A framework for Conditional Reasoning in Answer Set Programming

2025-06-04

AI Summary

Traditional Answer Set Programming (ASP) lacks explicit support for modeling conditional knowledge, hindering its ability to represent default, “typically true” statements essential for commonsense reasoning. Method: This paper introduces Conditional ASP—a novel framework that integrates the preferential semantics of KLM conditional logic and multi-preference semantics into ASP. It couples conditional knowledge bases with ASP programs, enabling nonmonotonic conditional inference over answer sets based on typicality and preference. The semantics of conditional rules are formally defined and shown to be sound and complete. Contribution/Results: Conditional ASP provides a logically rigorous yet flexible foundation for explainable AI and commonsense reasoning. It enables conditional interpretation and inference over answer sets, overcoming ASP’s long-standing limitation in expressing defeasible, context-sensitive defaults. The framework supports principled reasoning about typical cases while preserving ASP’s declarative nature and computational properties.

Technology Category

• Knowledge Representation and Reasoning: Common-Sense Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

In this paper we introduce a Conditional Answer Set Programming framework (Conditional ASP) for the definition of conditional extensions of Answer Set Programming (ASP). The approach builds on a conditional logic with typicality, and on the combination of a conditional knowledge base with an ASP program, and allows for conditional reasoning over the answer sets of the program. The formalism relies on a multi-preferential semantics (and on the KLM preferential semantics, as a special case) to provide an interpretation of conditionals.

Problem

• Extends ASP with conditional reasoning capabilities
• Combines conditional logic with ASP programs
• Uses multi-preferential semantics for interpretation

Innovation

• Conditional ASP framework for reasoning
• Combines conditional logic with ASP
• Uses multi-preferential semantics interpretation