Three valued logic of Lukasiewicz for modeling semantics of logic programs

Abstract

In order to really understand all aspects of logic-based program development of different semantics, it would be useful to have a common solid logical foundation. The stable semantics are based on G3 but we show that stable semantics can be fully represented in the three valued logic of Łukasiewicz. We construct a particular semantics that we call Ł3-WFS wich is defined over general propositional theories, can be defined via three valued logic of Łukasiewicz. Interesting Ł3-WFS seems to satisfy most of the principles of a well behaved semantics. Hence we propose the three valued Łukasiewicz logic to model WFS, extensions of WFS, and the Stable semantics. © Springer-Verlag Berlin Heidelberg 2004.