Recently there have been some unexpected results concerning Fuzzy Description Logics (FDLs) with General Concept Inclusions (GCIs). They show that, unlike the classical case, the DL ALC with GCIs does not have the finite model property under Lukasiewicz Logic or Product Logic and, specifically, knowledge base satisfiability is an undecidable problem for Product Logic. We complete here the analy...

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages ...

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product trian...

We show that the set of valid formulas in Lukasiewicz predicate logic is a complete Π 2 set. We also show that the classically valid formulas are exactly those formulas in the classical language whose fuzzy value is 1/2. Lukasiewicz’ infinite valued logic can be seen as a particular “implementation” of fuzzy logic. The set of possible “truth values” (or, in another interpretation, degrees of ce...

The paper deals with estimating the condition number of triangular matrices in the Euclidean norm. The two main incremental methods, based on the work of Bischof and on the later work of Duff and Vömel, are compared. The paper presents new theoretical results revealing their similarities and differences. As typical in condition number estimation, there is no universal always-winning strategy, b...

This paper is a humble homage to Enric Trillas. Following his foundational contributions on models of ordinary reasoning in an algebraic setting, we study here elements of these models, like conjectures and hypothesis, in the logical framework of continuous t-norm based fuzzy logics. We consider notions of consistency, conjecture and hypothesis arising from two natural families of consequence o...

We consider propositional logic. Three-valued logics are old: the first one is Lukasiewicz three valued logic from 1920 [8]. Gödel in [5] from 1932 studied a hierarchy of finite-valued logics, containing Gödel three-valued logic. Our main interest pays to Kleene three-valued logic [6]. Other threevalued logics will not be considered here. Let us agree that the three truth values are 0, 1 2 , 1 ...