td>\n",
       "      <td>8068178897_839</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15578</th>\n",
       "      <td>2647</td>\n",
       "      <td>33570932693</td>\n",
       "      <td>1</td>\n",
       "      <td>1258733</td>\n",
       "      <td>14</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>7.944497e-07</td>\n",
       "      <td>0.071429</td>\n",
       "      <td>1.588882e-06</td>\n",
       "      <td>33570932693_2647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>205</th>\n",
       "      <td>211</td>\n",
       "      <td>9616423</td>\n",
       "      <td>1</td>\n",
       "      <td>2403292</td>\n",
       "      <td>1011</td>\n",
       "      <td>2</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>4.160959e-07</td>\n",
       "      <td>0.000989</td>\n",
       "      <td>8.318419e-07</td>\n",
       "      <td>9616423_211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10021</th>\n",
       "      <td>1049</td>\n",
       "      <td>2029065253</td>\n",
       "      <td>1</td>\n",
       "      <td>2618367</td>\n",
       "      <td>2339</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>3.819174e-07</td>\n",
       "      <td>0.000428</td>\n",
       "      <td>7.631531e-07</td>\n",
       "      <td>2029065253_1049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10036</th>\n",
       "      <td>1049</td>\n",
       "      <td>8068178897</td>\n",
       "      <td>1</td>\n",
       "      <td>3101484</td>\n",
       "      <td>2339</td>\n",
       "      <td>3</td>\n",
       "      <td>same_cell</td>\n",
       "      <td>3.224263e-07</td>\n",
       "      <td>0.000428</td>\n",
       "      <td>6.443666e-07</td>\n",
       "      <td>8068178897_1049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>28439 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       head_rel               body  head_body_count  body_count  head_count  \\\n",
       "71         2851               1049              992        2566        1587   \n",
       "9902       1049  25500143730021451              619         731        2339   \n",
       "1180       2221            2556371              718        2335        1252   \n",
       "21132      2953        11743094698                1           1           4   \n",
       "865        1361            1566511             1391        2230        5155   \n",
       "...         ...                ...              ...         ...         ...   \n",
       "7918        839         8068178897                3     3101484        4737   \n",
       "15578      2647        33570932693                1     1258733          14   \n",
       "205         211            9616423                1     2403292        1011   \n",
       "10021      1049         2029065253                1     2618367        2339   \n",
       "10036      1049         8068178897                1     3101484        2339   \n",
       "\n",
       "       hop       type          conf  head_coverage         score  \\\n",
       "71       1  same_cell  3.865939e-01       0.625079  4.777269e-01   \n",
       "9902     3  same_cell  8.467852e-01       0.264643  4.032573e-01   \n",
       "1180     2  same_cell  3.074946e-01       0.573482  4.003345e-01   \n",
       "21132    3  same_cell  1.000000e+00       0.250000  4.000000e-01   \n",
       "865      2  same_cell  6.237668e-01       0.269835  3.767095e-01   \n",
       "...    ...        ...           ...            ...           ...   \n",
       "7918     3  same_cell  9.672789e-07       0.000633  1.931608e-06   \n",
       "15578    3  same_cell  7.944497e-07       0.071429  1.588882e-06   \n",
       "205      2  same_cell  4.160959e-07       0.000989  8.318419e-07   \n",
       "10021    3  same_cell  3.819174e-07       0.000428  7.631531e-07   \n",
       "10036    3  same_cell  3.224263e-07       0.000428  6.443666e-07   \n",
       "\n",
       "                body_head_str  \n",
       "71                  1049_2851  \n",
       "9902   25500143730021451_1049  \n",
       "1180             2556371_2221  \n",
       "21132        11743094698_2953  \n",
       "865              1566511_1361  \n",
       "...                       ...  \n",
       "7918           8068178897_839  \n",
       "15578        33570932693_2647  \n",
       "205               9616423_211  \n",
       "10021         2029065253_1049  \n",
       "10036         8068178897_1049  \n",
       "\n",
       "[28439 rows x 11 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_hop = len(pam_powers)\n",
    "laplace_smoothing_alpha = 0\n",
    "\n",
    "time_s = time.time()\n",
    "\n",
    "rows, cols = pam_1hop_lossless.nonzero()\n",
    "head_rels = np.array(pam_1hop_lossless[rows,cols]).flatten()\n",
    "for cur_hop in range(1,max_hop):\n",
    "    cur_power = pam_powers[cur_hop]\n",
    "    cur_rules = []\n",
    "    for index_nonzero, body_rel in enumerate(np.array(cur_power[rows, cols]).flatten()):\n",
    "        cur_prime_factors = get_primefactors(head_rels[index_nonzero])\n",
    "        if body_rel != 0:\n",
    "            for head_rel in cur_prime_factors:\n",
    "                if head_rel in rel2id.values():\n",
    "                    cur_rules.append(\n",
    "                        {\n",
    "                            'head_rel':head_rel, \n",
    "                            \"body\":body_rel, \n",
    "                            \"hop\":cur_hop + 1, \n",
    "                            'type':'same_cell',\n",
    "                            'row': rows[index_nonzero],\n",
    "                            'col': cols[index_nonzero]\n",
    "                        }\n",
    "                    )\n",
    "                \n",
    "    df_rules = pd.DataFrame(cur_rules)\n",
    "    grouped_by_head_and_body = df_rules.groupby([\"head_rel\", 'type'])['body'].value_counts().to_dict()\n",
    "    head_support = df_rules['head_rel'].value_counts().to_dict()\n",
    "    body_support = pd.Series(cur_power.data).value_counts().to_dict()\n",
    "    for key in grouped_by_head_and_body:\n",
    "        head_value, type_, body_value  = key\n",
    "        all_rules.append({\n",
    "            \"head_rel\": head_value, \n",
    "            'body':body_value, \n",
    "            'head_body_count':grouped_by_head_and_body[key], \n",
    "            'body_count':body_support[body_value],\n",
    "            'head_count':head_support[head_value],\n",
    "            'hop':cur_hop + 1,\n",
    "            'type':type_})\n",
    "\n",
    "    print(f'{cur_hop + 1}-hop level rules: {len(grouped_by_head_and_body)}')\n",
    "print(f'Total # rules: {len(all_rules)}')\n",
    "\n",
    "time_prev = time.time()\n",
    "time_needed = time_prev - time_s\n",
    "print(f'Total time: {time_needed:.5f} secs ({time_needed/60:.2f} mins)')\n",
    "\n",
    "\n",
    "all_rules_df = pd.DataFrame(all_rules)\n",
    "all_rules_df['conf'] = all_rules_df['head_body_count'] / (all_rules_df['body_count'] + laplace_smoothing_alpha)\n",
    "all_rules_df['head_coverage'] = all_rules_df['head_body_count'] / (all_rules_df['head_count'])\n",
    "all_rules_df['score'] = 2*(all_rules_df['conf']*all_rules_df['head_coverage']/(all_rules_df['head_coverage'] + all_rules_df['conf'] ))\n",
    "\n",
    "all_rules_df['body_head_str'] = all_rules_df['body'].astype(str) + \"_\" + all_rules_df['head_rel'].astype(str)\n",
    "all_rules_df.sort_values(['score'], ascending=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have generated $28439$ patterns that may imply (with different confidence, support levels) different relations in a matter of seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "id2rel = dict(zip(rel2id.values(), rel2id.keys()))\n",
    "\n",
    "def generate_rule_string(chain_of_relations:list[str], head_rel:str, type_of_rule:str):\n",
    "    \"\"\"Helper function to create the rule\n",
    "\n",
    "    Args:\n",
    "        chain_of_relations (list[str]): The chain of relations followed.\n",
    "        head_rel (str): The relation implied in the head.\n",
    "        type_of_rule (str): The type of the rule. 'same_cell' or 'symmetric'.\n",
    "        The difference in the cases is:\n",
    "        'same_cell': r1(A,B)^r2(B,C)->r3(A,C)\n",
    "        or\n",
    "        'symmetric': r1(A,B)^r2(B,C)->r3(C,A)\n",
    "\n",
    "    Returns:\n",
    "        str: the rule as a Horn clause\n",
    "    \"\"\"\n",
    "\n",
    "    possible_letters = string.ascii_uppercase\n",
    "    first_letter = possible_letters[0]\n",
    "    rule_str = \"\"\n",
    "    for i_rel, relation in enumerate(chain_of_relations):\n",
    "        next_letter = possible_letters[possible_letters.index(first_letter) + 1]\n",
    "        rule_str += f\"{relation}({first_letter}, {next_letter}) ^ \"\n",
    "        first_letter = next_letter\n",
    "\n",
    "    rule_str = rule_str[:-2]\n",
    "    \n",
    "    if type_of_rule == 'same_cell':\n",
    "        head = f\"-> {head_rel}({possible_letters[0]}, {next_letter})\"\n",
    "    else:\n",
    "        head = f\"-> {head_rel}({next_letter}, {possible_letters[0]})\"\n",
    "\n",
    "    rule_str += head\n",
    "    return rule_str"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4777 : hasCapital(A, B) -> isLocatedIn(A, B)\t\n",
      "Chain: ['hasCapital'] [1049]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.4003 : hasChild(A, B) ^ isAffiliatedTo(B, C) -> isAffiliatedTo(A, C)\t\n",
      "Chain: ['hasChild', 'isAffiliatedTo'] [1151, 2221]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.3767 : hasChild(A, B) ^ hasGender(B, C) -> hasGender(A, C)\t\n",
      "Chain: ['hasChild', 'hasGender'] [1151, 1361]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.3077 : directed(A, B) -> created(A, B)\t\n",
      "Chain: ['directed'] [419]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.3043 : isLocatedIn(A, B) -> isLocatedIn(A, B)\t\n",
      "Chain: ['isLocatedIn'] [2851]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.3030 : isKnownFor(A, B) -> influences(A, B)\t\n",
      "Chain: ['isKnownFor'] [2647]\n",
      "Predicts: influences [2113] (same_cell)\n",
      "\n",
      "0.2999 : worksAt(A, B) -> graduatedFrom(A, B)\t\n",
      "Chain: ['worksAt'] [3593]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.2740 : exports(A, B) -> imports(A, B)\t\n",
      "Chain: ['exports'] [631]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.2734 : created(A, B) -> directed(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.2696 : hasMusicalRole(A, B) ^ influences(B, C) -> hasMusicalRole(A, C)\t\n",
      "Chain: ['hasMusicalRole', 'influences'] [1471, 2113]\n",
      "Predicts: hasMusicalRole [1471] (same_cell)\n",
      "\n",
      "0.2662 : hasAcademicAdvisor(A, B) ^ worksAt(B, C) -> graduatedFrom(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'worksAt'] [941, 3593]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.2649 : imports(A, B) -> exports(A, B)\t\n",
      "Chain: ['imports'] [2011]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.2376 : hasGender(A, B) ^ influences(B, C) -> hasGender(A, C)\t\n",
      "Chain: ['hasGender', 'influences'] [1361, 2113]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.2304 : livesIn(A, B) -> isCitizenOf(A, B)\t\n",
      "Chain: ['livesIn'] [3163]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.2222 : influences(A, B) ^ isKnownFor(B, C) -> isKnownFor(A, C)\t\n",
      "Chain: ['influences', 'isKnownFor'] [2113, 2647]\n",
      "Predicts: isKnownFor [2647] (same_cell)\n",
      "\n",
      "0.2207 : hasChild(A, B) ^ hasWonPrize(B, C) -> hasWonPrize(A, C)\t\n",
      "Chain: ['hasChild', 'hasWonPrize'] [1151, 1907]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.2145 : diedIn(A, B) -> wasBornIn(A, B)\t\n",
      "Chain: ['diedIn'] [313]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.2128 : hasChild(A, B) ^ owns(B, C) -> owns(A, C)\t\n",
      "Chain: ['hasChild', 'owns'] [1151, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.2013 : isLeaderOf(A, B) -> isPoliticianOf(A, B)\t\n",
      "Chain: ['isLeaderOf'] [2749]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.2000 : influences(A, B) ^ isKnownFor(B, C) -> isKnownFor(A, C)\t\n",
      "Chain: ['influences', 'isKnownFor'] [2113, 2647]\n",
      "Predicts: isKnownFor [2647] (same_cell)\n",
      "\n",
      "0.1948 : isCitizenOf(A, B) -> livesIn(A, B)\t\n",
      "Chain: ['isCitizenOf'] [2333]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.1920 : hasAcademicAdvisor(A, B) ^ hasGender(B, C) -> hasGender(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'hasGender'] [941, 1361]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.1897 : hasAcademicAdvisor(A, B) ^ hasWonPrize(B, C) -> hasWonPrize(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'hasWonPrize'] [941, 1907]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.1788 : actedIn(A, B) ^ dealsWith(B, C) -> dealsWith(A, C)\t\n",
      "Chain: ['actedIn', 'dealsWith'] [3, 211]\n",
      "Predicts: dealsWith [211] (same_cell)\n",
      "\n",
      "0.1701 : directed(A, B) -> actedIn(A, B)\t\n",
      "Chain: ['directed'] [419]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.1686 : happenedIn(A, B) -> isLocatedIn(A, B)\t\n",
      "Chain: ['happenedIn'] [839]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.1668 : graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) ^ worksAt(C, D) -> graduatedFrom(A, D)\t\n",
      "Chain: ['graduatedFrom', 'hasAcademicAdvisor', 'worksAt'] [733, 941, 3593]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.1627 : graduatedFrom(A, B) ^ hasChild(B, C) -> graduatedFrom(A, C)\t\n",
      "Chain: ['graduatedFrom', 'hasChild'] [733, 1151]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.1553 : graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) ^ worksAt(C, D) -> worksAt(A, D)\t\n",
      "Chain: ['graduatedFrom', 'hasAcademicAdvisor', 'worksAt'] [733, 941, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.1548 : isLeaderOf(A, B) -> isAffiliatedTo(A, B)\t\n",
      "Chain: ['isLeaderOf'] [2749]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.1541 : hasAcademicAdvisor(A, B) ^ worksAt(B, C) -> worksAt(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'worksAt'] [941, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.1506 : graduatedFrom(A, B) -> worksAt(A, B)\t\n",
      "Chain: ['graduatedFrom'] [733]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.1468 : created(A, B) -> wroteMusicFor(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.1422 : dealsWith(A, B) ^ hasOfficialLanguage(B, C) -> hasOfficialLanguage(A, C)\t\n",
      "Chain: ['dealsWith', 'hasOfficialLanguage'] [211, 1693]\n",
      "Predicts: hasOfficialLanguage [1693] (same_cell)\n",
      "\n",
      "0.1421 : isPoliticianOf(A, B) -> isCitizenOf(A, B)\t\n",
      "Chain: ['isPoliticianOf'] [3061]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.1382 : dealsWith(A, B) ^ exports(B, C) -> exports(A, C)\t\n",
      "Chain: ['dealsWith', 'exports'] [211, 631]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.1375 : dealsWith(A, B) ^ imports(B, C) -> imports(A, C)\t\n",
      "Chain: ['dealsWith', 'imports'] [211, 2011]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.1333 : created(A, B) ^ directed(B, C) ^ hasChild(C, D) ^ wroteMusicFor(D, E) -> wroteMusicFor(A, E)\t\n",
      "Chain: ['created', 'directed', 'hasChild', 'wroteMusicFor'] [107, 419, 1151, 3697]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.1327 : wroteMusicFor(A, B) -> created(A, B)\t\n",
      "Chain: ['wroteMusicFor'] [3697]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.1327 : happenedIn(A, B) ^ isLocatedIn(B, C) -> happenedIn(A, C)\t\n",
      "Chain: ['happenedIn', 'isLocatedIn'] [839, 2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.1327 : graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) -> graduatedFrom(A, C)\t\n",
      "Chain: ['graduatedFrom', 'hasAcademicAdvisor'] [733, 941]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.1320 : hasChild(A, B) -> hasChild(A, B)\t\n",
      "Chain: ['hasChild'] [1151]\n",
      "Predicts: hasChild [1151] (same_cell)\n",
      "\n",
      "0.1314 : actedIn(A, B) ^ isConnectedTo(B, C) -> isConnectedTo(A, C)\t\n",
      "Chain: ['actedIn', 'isConnectedTo'] [3, 2437]\n",
      "Predicts: isConnectedTo [2437] (same_cell)\n",
      "\n",
      "0.1304 : actedIn(A, B) ^ dealsWith(B, C) ^ hasCurrency(C, D) -> hasCurrency(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'hasCurrency'] [3, 211, 1259]\n",
      "Predicts: hasCurrency [1259] (same_cell)\n",
      "\n",
      "0.1256 : dealsWith(A, B) -> dealsWith(A, B)\t\n",
      "Chain: ['dealsWith'] [211]\n",
      "Predicts: dealsWith [211] (same_cell)\n",
      "\n",
      "0.1212 : dealsWith(A, B) ^ hasCurrency(B, C) ^ isLocatedIn(C, D) -> hasCurrency(A, D)\t\n",
      "Chain: ['dealsWith', 'hasCurrency', 'isLocatedIn'] [211, 1259, 2851]\n",
      "Predicts: hasCurrency [1259] (same_cell)\n",
      "\n",
      "0.1209 : happenedIn(A, B) ^ isLocatedIn(B, C) -> happenedIn(A, C)\t\n",
      "Chain: ['happenedIn', 'isLocatedIn'] [839, 2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.1200 : hasWebsite(A, B) ^ isLocatedIn(B, C) -> hasWebsite(A, C)\t\n",
      "Chain: ['hasWebsite', 'isLocatedIn'] [1801, 2851]\n",
      "Predicts: hasWebsite [1801] (same_cell)\n",
      "\n",
      "0.1189 : actedIn(A, B) ^ dealsWith(B, C) ^ hasOfficialLanguage(C, D) -> hasOfficialLanguage(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'hasOfficialLanguage'] [3, 211, 1693]\n",
      "Predicts: hasOfficialLanguage [1693] (same_cell)\n",
      "\n",
      "0.1182 : actedIn(A, B) ^ influences(B, C) -> influences(A, C)\t\n",
      "Chain: ['actedIn', 'influences'] [3, 2113]\n",
      "Predicts: influences [2113] (same_cell)\n",
      "\n",
      "0.1173 : created(A, B) -> actedIn(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.1139 : isLocatedIn(A, B) ^ livesIn(B, C) -> livesIn(A, C)\t\n",
      "Chain: ['isLocatedIn', 'livesIn'] [2851, 3163]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.1132 : hasChild(A, B) ^ wroteMusicFor(B, C) -> wroteMusicFor(A, C)\t\n",
      "Chain: ['hasChild', 'wroteMusicFor'] [1151, 3697]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.1122 : isPoliticianOf(A, B) -> isLeaderOf(A, B)\t\n",
      "Chain: ['isPoliticianOf'] [3061]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.1111 : dealsWith(A, B) ^ isKnownFor(B, C) -> isKnownFor(A, C)\t\n",
      "Chain: ['dealsWith', 'isKnownFor'] [211, 2647]\n",
      "Predicts: isKnownFor [2647] (same_cell)\n",
      "\n",
      "0.1075 : owns(A, B) -> owns(A, B)\t\n",
      "Chain: ['owns'] [3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.1053 : isMarriedTo(A, B) ^ wroteMusicFor(B, C) -> wroteMusicFor(A, C)\t\n",
      "Chain: ['isMarriedTo', 'wroteMusicFor'] [2953, 3697]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.1018 : isCitizenOf(A, B) -> isPoliticianOf(A, B)\t\n",
      "Chain: ['isCitizenOf'] [2333]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.0952 : isKnownFor(A, B) -> isInterestedIn(A, B)\t\n",
      "Chain: ['isKnownFor'] [2647]\n",
      "Predicts: isInterestedIn [2539] (same_cell)\n",
      "\n",
      "0.0950 : isConnectedTo(A, B) -> isConnectedTo(A, B)\t\n",
      "Chain: ['isConnectedTo'] [2437]\n",
      "Predicts: isConnectedTo [2437] (same_cell)\n",
      "\n",
      "0.0936 : hasGender(A, B) ^ isAffiliatedTo(B, C) -> hasGender(A, C)\t\n",
      "Chain: ['hasGender', 'isAffiliatedTo'] [1361, 2221]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.0909 : hasNeighbor(A, B) -> dealsWith(A, B)\t\n",
      "Chain: ['hasNeighbor'] [1579]\n",
      "Predicts: dealsWith [211] (same_cell)\n",
      "\n",
      "0.0903 : hasWonPrize(A, B) ^ influences(B, C) -> hasWonPrize(A, C)\t\n",
      "Chain: ['hasWonPrize', 'influences'] [1907, 2113]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0833 : created(A, B) -> directed(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0799 : graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) -> worksAt(A, C)\t\n",
      "Chain: ['graduatedFrom', 'hasAcademicAdvisor'] [733, 941]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.0797 : dealsWith(A, B) ^ happenedIn(B, C) -> happenedIn(A, C)\t\n",
      "Chain: ['dealsWith', 'happenedIn'] [211, 839]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0795 : actedIn(A, B) ^ influences(B, C) ^ isInterestedIn(C, D) -> isInterestedIn(A, D)\t\n",
      "Chain: ['actedIn', 'influences', 'isInterestedIn'] [3, 2113, 2539]\n",
      "Predicts: isInterestedIn [2539] (same_cell)\n",
      "\n",
      "0.0787 : influences(A, B) -> influences(A, B)\t\n",
      "Chain: ['influences'] [2113]\n",
      "Predicts: influences [2113] (same_cell)\n",
      "\n",
      "0.0784 : diedIn(A, B) ^ hasWonPrize(B, C) -> hasWonPrize(A, C)\t\n",
      "Chain: ['diedIn', 'hasWonPrize'] [313, 1907]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0760 : isLeaderOf(A, B) -> livesIn(A, B)\t\n",
      "Chain: ['isLeaderOf'] [2749]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0757 : isAffiliatedTo(A, B) ^ isLocatedIn(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['isAffiliatedTo', 'isLocatedIn'] [2221, 2851]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0741 : actedIn(A, B) ^ dealsWith(B, C) ^ exports(C, D) -> exports(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'exports'] [3, 211, 631]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.0737 : actedIn(A, B) ^ dealsWith(B, C) ^ participatedIn(C, D) -> participatedIn(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'participatedIn'] [3, 211, 3373]\n",
      "Predicts: participatedIn [3373] (same_cell)\n",
      "\n",
      "0.0714 : created(A, B) -> actedIn(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0709 : influences(A, B) ^ isInterestedIn(B, C) -> isInterestedIn(A, C)\t\n",
      "Chain: ['influences', 'isInterestedIn'] [2113, 2539]\n",
      "Predicts: isInterestedIn [2539] (same_cell)\n",
      "\n",
      "0.0704 : hasChild(A, B) ^ isPoliticianOf(B, C) -> isPoliticianOf(A, C)\t\n",
      "Chain: ['hasChild', 'isPoliticianOf'] [1151, 3061]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.0680 : hasCapital(A, B) ^ livesIn(B, C) -> livesIn(A, C)\t\n",
      "Chain: ['hasCapital', 'livesIn'] [1049, 3163]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0671 : actedIn(A, B) ^ hasGender(B, C) ^ influences(C, D) -> hasGender(A, D)\t\n",
      "Chain: ['actedIn', 'hasGender', 'influences'] [3, 1361, 2113]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.0659 : directed(A, B) ^ hasChild(B, C) -> wroteMusicFor(A, C)\t\n",
      "Chain: ['directed', 'hasChild'] [419, 1151]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.0634 : livesIn(A, B) -> wasBornIn(A, B)\t\n",
      "Chain: ['livesIn'] [3163]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0629 : dealsWith(A, B) ^ hasOfficialLanguage(B, C) ^ isLocatedIn(C, D) -> hasOfficialLanguage(A, D)\t\n",
      "Chain: ['dealsWith', 'hasOfficialLanguage', 'isLocatedIn'] [211, 1693, 2851]\n",
      "Predicts: hasOfficialLanguage [1693] (same_cell)\n",
      "\n",
      "0.0627 : isAffiliatedTo(A, B) -> isAffiliatedTo(A, B)\t\n",
      "Chain: ['isAffiliatedTo'] [2221]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0625 : hasCurrency(A, B) ^ hasNeighbor(B, C) -> hasCurrency(A, C)\t\n",
      "Chain: ['hasCurrency', 'hasNeighbor'] [1259, 1579]\n",
      "Predicts: hasCurrency [1259] (same_cell)\n",
      "\n",
      "0.0625 : actedIn(A, B) ^ created(B, C) ^ directed(C, D) -> created(A, D)\t\n",
      "Chain: ['actedIn', 'created', 'directed'] [3, 107, 419]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0621 : actedIn(A, B) ^ isLocatedIn(B, C) -> isLocatedIn(A, C)\t\n",
      "Chain: ['actedIn', 'isLocatedIn'] [3, 2851]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0618 : actedIn(A, B) ^ hasChild(B, C) ^ hasGender(C, D) -> hasGender(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'hasGender'] [3, 1151, 1361]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.0617 : created(A, B) ^ owns(B, C) -> created(A, C)\t\n",
      "Chain: ['created', 'owns'] [107, 3271]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0606 : actedIn(A, B) ^ dealsWith(B, C) ^ imports(C, D) -> imports(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'imports'] [3, 211, 2011]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.0606 : actedIn(A, B) ^ created(B, C) ^ directed(C, D) -> actedIn(A, D)\t\n",
      "Chain: ['actedIn', 'created', 'directed'] [3, 107, 419]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0599 : actedIn(A, B) ^ dealsWith(B, C) ^ imports(C, D) -> imports(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'imports'] [3, 211, 2011]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.0597 : hasChild(A, B) ^ wroteMusicFor(B, C) -> directed(A, C)\t\n",
      "Chain: ['hasChild', 'wroteMusicFor'] [1151, 3697]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0588 : created(A, B) ^ directed(B, C) ^ hasChild(C, D) -> wroteMusicFor(A, D)\t\n",
      "Chain: ['created', 'directed', 'hasChild'] [107, 419, 1151]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.0587 : dealsWith(A, B) ^ hasCurrency(B, C) -> hasCurrency(A, C)\t\n",
      "Chain: ['dealsWith', 'hasCurrency'] [211, 1259]\n",
      "Predicts: hasCurrency [1259] (same_cell)\n",
      "\n",
      "0.0567 : actedIn(A, B) ^ hasChild(B, C) ^ isAffiliatedTo(C, D) -> isAffiliatedTo(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'isAffiliatedTo'] [3, 1151, 2221]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0566 : isPoliticianOf(A, B) -> livesIn(A, B)\t\n",
      "Chain: ['isPoliticianOf'] [3061]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0560 : isLocatedIn(A, B) ^ worksAt(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['isLocatedIn', 'worksAt'] [2851, 3593]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0526 : hasChild(A, B) ^ hasMusicalRole(B, C) -> hasMusicalRole(A, C)\t\n",
      "Chain: ['hasChild', 'hasMusicalRole'] [1151, 1471]\n",
      "Predicts: hasMusicalRole [1471] (same_cell)\n",
      "\n",
      "0.0525 : dealsWith(A, B) ^ exports(B, C) ^ imports(C, D) -> exports(A, D)\t\n",
      "Chain: ['dealsWith', 'exports', 'imports'] [211, 631, 2011]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.0522 : hasChild(A, B) ^ wasBornIn(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['hasChild', 'wasBornIn'] [1151, 3491]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0515 : isLeaderOf(A, B) ^ isLocatedIn(B, C) -> isLeaderOf(A, C)\t\n",
      "Chain: ['isLeaderOf', 'isLocatedIn'] [2749, 2851]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0499 : hasChild(A, B) ^ isMarriedTo(B, C) -> hasChild(A, C)\t\n",
      "Chain: ['hasChild', 'isMarriedTo'] [1151, 2953]\n",
      "Predicts: hasChild [1151] (same_cell)\n",
      "\n",
      "0.0494 : actedIn(A, B) ^ directed(B, C) ^ hasChild(C, D) -> actedIn(A, D)\t\n",
      "Chain: ['actedIn', 'directed', 'hasChild'] [3, 419, 1151]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0492 : livesIn(A, B) -> isPoliticianOf(A, B)\t\n",
      "Chain: ['livesIn'] [3163]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.0490 : wasBornIn(A, B) -> diedIn(A, B)\t\n",
      "Chain: ['wasBornIn'] [3491]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0483 : livesIn(A, B) -> diedIn(A, B)\t\n",
      "Chain: ['livesIn'] [3163]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0477 : hasAcademicAdvisor(A, B) -> hasAcademicAdvisor(A, B)\t\n",
      "Chain: ['hasAcademicAdvisor'] [941]\n",
      "Predicts: hasAcademicAdvisor [941] (same_cell)\n",
      "\n",
      "0.0473 : hasCapital(A, B) ^ isLocatedIn(B, C) -> isLocatedIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isLocatedIn'] [1049, 2851]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0460 : actedIn(A, B) ^ hasMusicalRole(B, C) ^ influences(C, D) -> hasMusicalRole(A, D)\t\n",
      "Chain: ['actedIn', 'hasMusicalRole', 'influences'] [3, 1471, 2113]\n",
      "Predicts: hasMusicalRole [1471] (same_cell)\n",
      "\n",
      "0.0458 : actedIn(A, B) ^ happenedIn(B, C) ^ isLocatedIn(C, D) -> happenedIn(A, D)\t\n",
      "Chain: ['actedIn', 'happenedIn', 'isLocatedIn'] [3, 839, 2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0435 : actedIn(A, B) ^ influences(B, C) ^ isInterestedIn(C, D) -> isInterestedIn(A, D)\t\n",
      "Chain: ['actedIn', 'influences', 'isInterestedIn'] [3, 2113, 2539]\n",
      "Predicts: isInterestedIn [2539] (same_cell)\n",
      "\n",
      "0.0435 : isMarriedTo(A, B) -> hasChild(A, B)\t\n",
      "Chain: ['isMarriedTo'] [2953]\n",
      "Predicts: hasChild [1151] (same_cell)\n",
      "\n",
      "0.0429 : actedIn(A, B) ^ hasWonPrize(B, C) ^ influences(C, D) -> hasWonPrize(A, D)\t\n",
      "Chain: ['actedIn', 'hasWonPrize', 'influences'] [3, 1907, 2113]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0419 : graduatedFrom(A, B) ^ isLocatedIn(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn'] [733, 2851]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0413 : diedIn(A, B) ^ hasChild(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['diedIn', 'hasChild'] [313, 1151]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0411 : dealsWith(A, B) ^ exports(B, C) ^ imports(C, D) -> imports(A, D)\t\n",
      "Chain: ['dealsWith', 'exports', 'imports'] [211, 631, 2011]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.0406 : influences(A, B) ^ worksAt(B, C) -> worksAt(A, C)\t\n",
      "Chain: ['influences', 'worksAt'] [2113, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.0406 : dealsWith(A, B) ^ imports(B, C) -> exports(A, C)\t\n",
      "Chain: ['dealsWith', 'imports'] [211, 2011]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.0405 : livesIn(A, B) -> isLeaderOf(A, B)\t\n",
      "Chain: ['livesIn'] [3163]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0395 : hasChild(A, B) ^ isAffiliatedTo(B, C) ^ isLeaderOf(C, D) -> isAffiliatedTo(A, D)\t\n",
      "Chain: ['hasChild', 'isAffiliatedTo', 'isLeaderOf'] [1151, 2221, 2749]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0351 : hasChild(A, B) ^ isAffiliatedTo(B, C) ^ isLeaderOf(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['hasChild', 'isAffiliatedTo', 'isLeaderOf'] [1151, 2221, 2749]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0347 : hasCapital(A, B) ^ isLocatedIn(B, C) -> isLocatedIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isLocatedIn'] [1049, 2851]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0339 : isAffiliatedTo(A, B) ^ owns(B, C) -> isAffiliatedTo(A, C)\t\n",
      "Chain: ['isAffiliatedTo', 'owns'] [2221, 3271]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0337 : graduatedFrom(A, B) ^ influences(B, C) ^ worksAt(C, D) -> worksAt(A, D)\t\n",
      "Chain: ['graduatedFrom', 'influences', 'worksAt'] [733, 2113, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.0333 : dealsWith(A, B) ^ participatedIn(B, C) -> participatedIn(A, C)\t\n",
      "Chain: ['dealsWith', 'participatedIn'] [211, 3373]\n",
      "Predicts: participatedIn [3373] (same_cell)\n",
      "\n",
      "0.0328 : actedIn(A, B) ^ hasChild(B, C) -> hasChild(A, C)\t\n",
      "Chain: ['actedIn', 'hasChild'] [3, 1151]\n",
      "Predicts: hasChild [1151] (same_cell)\n",
      "\n",
      "0.0328 : actedIn(A, B) -> directed(A, B)\t\n",
      "Chain: ['actedIn'] [3]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0327 : hasCapital(A, B) ^ isLocatedIn(B, C) ^ livesIn(C, D) -> livesIn(A, D)\t\n",
      "Chain: ['hasCapital', 'isLocatedIn', 'livesIn'] [1049, 2851, 3163]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0308 : actedIn(A, B) ^ hasChild(B, C) -> actedIn(A, C)\t\n",
      "Chain: ['actedIn', 'hasChild'] [3, 1151]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0306 : actedIn(A, B) ^ dealsWith(B, C) ^ exports(C, D) -> imports(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'exports'] [3, 211, 631]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.0303 : created(A, B) ^ hasChild(B, C) ^ influences(C, D) -> created(A, D)\t\n",
      "Chain: ['created', 'hasChild', 'influences'] [107, 1151, 2113]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0303 : isLeaderOf(A, B) ^ isLocatedIn(B, C) ^ livesIn(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['isLeaderOf', 'isLocatedIn', 'livesIn'] [2749, 2851, 3163]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0294 : dealsWith(A, B) ^ exports(B, C) -> imports(A, C)\t\n",
      "Chain: ['dealsWith', 'exports'] [211, 631]\n",
      "Predicts: imports [2011] (same_cell)\n",
      "\n",
      "0.0293 : diedIn(A, B) ^ hasChild(B, C) ^ wasBornIn(C, D) -> diedIn(A, D)\t\n",
      "Chain: ['diedIn', 'hasChild', 'wasBornIn'] [313, 1151, 3491]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0292 : actedIn(A, B) ^ dealsWith(B, C) -> dealsWith(A, C)\t\n",
      "Chain: ['actedIn', 'dealsWith'] [3, 211]\n",
      "Predicts: dealsWith [211] (same_cell)\n",
      "\n",
      "0.0290 : actedIn(A, B) ^ created(B, C) ^ hasChild(C, D) -> actedIn(A, D)\t\n",
      "Chain: ['actedIn', 'created', 'hasChild'] [3, 107, 1151]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0288 : actedIn(A, B) ^ isAffiliatedTo(B, C) ^ isLocatedIn(C, D) -> wasBornIn(A, D)\t\n",
      "Chain: ['actedIn', 'isAffiliatedTo', 'isLocatedIn'] [3, 2221, 2851]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0288 : actedIn(A, B) ^ created(B, C) ^ influences(C, D) -> created(A, D)\t\n",
      "Chain: ['actedIn', 'created', 'influences'] [3, 107, 2113]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0286 : created(A, B) ^ hasAcademicAdvisor(B, C) ^ worksAt(C, D) -> created(A, D)\t\n",
      "Chain: ['created', 'hasAcademicAdvisor', 'worksAt'] [107, 941, 3593]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0284 : dealsWith(A, B) ^ happenedIn(B, C) ^ isLocatedIn(C, D) -> happenedIn(A, D)\t\n",
      "Chain: ['dealsWith', 'happenedIn', 'isLocatedIn'] [211, 839, 2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0284 : actedIn(A, B) ^ created(B, C) ^ influences(C, D) -> actedIn(A, D)\t\n",
      "Chain: ['actedIn', 'created', 'influences'] [3, 107, 2113]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0280 : hasCapital(A, B) ^ isPoliticianOf(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isPoliticianOf'] [1049, 3061]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0273 : actedIn(A, B) -> created(A, B)\t\n",
      "Chain: ['actedIn'] [3]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0270 : actedIn(A, B) ^ created(B, C) ^ directed(C, D) ^ hasChild(D, E) -> actedIn(A, E)\t\n",
      "Chain: ['actedIn', 'created', 'directed', 'hasChild'] [3, 107, 419, 1151]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0267 : diedIn(A, B) ^ influences(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['diedIn', 'influences'] [313, 2113]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0260 : isLocatedIn(A, B) ^ worksAt(B, C) -> livesIn(A, C)\t\n",
      "Chain: ['isLocatedIn', 'worksAt'] [2851, 3593]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0260 : isLeaderOf(A, B) ^ isLocatedIn(B, C) ^ wasBornIn(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['isLeaderOf', 'isLocatedIn', 'wasBornIn'] [2749, 2851, 3491]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0256 : isLeaderOf(A, B) -> wasBornIn(A, B)\t\n",
      "Chain: ['isLeaderOf'] [2749]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0256 : hasChild(A, B) ^ wasBornIn(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['hasChild', 'wasBornIn'] [1151, 3491]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0248 : hasCapital(A, B) ^ isCitizenOf(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isCitizenOf'] [1049, 2333]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0244 : created(A, B) -> created(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0244 : happenedIn(A, B) ^ hasCapital(B, C) ^ isLocatedIn(C, D) -> happenedIn(A, D)\t\n",
      "Chain: ['happenedIn', 'hasCapital', 'isLocatedIn'] [839, 1049, 2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0240 : isConnectedTo(A, B) ^ owns(B, C) -> owns(A, C)\t\n",
      "Chain: ['isConnectedTo', 'owns'] [2437, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.0233 : graduatedFrom(A, B) ^ isLocatedIn(B, C) ^ worksAt(C, D) -> diedIn(A, D)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn', 'worksAt'] [733, 2851, 3593]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0233 : graduatedFrom(A, B) ^ influences(B, C) -> graduatedFrom(A, C)\t\n",
      "Chain: ['graduatedFrom', 'influences'] [733, 2113]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.0231 : edited(A, B) -> directed(A, B)\t\n",
      "Chain: ['edited'] [521]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0229 : actedIn(A, B) ^ isConnectedTo(B, C) -> isConnectedTo(A, C)\t\n",
      "Chain: ['actedIn', 'isConnectedTo'] [3, 2437]\n",
      "Predicts: isConnectedTo [2437] (same_cell)\n",
      "\n",
      "0.0225 : created(A, B) ^ hasMusicalRole(B, C) -> hasMusicalRole(A, C)\t\n",
      "Chain: ['created', 'hasMusicalRole'] [107, 1471]\n",
      "Predicts: hasMusicalRole [1471] (same_cell)\n",
      "\n",
      "0.0224 : actedIn(A, B) ^ hasChild(B, C) ^ hasWonPrize(C, D) -> hasWonPrize(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'hasWonPrize'] [3, 1151, 1907]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0223 : hasCapital(A, B) ^ isCitizenOf(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isCitizenOf'] [1049, 2333]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0222 : hasCapital(A, B) ^ owns(B, C) -> owns(A, C)\t\n",
      "Chain: ['hasCapital', 'owns'] [1049, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.0221 : isLocatedIn(A, B) -> hasCapital(A, B)\t\n",
      "Chain: ['isLocatedIn'] [2851]\n",
      "Predicts: hasCapital [1049] (same_cell)\n",
      "\n",
      "0.0220 : actedIn(A, B) ^ dealsWith(B, C) ^ imports(C, D) -> exports(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'imports'] [3, 211, 2011]\n",
      "Predicts: exports [631] (same_cell)\n",
      "\n",
      "0.0217 : isInterestedIn(A, B) -> isInterestedIn(A, B)\t\n",
      "Chain: ['isInterestedIn'] [2539]\n",
      "Predicts: isInterestedIn [2539] (same_cell)\n",
      "\n",
      "0.0216 : actedIn(A, B) ^ dealsWith(B, C) ^ participatedIn(C, D) -> participatedIn(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'participatedIn'] [3, 211, 3373]\n",
      "Predicts: participatedIn [3373] (same_cell)\n",
      "\n",
      "0.0204 : actedIn(A, B) ^ hasChild(B, C) ^ owns(C, D) -> owns(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'owns'] [3, 1151, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.0204 : directed(A, B) -> edited(A, B)\t\n",
      "Chain: ['directed'] [419]\n",
      "Predicts: edited [521] (same_cell)\n",
      "\n",
      "0.0203 : diedIn(A, B) -> livesIn(A, B)\t\n",
      "Chain: ['diedIn'] [313]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0201 : hasCapital(A, B) ^ isLocatedIn(B, C) -> hasCapital(A, C)\t\n",
      "Chain: ['hasCapital', 'isLocatedIn'] [1049, 2851]\n",
      "Predicts: hasCapital [1049] (same_cell)\n",
      "\n",
      "0.0198 : hasChild(A, B) ^ wroteMusicFor(B, C) -> created(A, C)\t\n",
      "Chain: ['hasChild', 'wroteMusicFor'] [1151, 3697]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0197 : isLeaderOf(A, B) ^ isLocatedIn(B, C) ^ livesIn(C, D) ^ wasBornIn(D, E) -> isLeaderOf(A, E)\t\n",
      "Chain: ['isLeaderOf', 'isLocatedIn', 'livesIn', 'wasBornIn'] [2749, 2851, 3163, 3491]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0193 : owns(A, B) ^ wasBornIn(B, C) -> isAffiliatedTo(A, C)\t\n",
      "Chain: ['owns', 'wasBornIn'] [3271, 3491]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0191 : graduatedFrom(A, B) ^ influences(B, C) -> worksAt(A, C)\t\n",
      "Chain: ['graduatedFrom', 'influences'] [733, 2113]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.0190 : directed(A, B) ^ hasChild(B, C) -> directed(A, C)\t\n",
      "Chain: ['directed', 'hasChild'] [419, 1151]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0188 : actedIn(A, B) ^ dealsWith(B, C) ^ happenedIn(C, D) -> happenedIn(A, D)\t\n",
      "Chain: ['actedIn', 'dealsWith', 'happenedIn'] [3, 211, 839]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0177 : influences(A, B) ^ wroteMusicFor(B, C) -> directed(A, C)\t\n",
      "Chain: ['influences', 'wroteMusicFor'] [2113, 3697]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0176 : hasCapital(A, B) -> hasCapital(A, B)\t\n",
      "Chain: ['hasCapital'] [1049]\n",
      "Predicts: hasCapital [1049] (same_cell)\n",
      "\n",
      "0.0176 : graduatedFrom(A, B) ^ isLocatedIn(B, C) -> diedIn(A, C)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn'] [733, 2851]\n",
      "Predicts: diedIn [313] (same_cell)\n",
      "\n",
      "0.0176 : influences(A, B) ^ worksAt(B, C) -> graduatedFrom(A, C)\t\n",
      "Chain: ['influences', 'worksAt'] [2113, 3593]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.0170 : isLocatedIn(A, B) ^ livesIn(B, C) ^ wasBornIn(C, D) -> livesIn(A, D)\t\n",
      "Chain: ['isLocatedIn', 'livesIn', 'wasBornIn'] [2851, 3163, 3491]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0168 : graduatedFrom(A, B) ^ influences(B, C) ^ worksAt(C, D) -> graduatedFrom(A, D)\t\n",
      "Chain: ['graduatedFrom', 'influences', 'worksAt'] [733, 2113, 3593]\n",
      "Predicts: graduatedFrom [733] (same_cell)\n",
      "\n",
      "0.0165 : actedIn(A, B) ^ influences(B, C) -> actedIn(A, C)\t\n",
      "Chain: ['actedIn', 'influences'] [3, 2113]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0162 : happenedIn(A, B) ^ hasCapital(B, C) -> happenedIn(A, C)\t\n",
      "Chain: ['happenedIn', 'hasCapital'] [839, 1049]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0161 : created(A, B) ^ hasChild(B, C) -> directed(A, C)\t\n",
      "Chain: ['created', 'hasChild'] [107, 1151]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0156 : influences(A, B) ^ isKnownFor(B, C) -> isKnownFor(A, C)\t\n",
      "Chain: ['influences', 'isKnownFor'] [2113, 2647]\n",
      "Predicts: isKnownFor [2647] (same_cell)\n",
      "\n",
      "0.0153 : hasAcademicAdvisor(A, B) ^ isCitizenOf(B, C) -> isCitizenOf(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'isCitizenOf'] [941, 2333]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.0153 : actedIn(A, B) ^ hasChild(B, C) ^ influences(C, D) -> hasChild(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'influences'] [3, 1151, 2113]\n",
      "Predicts: hasChild [1151] (same_cell)\n",
      "\n",
      "0.0145 : dealsWith(A, B) ^ isLocatedIn(B, C) -> isLocatedIn(A, C)\t\n",
      "Chain: ['dealsWith', 'isLocatedIn'] [211, 2851]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0144 : directed(A, B) ^ hasChild(B, C) -> created(A, C)\t\n",
      "Chain: ['directed', 'hasChild'] [419, 1151]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0144 : directed(A, B) -> wroteMusicFor(A, B)\t\n",
      "Chain: ['directed'] [419]\n",
      "Predicts: wroteMusicFor [3697] (same_cell)\n",
      "\n",
      "0.0142 : directed(A, B) ^ hasChild(B, C) -> actedIn(A, C)\t\n",
      "Chain: ['directed', 'hasChild'] [419, 1151]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0140 : actedIn(A, B) ^ hasChild(B, C) -> directed(A, C)\t\n",
      "Chain: ['actedIn', 'hasChild'] [3, 1151]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0138 : hasChild(A, B) ^ isLeaderOf(B, C) ^ isPoliticianOf(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['hasChild', 'isLeaderOf', 'isPoliticianOf'] [1151, 2749, 3061]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0138 : owns(A, B) -> isLocatedIn(A, B)\t\n",
      "Chain: ['owns'] [3271]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0136 : isLocatedIn(A, B) ^ owns(B, C) -> owns(A, C)\t\n",
      "Chain: ['isLocatedIn', 'owns'] [2851, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.0134 : influences(A, B) ^ isCitizenOf(B, C) -> isCitizenOf(A, C)\t\n",
      "Chain: ['influences', 'isCitizenOf'] [2113, 2333]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.0129 : graduatedFrom(A, B) ^ isLocatedIn(B, C) ^ worksAt(C, D) -> livesIn(A, D)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn', 'worksAt'] [733, 2851, 3593]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0128 : graduatedFrom(A, B) ^ isLocatedIn(B, C) -> livesIn(A, C)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn'] [733, 2851]\n",
      "Predicts: livesIn [3163] (same_cell)\n",
      "\n",
      "0.0128 : graduatedFrom(A, B) ^ hasChild(B, C) ^ worksAt(C, D) -> worksAt(A, D)\t\n",
      "Chain: ['graduatedFrom', 'hasChild', 'worksAt'] [733, 1151, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n",
      "0.0128 : graduatedFrom(A, B) ^ isLocatedIn(B, C) -> isCitizenOf(A, C)\t\n",
      "Chain: ['graduatedFrom', 'isLocatedIn'] [733, 2851]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.0127 : created(A, B) ^ hasChild(B, C) -> created(A, C)\t\n",
      "Chain: ['created', 'hasChild'] [107, 1151]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0126 : diedIn(A, B) ^ hasWonPrize(B, C) ^ wasBornIn(C, D) -> hasWonPrize(A, D)\t\n",
      "Chain: ['diedIn', 'hasWonPrize', 'wasBornIn'] [313, 1907, 3491]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0126 : actedIn(A, B) ^ isLeaderOf(B, C) ^ isLocatedIn(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['actedIn', 'isLeaderOf', 'isLocatedIn'] [3, 2749, 2851]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0126 : edited(A, B) -> created(A, B)\t\n",
      "Chain: ['edited'] [521]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0126 : isLocatedIn(A, B) -> happenedIn(A, B)\t\n",
      "Chain: ['isLocatedIn'] [2851]\n",
      "Predicts: happenedIn [839] (same_cell)\n",
      "\n",
      "0.0123 : directed(A, B) ^ influences(B, C) -> created(A, C)\t\n",
      "Chain: ['directed', 'influences'] [419, 2113]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0122 : hasWonPrize(A, B) ^ isAffiliatedTo(B, C) -> hasWonPrize(A, C)\t\n",
      "Chain: ['hasWonPrize', 'isAffiliatedTo'] [1907, 2221]\n",
      "Predicts: hasWonPrize [1907] (same_cell)\n",
      "\n",
      "0.0121 : actedIn(A, B) ^ hasChild(B, C) ^ isAffiliatedTo(C, D) -> isLeaderOf(A, D)\t\n",
      "Chain: ['actedIn', 'hasChild', 'isAffiliatedTo'] [3, 1151, 2221]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0116 : graduatedFrom(A, B) ^ owns(B, C) -> created(A, C)\t\n",
      "Chain: ['graduatedFrom', 'owns'] [733, 3271]\n",
      "Predicts: created [107] (same_cell)\n",
      "\n",
      "0.0115 : isAffiliatedTo(A, B) ^ owns(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['isAffiliatedTo', 'owns'] [2221, 3271]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0115 : hasChild(A, B) ^ isAffiliatedTo(B, C) -> isLeaderOf(A, C)\t\n",
      "Chain: ['hasChild', 'isAffiliatedTo'] [1151, 2221]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0115 : hasCapital(A, B) ^ isPoliticianOf(B, C) -> wasBornIn(A, C)\t\n",
      "Chain: ['hasCapital', 'isPoliticianOf'] [1049, 3061]\n",
      "Predicts: wasBornIn [3491] (same_cell)\n",
      "\n",
      "0.0114 : isLeaderOf(A, B) -> isCitizenOf(A, B)\t\n",
      "Chain: ['isLeaderOf'] [2749]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.0113 : hasChild(A, B) ^ isLeaderOf(B, C) -> isLeaderOf(A, C)\t\n",
      "Chain: ['hasChild', 'isLeaderOf'] [1151, 2749]\n",
      "Predicts: isLeaderOf [2749] (same_cell)\n",
      "\n",
      "0.0112 : wroteMusicFor(A, B) -> actedIn(A, B)\t\n",
      "Chain: ['wroteMusicFor'] [3697]\n",
      "Predicts: actedIn [3] (same_cell)\n",
      "\n",
      "0.0111 : wroteMusicFor(A, B) -> directed(A, B)\t\n",
      "Chain: ['wroteMusicFor'] [3697]\n",
      "Predicts: directed [419] (same_cell)\n",
      "\n",
      "0.0111 : dealsWith(A, B) -> isLocatedIn(A, B)\t\n",
      "Chain: ['dealsWith'] [211]\n",
      "Predicts: isLocatedIn [2851] (same_cell)\n",
      "\n",
      "0.0110 : hasChild(A, B) ^ isLeaderOf(B, C) ^ isPoliticianOf(C, D) -> isPoliticianOf(A, D)\t\n",
      "Chain: ['hasChild', 'isLeaderOf', 'isPoliticianOf'] [1151, 2749, 3061]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.0109 : diedIn(A, B) ^ isLocatedIn(B, C) -> isCitizenOf(A, C)\t\n",
      "Chain: ['diedIn', 'isLocatedIn'] [313, 2851]\n",
      "Predicts: isCitizenOf [2333] (same_cell)\n",
      "\n",
      "0.0109 : participatedIn(A, B) -> participatedIn(A, B)\t\n",
      "Chain: ['participatedIn'] [3373]\n",
      "Predicts: participatedIn [3373] (same_cell)\n",
      "\n",
      "0.0108 : created(A, B) -> isAffiliatedTo(A, B)\t\n",
      "Chain: ['created'] [107]\n",
      "Predicts: isAffiliatedTo [2221] (same_cell)\n",
      "\n",
      "0.0104 : created(A, B) ^ hasGender(B, C) -> hasGender(A, C)\t\n",
      "Chain: ['created', 'hasGender'] [107, 1361]\n",
      "Predicts: hasGender [1361] (same_cell)\n",
      "\n",
      "0.0102 : created(A, B) ^ owns(B, C) -> owns(A, C)\t\n",
      "Chain: ['created', 'owns'] [107, 3271]\n",
      "Predicts: owns [3271] (same_cell)\n",
      "\n",
      "0.0102 : hasAcademicAdvisor(A, B) ^ influences(B, C) -> hasAcademicAdvisor(A, C)\t\n",
      "Chain: ['hasAcademicAdvisor', 'influences'] [941, 2113]\n",
      "Predicts: hasAcademicAdvisor [941] (same_cell)\n",
      "\n",
      "0.0100 : isLocatedIn(A, B) ^ livesIn(B, C) -> isPoliticianOf(A, C)\t\n",
      "Chain: ['isLocatedIn', 'livesIn'] [2851, 3163]\n",
      "Predicts: isPoliticianOf [3061] (same_cell)\n",
      "\n",
      "0.0100 : owns(A, B) ^ worksAt(B, C) -> worksAt(A, C)\t\n",
      "Chain: ['owns', 'worksAt'] [3271, 3593]\n",
      "Predicts: worksAt [3593] (same_cell)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "num_hops = 2\n",
    "rules_mapped = []\n",
    "for i,row in all_rules_df[(all_rules_df['hop']<=num_hops) & (all_rules_df['score']>=0.01)].sort_values(['score'], ascending=False).iterrows():\n",
    "    try:\n",
    "        chain = [id2rel[pf] for pf in get_primefactors(row['body'])]\n",
    "    except KeyError:\n",
    "        continue\n",
    "    if len(chain) <= num_hops:\n",
    "        pass\n",
    "    \n",
    "    head_rel = id2rel[row['head_rel']]\n",
    "    rule_str = generate_rule_string(chain, head_rel, row['type'])\n",
    "    print(f\"{row['score']:.4f} : {rule_str}\\t\")\n",
    "    print('Chain:',chain, [pf for pf in get_primefactors(row['body'])])\n",
    "    print('Predicts:', id2rel[row['head_rel']],[row['head_rel']], f\"({row['type']})\")\n",
    "    print()\n",
    "    rules_mapped.append({'Score': row['score'],'Head Rel':head_rel, 'Rule': rule_str})\n",
    "rules_df = pd.DataFrame(rules_mapped)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Focus on the worksAt relation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Score</th>\n",
       "      <th>Head Rel</th>\n",
       "      <th>Rule</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.155268</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) ^ worksAt(C, D) -&gt; worksAt(A, D)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.154072</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>hasAcademicAdvisor(A, B) ^ worksAt(B, C) -&gt; worksAt(A, C)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>0.150616</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) -&gt; worksAt(A, B)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>0.079935</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) -&gt; worksAt(A, C)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>0.040562</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>influences(A, B) ^ worksAt(B, C) -&gt; worksAt(A, C)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122</th>\n",
       "      <td>0.033708</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) ^ influences(B, C) ^ worksAt(C, D) -&gt; worksAt(A, D)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>171</th>\n",
       "      <td>0.019118</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) ^ influences(B, C) -&gt; worksAt(A, C)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>0.012821</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>graduatedFrom(A, B) ^ hasChild(B, C) ^ worksAt(C, D) -&gt; worksAt(A, D)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>224</th>\n",
       "      <td>0.010025</td>\n",
       "      <td>worksAt</td>\n",
       "      <td>owns(A, B) ^ worksAt(B, C) -&gt; worksAt(A, C)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Score  \\\n",
       "28   0.155268   \n",
       "30   0.154072   \n",
       "31   0.150616   \n",
       "64   0.079935   \n",
       "115  0.040562   \n",
       "122  0.033708   \n",
       "171  0.019118   \n",
       "197  0.012821   \n",
       "224  0.010025   \n",
       "\n",
       "    Head Rel  \\\n",
       "28   worksAt   \n",
       "30   worksAt   \n",
       "31   worksAt   \n",
       "64   worksAt   \n",
       "115  worksAt   \n",
       "122  worksAt   \n",
       "171  worksAt   \n",
       "197  worksAt   \n",
       "224  worksAt   \n",
       "\n",
       "                                                                                Rule  \n",
       "28   graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) ^ worksAt(C, D) -> worksAt(A, D)  \n",
       "30                         hasAcademicAdvisor(A, B) ^ worksAt(B, C) -> worksAt(A, C)  \n",
       "31                                              graduatedFrom(A, B) -> worksAt(A, B)  \n",
       "64                   graduatedFrom(A, B) ^ hasAcademicAdvisor(B, C) -> worksAt(A, C)  \n",
       "115                                influences(A, B) ^ worksAt(B, C) -> worksAt(A, C)  \n",
       "122          graduatedFrom(A, B) ^ influences(B, C) ^ worksAt(C, D) -> worksAt(A, D)  \n",
       "171                          graduatedFrom(A, B) ^ influences(B, C) -> worksAt(A, C)  \n",
       "197            graduatedFrom(A, B) ^ hasChild(B, C) ^ worksAt(C, D) -> worksAt(A, D)  \n",
       "224                                      owns(A, B) ^ worksAt(B, C) -> worksAt(A, C)  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.set_option('display.max_colwidth', None)\n",
    "rules_df[rules_df['Head Rel'] == 'worksAt'].sort_values('Score', ascending=False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "We show an elegant and fast way of utilizing PAM for rule generation.\n",
    "\n",
    "The whole procedure takes less than 30 seconds on a commercial laptop and we generate almost 30 thousand rules (for body length up to $k=3$ atoms).\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "c01865829f576eaff008cd308e2ea27c464a4f8737e86651bac34bc9029f3de9"
  },
  "kernelspec": {
   "display_name": "prime",
   "language": "python",
   "name": "prime"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}