2014/05/15 by Angelos Charalambidis, Zoltán Ésik, Panos Rondogiannis
Computer Science · Mathematics · #Advanced Algebra and Logic #Autoepistemic logic #Computer science #Denotational semantics #Description logic #Generalization #Higher-order logic #Logic programming #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Multimodal logic #Negation #Negation as failure #Operational semantics #Programming language #Semantics (computer science) #Stable model semantics #Theoretical computer science #Well-founded semantics #cs.AI #cs.LO #cs.PL
paper · pdf · doi:10.1017/s1471068414000313
published as Theory and Practice of Logic Programming 14 (2014) 725-737
arxiv created 2014/05/15 · openalex publication_date 2014/07/01 · openalex created_date 2016/06/24 · arxiv updated 2020/02/19 · openalex updated_date 2026/08/05
Abstract Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensional higher-order logic programming. Using our approach, we resolve an old paradox that was introduced by W. W. Wadge in order to demonstrate the semantic difficulties of higher-order logic programming.