Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation
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.
Cite
@article{arxiv.1405.3792,
title = {Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation},
author = {Angelos Charalambidis and Zoltán Ésik and Panos Rondogiannis},
journal= {arXiv preprint arXiv:1405.3792},
year = {2020}
}