Logic Programs with Contested Information

Shekhar Pradhan

Abstract: We generalize reasoning with logically inconsistent information to reasoning with contested information. We provide a semantics for normal logic programs with contested information in terms of C4, a four-valued logic. In terms of this semantics we define strong and weak entailments of normal logic programs with contested information. C4 also provides a new semantics for normal logic programs. We show that a normal logic program strongly entails a sentence under C4 if, and only if, that sentence is also entailed by the well-founded semantics and in case the program has a two-valued stable model, the program weakly entails a sentence under C4 if, and only if, it is also entailed by the stable model semantics. We use this result to argue that the difference between the well-founded semantics and the stable model semantics can be characterized in terms of what we call completely contested information. We also use C4 to provide an intuitively satisfactory semantics for databases that violate denial integrity constraints.