The Stable Model Semantics for Higher-Order Logic Programming

TL;DR

This paper introduces a stable model semantics for higher-order logic programming using Approximation Fixpoint Theory, extending classical semantics and enabling new applications in Answer Set Programming.

Contribution

It generalizes existing stable model semantics to higher-order logic programs and introduces alternative semantics like supported, Kripke-Kleene, and well-founded models.

Findings

Supported the existence of a unique two-valued stable model for stratified programs.

Demonstrated the applicability of higher-order logic programming with stable semantics in various domains.

Showed that the proposed semantics retains desirable properties of classical stable models.

Abstract

We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems.