Semantics of normal logic programs and contested information

Abstract

We propose C4, a four-valued semantics for normal, logic programs. Using this semantics, we define two types of entailment: strong and weak. We show that a normal, logic program strongly entails a sentence under C4 if, and only if, the program entails that sentence under the well founded semantics and it weakly entails a sentence if, and only if, the program entails that sentence under the two-valued stable model semantics in case the program has any stable models. We argue that this shows that the difference between the well founded semantics and the stable model semantics can be characterized in terms of their attitude to what we call contested information. We use this insight to propose a general theory of contested reasoning.