A Novel Framework for Reasoning over Optimization Problems in Probabilistic Answer Set Programming

Probabilistic logic-based languages offer an expressive

framework for encoding uncertain information in a

human-interpretable way.

Among existing formalisms, Probabilistic Answer Set

Programming (PASP) stands out for its ease of modeling

complex scenarios.

The current definition of PASP is limited to programs

consisting of disjunctive rules and probabilistic facts

only. To enhance the expressivity of the framework, we

introduce Optimal Probabilistic Answer Set Programming,

which extends the language by allowing the inclusion of

weak constraints within PASP specifications. We motivate

this extension through some real-world application

scenarios and present a detailed computational complexity

analysis for both the inference and Most Probable

Explanation (MPE) tasks.