The Stable Model Semantics for Higher-Order Logic Programming

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-va...

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Bibliographic Details
Published in:Theory and practice of logic programming Vol. 24; no. 4; pp. 737 - 754
Main Authors: BOGAERTS, BART, CHARALAMBIDIS, ANGELOS, CHATZIAGAPIS, GIANNOS, KOSTOPOULOS, BABIS, POLLACI, SAMUELE, RONDOGIANNIS, PANOS
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.07.2024
Subjects:
Boolean
Formalism
Logic programming
Logic programs
Original Article
Power
Programming languages
Semantic web
Semantics
approximation fixpoint theory
stable model semantics
higher-order logic programming
ISSN:1471-0684, 1475-3081
Online Access:Get full text
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Summary: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 as well as the three-valued one of Przymusinski, 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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ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068424000231