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arXiv · 2408.10563

The Stable Model Semantics for Higher-Order Logic Programming

Bart Bogaerts·Angelos Charalambidis·Giannos Chatziagapis·Babis Kostopoulos·Samuele Pollaci·Panos Rondogiannis
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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.

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Bart Bogaerts, Angelos Charalambidis, Giannos Chatziagapis, Babis Kostopoulos, Samuele Pollaci, Panos Rondogiannis. 2024-08-20. The Stable Model Semantics for Higher-Order Logic Programming. https://doi.org/10.1017/s1471068424000231

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