Extensional semantics for higher-order logic programs with negation

Abstract

We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [2,3] for positive higher-order programs. In this way we provide an alternative extensional semantics for higher-order logic programs with negation to the one proposed in [6]. As an immediate useful consequence of our developments, we define for the language we consider the notions of stratification and local stratification, which generalize the familiar such notions from classical logic programming. We demonstrate that for stratified and locally stratified higher-order logic programs, the proposed semantics never assigns the unknown truth value.