Expressiveness of Logic Programs under General Stable Model Semantics

TL;DR

This paper investigates the expressiveness of normal and disjunctive logic programs under the general stable model semantics, exploring translations, limitations, and connections to second-order logic over various structures.

Contribution

It provides translations from disjunctive to normal programs for infinite structures and characterizes expressiveness equivalences related to complexity classes and second-order logic.

Findings

Disjunctive programs can be translated to normal programs over infinite structures.

Some disjunctive programs are intranslatable to normal programs over finite structures with bounded arities.

Expressiveness equivalence relates to whether NP is closed under complement.

Abstract

The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of normal and disjunctive programs under the general stable model semantics. A translation from disjunctive programs to normal programs is proposed for infinite structures. Over finite structures, some disjunctive programs are proved to be intranslatable to normal programs if the arities of auxiliary predicates and functions are bounded in a certain way. The equivalence of the expressiveness of normal programs and disjunctive programs over arbitrary structures is also shown to coincide with that over finite structures, and coincide with whether NP is closed under complement. Moreover, to capture the exact expressiveness, some intertranslatability results between logic program classes and fragments of second-order logic are obtained.