Overview of an abstract fixed point theory for non-monotonic functions and its applications to logic programming

Abstract

The purpose of the present paper is to give an overview of our joint work with Zoltán Ésik, namely the development of an abstract fixed point theory for a class of non-monotonic functions [4] and its use in providing a novel denotational semantics for a very broad extension of classical logic programming [1]. Our purpose is to give a high-level presentation of the main developments of these two works, that avoids as much as possible the underlying technical details, and which can be used as a mild introduction to the area.