ABSTRACT
This book provides comprehensive treatment of logic programming semantics from the perspective of fixed-point semantics. The classical semantic analysis of programs in the sense of denotational semantics is based on monotonic, order-continuous operators, via their least fixed points using Theorems. Domain theory, based on order continuity of semantic operators, is the dominant theory underlying the denotational semantics of programming languages. However, an alternative tradition in the semantics of programming languages to that using domains is an approach based on the use of metric spaces. Fixed-point theorems have a rightful place in the core arsenal of mathematical tools applicable to theoretical computer science. Knowledge Representation and Reasoning is one of the classical branches of Artificial Intelligence. The topology-driven view of logic programming semantics provides a conceptual bridge between the discrete (symbolic) world of logic and the continuous (subsymbolic) world of topology and analysis on the reals.
