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The intricacies of three-valued extensional semantics for higher-order logic programs

THEORY AND PRACTICE OF logic programming 2017年第5-6期17卷 974-991页

作者： Rondogiannis, Panos Symeonidou, Ioanna Univ Athens Athens Greece

M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extension fails to retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.

关键词： extensional higher-order logic programming Negation in logic programming

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The intricacies of three-valued extensional semantics for higher-order logic programs

The intricacies of three-valued extensional semantics for hi...

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33rd International Conference on logic programming colocated with the 23rd International Conference on Principles and Practice of Constraint programming / 20th International Conference on Theory and Applications of Satisfiability Testing

作者： Rondogiannis, Panos Symeonidou, Ioanna Univ Athens Athens Greece

关键词： extensional higher-order logic programming Negation in logic programming

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Equivalence of two fixed-point semantics for definitional higher-order logic programs

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THEORETICAL COMPUTER SCIENCE 2017年 668卷 27-42页

作者： Charalambidis, Angelos Rondogiannis, Panos Symeonidou, Ioanna Univ Athens Dept Informat & Telecommun Athens 15784 Greece

Two distinct research approaches have been proposed for assigning extensional semantics to higher-order logic programming. The former approach [11] uses classical domain theoretic tools while the latter [1] builds on a fixed-point construction defined on a syntactic instantiation of the source program. The relationships between these two approaches had not been investigated until now. In this paper we demonstrate that for a very broad class of programs, namely the class of definitional programs introduced by W.W. Wadge, the two approaches coincide with respect to ground atoms that involve symbols of the program. On the other hand, we argue that if existential higher-order variables are allowed to appear in the bodies of program rules, the two approaches are in general different. The results of the paper contribute to a better understanding of the semantics of higher-order logic programming. (C) 2017 Elsevier B.V. All rights reserved.

关键词： extensional higher-order logic programming Semantics of logic programming

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