Argumentation as metaphor for logic programming semantics is a sound basis to define negotiating agents. If such agents operate in an open system, they have to be able to negotiate and argue efficiently in a goal-directed fashion and they have to deal with uncertain and vague knowledge. In this paper, we define an argumentation framework with fuzzy unification and reasoning for the well-founded...

In order to obtain a demanded fuzzy implication, a number of properties have been proposed, among which the first place antitonicity, the second place monotonicity and the boundary conditions are the most important ones. The three classes of fuzzy implications derived from the implication in binary logic, S-, Rand QL-implications all satisfy the second place monotonicity and the boundary condit...

Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, dis...

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its ne...

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 ...

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...