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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Vydáno v:Theory and practice of logic programming Ročník 24; číslo 4; s. 737 - 754
Hlavní autoři: BOGAERTS, BART, CHARALAMBIDIS, ANGELOS, CHATZIAGAPIS, GIANNOS, KOSTOPOULOS, BABIS, POLLACI, SAMUELE, RONDOGIANNIS, PANOS
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.07.2024
Témata:
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
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1471-0684
1475-3081
DOI:10.1017/S1471068424000231