Refining Gelfond Rationality Principle: Towards More Comprehensive Foundational Principles for Answer Set Semantics
Yi-Dong Shen, Thomas Eiter

TL;DR
This paper refines the Gelfond answer set principles to develop more comprehensive foundational criteria for answer set semantics, addressing limitations of existing conditions and proposing new semantics based on well-supportedness and minimality.
Contribution
It introduces refined GAS principles that extend well-supportedness and minimality, providing a new foundation for answer set semantics and evaluating existing semantics against these principles.
Findings
Refined GAS principles ensure answer sets are free of circular justification.
New semantics based on these principles better capture expected answer sets.
Analysis of computational complexity of the proposed semantics.
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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
