First-Order Stable Model Semantics with Intensional Functions

TL;DR

This paper extends first-order stable model semantics to include intensional functions, enabling more natural modeling of non-Boolean fluents and introducing ASPMT, which combines answer set programming with SMT techniques for enhanced reasoning.

Contribution

It introduces a formalism for intensional functions within stable model semantics and develops ASPMT, a framework integrating ASP with SMT for first-order reasoning.

Findings

Extended stable model semantics to include intensional functions.

Defined ASPMT, combining ASP and SMT techniques.

Applied ASPMT to domains with real numbers, reducing grounding issues.

Abstract

In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee, and Lifschitz to allow intensional functions -- functions that are specified by a logic program just like predicates are specified. We show that many known properties of the stable model semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of ASP. Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non-intensional ones.