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

ANGELOS CHARALAMBIDIS, ZOLTÁN ÉSIK, PANOS RONDOGIANNIS
2014 Theory and Practice of Logic Programming  
AbstractExtensional 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
more » ... -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.
doi:10.1017/s1471068414000313 fatcat:np53agfr2jcijofn6elbi2m3jy