Towards sophisticated representation and reasoning techniques that allow for probabilistic uncertainty in the Rules, Logic, and Proof layers of the Semantic Web, we present probabilistic description logic programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set semantics and the well-founded semantics with Poole’s independent choice...

We introduce two chains of unary operations in the MVn algebra of Revaz Grigolia; they will be used in establishing many connections between these algebras and n-valued Lukasiewicz-Moisil algebras (LMn algebras for short). The study has four parts. It is by and large self-contained. The main result of the rst part is that MV4 algebras coincide with LM4 algebras. The larger class of \relaxed"-MV...

In previous work, I have introduced nonmonotonic probabilistic logics under variablestrength inheritance with overriding. They are formalisms for probabilistic reasoning from sets of strict logical, default logical, and default probabilistic sentences, which are parameterized through a value λ∈ [0, 1] that describes the strength of the inheritance of default probabilistic knowledge. In this pap...

We present new probabilistic generalizations of Pearl’s entailment in System [50, 32] and Lehmann’s lexicographic entailment [39], called and -entailment, which are parameterized through a value that describes the strength of the inheritance of purely probabilistic knowledge. In the special cases of and , the notions of and -entailment coincide with the probabilistic notions of and -entailment ...

In this paper we propose clustering methods based on weighted quasiarithmetic means of T -transitive fuzzy relations. We first generate a T -transitive closure R from a proximity relation R based on a max-T composition and produce a T -transitive lower approximation or opening RT from the proximity relation R through the residuation operator. We then aggregate a new T -indistinguishability fuzz...

In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl’s causes and explanations in the structural-model approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which show that under suitable restrictions deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability...

Recently, it has been shown that probabilistic entailment under coherence is weaker than model-theoretic probabilistic entailment. Moreover, probabilistic entailment under coherence is a generalization of default entailment in System P . In this paper, we continue this line of research by presenting probabilistic generalizations of more sophisticated notions of classical default entailment that...