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Computer Science > Logic in Computer Science

arXiv:2408.10563 (cs)
[Submitted on 20 Aug 2024]

Title:The Stable Model Semantics for Higher-Order Logic Programming

Authors: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.
Subjects: Logic in Computer Science (cs.LO); Artificial Intelligence (cs.AI); Programming Languages (cs.PL)
ACM classes: I.2.3; I.2.5; F.3.2
Cite as: arXiv:2408.10563 [cs.LO]
  (or arXiv:2408.10563v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.2408.10563

Submission history

From: Angelos Charalambidis [view email]
[v1] Tue, 20 Aug 2024 06:03:52 UTC (56 KB)
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