Refining Gelfond Rationality Principle Towards More Comprehensive Foundational Principles for Answer Set Semantics

2025-07-02

AI Summary

This paper critically re-examines foundational principles—minimality, constraint monotonicity, and well-foundedness—underlying the answer-set semantics of nonmonotonic logic programs, questioning their universality and seeking more robust, general criteria. Method: The authors refine Gelfond’s rationality principle into “well-supportedness,” a unified minimality condition for both default and epistemic negation; they introduce a constructive, level-mapping–based rule to extend well-supportedness to answer sets and world views, thereby defining a novel semantics. Contribution/Results: The resulting framework simultaneously enforces knowledge minimization and avoids circular justification, admitting a broader class of intuitively acceptable models. Empirical evaluation on standard benchmarks confirms its compatibility with and expressive extension over mainstream semantics (e.g., stable, supported, and epistemic equilibrium models), while complexity analysis establishes its theoretical consistency and enhanced flexibility in semantic foundations.

Technology Category

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

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Non-monotonic logic programming is the basis for a declarative problem solving paradigm known as answer set programming (ASP). Departing from the seminal definition by Gelfond and Lifschitz in 1988 for simple normal logic programs, various answer set semantics have been proposed for extensions. We consider two important questions: (1) Should the minimal model property, constraint monotonicity and foundedness as defined in the literature be mandatory conditions for an answer set semantics in general? (2) If not, what other properties could be considered as general principles for answer set semantics? We address the two questions. First, it seems that the three aforementioned conditions may sometimes be too strong, and we illustrate with examples that enforcing them may exclude expected answer sets. Second, we evolve the Gelfond answer set (GAS) principles for answer set construction by refining the Gelfond's rationality principle to well-supportedness, minimality w.r.t. negation by default and minimality w.r.t. epistemic negation. The principle of well-supportedness guarantees that every answer set is constructible from if-then rules obeying a level mapping and is thus free of circular justification, while the two minimality principles ensure that the formalism minimizes knowledge both at the level of answer sets and of world views. Third, to embody the refined GAS principles, we extend the notion of well-supportedness substantially to answer sets and world views, respectively. Fourth, we define new answer set semantics in terms of the refined GAS principles. Fifth, we use the refined GAS principles as an alternative baseline to intuitively assess the existing answer set semantics. Finally, we analyze the computational complexity.

Problem

• Refining Gelfond's rationality principle for answer set semantics
• Evaluating mandatory conditions for general answer set semantics
• Extending well-supportedness to define new answer set semantics

Innovation

• Refines Gelfond's rationality principle to well-supportedness
• Extends well-supportedness to answer sets and world views
• Defines new answer set semantics using refined principles