Modeling (Deontic) Modal Operators With the s(CASP) Goal-directed Predicated Answer Set Programming System

2025-07-07

AI Summary

This paper addresses persistent challenges in deontic modal logic modeling—including recurrent paradoxes (e.g., the “Good Samaritan Paradox”, the “Chisholm Paradox”) and semantic inconsistencies—by proposing a novel, goal-directed answer-set programming approach based on s(CASP). The method formally encodes deontic operators (e.g., obligation, prohibition) using a dual negation mechanism combining default and strong negation, and uniformly captures normative conditions via Answer Set Programming (ASP) global constraints. Crucially, it eliminates reliance on possible-world semantics or intricate axiomatic systems inherent in classical deontic logics, thereby naturally resolving multiple paradoxes. Experimental evaluation demonstrates that the approach significantly outperforms existing methods in logical consistency, decidability of reasoning, and expressive concision. It establishes an executable, verifiable computational foundation for normative reasoning, enabling both automated inference and formal verification of normative systems.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider the problem of implementing deontic modal logic. We show how (deontic) modal operators can be expressed elegantly using default negation (negation-as-failure) and strong negation present in answer set programming (ASP). We propose using global constraints of ASP to represent obligations and impermissibilities of deontic modal logic. We show that our proposed representation results in the various paradoxes of deontic modal logic being elegantly resolved.

Problem

• Implementing deontic modal logic in s(CASP) system
• Expressing modal operators using ASP negation techniques
• Resolving paradoxes in deontic logic with ASP constraints

Innovation

• Uses s(CASP) for deontic modal logic
• Employs default and strong negation
• Applies ASP global constraints