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.

References in corpus (1)

• A Fixed Point Theorem for Non-Monotonic Functions

Cited by in corpus (5)

• Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs
• Equivalence of two Fixed-Point Semantics for Definitional Higher-Order Logic Programs
• A representation theorem for stratified complete lattices
• A Fixed Point Theorem for Non-Monotonic Functions
• Higher-Order Constrained Horn Clauses and Refinement Types