Qualitative and quantitative optimization in answer set programming
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A general framework for qualitative and quantitative optimization in answer set programming.


asprin is a general framework for optimization in ASP that allows:

  • computing optimal stable models of logic programs with preferences, and
  • defining new preference types in a very easy way. Some preference types (subset, pareto...) are already defined in asprin's library, but many more can be defined simply writing a logic program.

For a formal description of asprin, please read our paper (bibtex).

Starting with version 3, asprin is documented in the Potassco guide. Older versions are documented in the Potassco guide on Sourceforge.


$ asprin [number_of_models] [options] [files]

By default, asprin loads its library asprin_lib.lp. This may be disabled with option --no-asprin-lib.

Option --help prints help.

Options --approximation=weak and --approximation=heuristic activate solving modes different than the basic ones, and are often faster than it.

Option --meta=query can be used to compute optimal models that contain the atom query.

Options --meta=simple or --meta=combine should be used to compute many optimal models using non stratified preference programs (in asprin's library this can only happen with CP nets, see below).

Option --on-opt-heur can be used to enumerate diverse (or similar) optimal stable models. For example, try with --on-opt-heur=+,p,1,false --on-opt-heur=-,p,1,true.

Option --improve-limit can be used to enumerate close to optimal stable models. For example, try with --improve-limit 2,1000.


The easiest way to obtain asprin is using Anaconda. Packages are available in the Potassco channel. First install either Anaconda or Miniconda and then run: conda install -c potassco asprin.

asprin can also be installed with pip via pip install asprin. For a local installation, add option --user. In this case, setting environment variable PYTHONUSERBASE to dir before running pip, asprin will be installed in dir/bin/asprin.

If that does not work, you can always download the sources from here in some directory dir, and run asprin with python dir/asprin/asprin/asprin.py.

System tests may be run with asprin --test and asprin --test --all.

asprin has been tested with Python 2.7.13 and 3.5.3, using clingo 5.3.0.

asprin uses the ply library, version 3.11, which is bundled in asprin/src/spec_parser/ply, and was retrieved from http://www.dabeaz.com/ply/.


$ cat examples/example1.lp
1 { a(X) : dom(X) }.
#show a/1.

#preference(p,subset) { 

$ asprin examples/example1.lp 0
asprin version 3.0.0
Reading from examples/example1.lp
Answer: 1
Answer: 2
Answer: 3

Models       : 3
  Optimum    : yes
  Optimal    : 3

$ cat examples/example2.lp
% base program

1 { a(X) : dom(X) } 2.
1 { b(X) : dom(X) } 2.
#show a/1.
#show b/1.

% basic preference statements


  X :: b(X)

  a(X) >> not a(X) || b(X)

  a(X) >> b(X)

% composite preference statements



% optimize statement


$ asprin examples/example2.lp 
asprin version 3.0.0
Reading from examples/example2.lp
Answer: 1
a(3) b(1)

Models       : 1+
  Optimum    : yes

CP nets

asprin preference library implements the preference type cp, that stands for CP nets.

CP nets where introduced in the following paper:

  • Craig Boutilier, Ronen I. Brafman, Carmel Domshlak, Holger H. Hoos, David Poole: CP-nets: A Tool for Representing and Reasoning with Conditional Ceteris Paribus Preference Statements. J. Artif. Intell. Res. 21: 135-191 (2004)

Propositional preference elements of type cp have one of the following forms:

  1. a >> not a || { l1; ...; ln }, or
  2. not a >> a || { l1; ...; ln }

where a is an atom and l1, ..., ln are literals.

The semantics is defined using the notion of improving flips. Let A be the set of atoms appearing in a cp preference statement, and let X and Y be two subsets of A. There is an improving flip from X to Y if there is some preference element such that X and Y satisfy all li's, and either the element has the form (1) and Y is the union of X and {a}, or the element has the form (2) and Y is X minus {a}. Then, for any two subsets W and Z of A, W is better than Z if there is a sequence of improving flips from W to Z. A CP net is consistent if there is no set X such that X is better than X. This definition for subsets of A is extended to the stable models of a logic program. A stable model X is better than Y if the intersection of X and A is better than the intersection of Y and A. Note that this implies that the ceteris-paribus assumption only applies to the atoms A appearing in the preference statement.

We provide various encoding and solving techniques for CP nets, that can be applied depending on the structure of the CP net. For tree-like CP nets, see example cp_tree.lp. For acyclic CP nets, see example cp_acyclic.lp. For general CP nets, see example cp_general.lp.

asprin implementation of CP nets is correct only for consistent CP nets. Note that tree-like and acyclic CP nets are always consistent, but this does not hold in general.


  • Javier Romero