Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilit...

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we a representation so called square root negation within this as operation which acts like cycling negation. define two variants logical matrices performing different orders over the set truth values. Purely formal result our study consists in ...

This paper continues our study in fuzzy interval logic based on the Checklist Paradigm(CP) semantics of Bandler and Kohout. We investigate the fuzzy interval system of negation which was defined by the Sheffer(NAND), the Nicod(NOR) and the implication connectives of m1 interval system in depth. The top-bottom(TOPBOT) pair of fuzzy negation interval shows non-involutive property; however, it sho...

In natural language, and in some knowledge representation systems, such as extended logic programs, there are two kinds of negation: a weak negation expressing non-truth, and a strong negation expressing explicit falsity. In this paper I argue that, like in several basic computational languages, such as OCL and SQL, two kinds of negation are also needed in the Semantic Web.

This paper introduces a logic ILED derived from standard intuitionistic sentence logic by adding two operators Dϕ for " Definitely ϕ " and ~ϕ for " Experience rejects ϕ ". A further negation ¬ϕ = def (ϕ→⊥) ∨ ~ϕ , which we call real negation, is introduced. Real negation is like intuitionistic negation when there are no D-operators but deviates when there are. We see that Dϕ ↔ ϕ is valid but ¬Dϕ...