The interpretations of conditionals and conditional inference are often disputed. The classic logic conditional called material implication can easily be proven to be invalid, and the conditional inference rule Modus Ponens represents a tautology that becomes invalid in the face of contrary evidence from realistic scenarios. The foundations of conditionals and conditional inference seem plagued...

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that...

The historical research line on the algebraic properties of structured CF languages initiated by McNaughton’s Parenthesis Languages has recently attracted much renewed interest with the Balanced Languages, the Visibly Pushdown Automata languages (VPDA), the Synchronized Languages, and the Height-deterministic ones. Such families preserve to a varying degree the basic algebraic properties of Reg...

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be again...

In the area of Description Logic (DL) based knowledge representation, research on reasoning w.r.t. general terminologies has mainly focused on very expressive DLs. Recently, though, it was shown for the DL EL, providing only the constructors conjunction and existential restriction, that the subsumption problem w.r.t. cyclic terminologies can be decided in polynomial time, a surprisingly low upp...

The aim of this chapter is to revisit an experiment of Kahneman and Tversky (1992) to arrive at conclusions about Prospect theory and the ways of human thinking, but using a fuzzy approach, especially the compensatory one. New results shall be proved and others well-known shall be changed or confirmed. The study comprises the examination of logical predicates like those expressed by the followi...

Rough set approximations of Pawlak [15] are sometimes generalized by using similarities between objects rather than elementary sets. In practical applications, both knowledge about properties of objects and knowledge of similarity between objects can be incomplete and inconsistent. The aim of this paper is to define set approximations when all sets, and their approximations, as well as similari...

An implication operator A is said to be tied if there is a binary operation T that ties A; that is, the identity A(a,A(b, z)) = A(T (a, b), z) holds for all a, b, z. We aim at the construction of a complete predicate logic for prelinear tied adjointness algebras. We realize this in three steps. In the first step, we establish a propositional calculus AdjTPC, complete for the class of all tied a...

In this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances (interpreted as benchmarks) and the ratings are given by symmetric triangular fuzzy numbers. We will show that using the possibilistic approach (i) small changes in the membership function of the importances can cau...

Feature structures are informational elements that have been used in several linguistic theories and in computational systems for natural language processing. A logical calculus has been developed and used as a description language for feature structures. In the present work, a framework in three-valued logic is suggested for defining the semantics of a feature structure description language, a...