Tyche is a Python library to support the representation of, and the reasoning about, aleatoric information. Aleatoric information is information that has an independent probability of being true each time it is observed (i.e., each observation is treated as a roll of the dice). For example, every text message that people send may include emojis, with a different probability for each individual that sent the message. Tyche provides functionality to reason about this aleatoric information using aleatoric description logic. This allows the probability of truth of logical statements to be efficiently queried, and allows the probability of the tendencies of individuals to be learnt through observation.

Tyche provides its main functionality through its tyche.individuals module, which facilitates the construction of ontological knowledge bases with probabilistic beliefs. This allows the simple representation of individuals, the probabilistic beliefs about them (termed concepts), and the probabilistic relationships between them (termed roles). Aleatoric description logic sentences may then be constructed using the tyche.language module to be used to query a knowledge base for a probability, or to be used as an observation to update a knowledge base. This allows fine-grained modelling of probabilistic belief systems, with a rigorous mathematical foundation.

Documentation: tychelibrary.github.io

Tyche Paper:

• "Tyche: A library for probabilistic reasoning and belief modelling in Python" by Padraig Lamont (2022): link and old arXiv link

Related Publications:

• "Aleatoric Description Logic for Probabilistic Reasoning" by Tim French and Thomas Smoker (2021): arXiv link
• "A modal aleatoric calculus for probabilistic reasoning" by Tim French, Andrew Gozzard and Mark Reynolds (2018): arXiv link

Usage

Tyche may be installed via pip from PyPi.

pip install Tyche

The functions and classes of Tyche can then be imported from the tyche package.

from tyche.language import *
from tyche.individuals import *
from tyche.distributions import *

Tyche does not yet have tutorials or documentation for its usage. However, example uses of Tyche are provided in the examples directory, and the source code contains doc comments to explain the functionality of classes and methods. In the future, more extensive documentation of Tyche is planned.

Structure

The tyche package consists of the following main modules:

• language. This is the aleatoric description logic language module for representing sentences. The language module also contains the representation used for the value of roles.
• individuals. This is the ontological knowledge base individuals module for representing ontologies of individuals, the probabilistic beliefs about them (concepts), and the probabilistic relationships between them (roles). The individuals module also contains classes and functions that may be used to learn from aleatoric description logic observations.
• distributions. This module contains utility classes for representing and manipulating probability distributions. These distributions may be used to convert continuous quantities into probabilities, and to learn the probability distributions from aleatoric description logic observations.

The Tyche project also consists of the package test that contains unit tests for the functionality of Tyche, and the package examples that contains example uses of Tyche.

License

Tyche is licensed under the MIT License.