We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze t...

We develop alternative semantics for à Lukasiewicz logic and for cancellative hoop logic according to the following idea. We formalize statements reflecting an inexact knowledge of certain (sharp) properties; we assume that all what can be known about a property is its expressive strength. To this end, we consider a Boolean algebra endowed with an automorphism group or, alternatively, with a me...

This paper is part of a general project of developing a systematic and algebraic proof theory for nonclassical logics. Generalizing our previous work on intuitionistic-substructural axioms and singleconclusion (hyper)sequent calculi, we define a hierarchy on Hilbert axioms in the language of classical linear logic without exponentials. We then give a systematic procedure to transform axioms up ...

We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment by adding inheritance with overriding. This is done by using recent approaches to probabilistic default reasoning with conditional constraints. We analyze t...

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (∈,∈ ∨ q)-fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these ge...

When the degree of intersections A∩B of events A,B is unknown arises a problem: how to evaluate the probability P(A ∩ B) and P(A ∩B) from P(A) and P(B). To treat related problems two models of valuation: interval and paired probabilities are proposed. It is shown that the valuation corresponding to the set operations ∩ (intersection), ∪ (union) and ∼ (complement) can be described by the truth f...

Fuzzy formal logics were introduced in or-der to handle graded truth values insteadof only ‘true’ and ‘false’. A wide range ofsuch logics were introduced successfully, likeMonoidal T-norm based Logic, Basic Logic,Gödel Logic, Lukasiewicz Logic etc. How-ever, in general, fuzzy set theory is not onlyconcerned with vagueness, but also with un-certainty. A possible s...

A systematic procedure for developing the unified signal flow graph model of a fuzzy PI controller is presented in this paper. From this unified model it is possible to determine the complete behavior of the Fuzzy PI controller. As a first step in constructing the signal flow graph the analytical structures oflinear fuzzy PI controller are needed. In view of this by considering triangular/trape...