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Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation*

  • ANGELOS CHARALAMBIDIS (a1), ZOLTÁN ÉSIK (a2) and PANOS RONDOGIANNIS (a3)

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.

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This research is being supported by the Greek General Secretariat for Research and Technology, the National Development Agency of Hungary, and the European Commission (European Regional Development Fund) under a Greek-Hungarian intergovernmental programme of Scientific and Technological collaboration. Project title: “Extensions and Applications of Fixed Point Theory for Non-Monotonic Formalisms”. It is also supported by grant no. ANN 110883 from the National Foundation of Hungary for Scientific Research.

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CHARALAMBIDIS et al.
Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation

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Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation*

  • ANGELOS CHARALAMBIDIS (a1), ZOLTÁN ÉSIK (a2) and PANOS RONDOGIANNIS (a3)

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