Two New Definitions of Stable Models of Logic Programs with Generalized Quantifiers

TL;DR

This paper introduces new definitions for stable model semantics of logic programs with generalized quantifiers, using reduct-based approaches, and demonstrates their equivalence under certain conditions.

Contribution

It proposes alternative reduct-based definitions for stable models with generalized quantifiers and shows their equivalence for a broad class of logic programs.

Findings

Redefinition of stable models using reducts instead of SM operator

Extension of stable model semantics to generalized quantifiers

Equivalence of the two semantics for a syntactic class of programs

Abstract

We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original definitions. Also, we extend the FLP stable model semantics to allow generalized quantifiers by referring to an operator that is similar to the $\sm$ operator. For a reasonable syntactic class of logic programs, we show that the two stable model semantics of generalized quantifiers are interchangeable.