Classical ontologies are not suitable to represent vague pieces of information, which has lead to the birth of Fuzzy Description Logics as an appropriate formalism to represent this type of knowledge. Different families of fuzzy operators lead to Fuzzy Description Logics with different properties. This paper studies Fuzzy Description Logics under a semantics given by the Gödel family of fuzzy o...

This paper develops a category-theoretic approach to uncertainty, informativeness and decision-making problems. It is based on appropriate first order fuzzy logic in which not only logical connectives but also quantifiers have fuzzy interpretation. It is shown that all fundamental concepts of probability and statistics such as joint distribution, conditional distribution, etc., have meaningful ...

Relevant contributions of fuzzy logic to the logical models in information retrieval is studied. It makes it possible to grasp the graduality of some relevant concepts and to model both imprecision and uncertainty inherent to the retrieval process, still in the framework of the broadly meant logical approach. In this perspective we discuss various extensions to the basic Boolean model which are...

In this paper we introduce split truth/falseness semantics for a multi-valued logical processing of fuzzy preference modelling. Our approach takes as starting point the standard framework of fuzzy outranking relations as proposed by the French multi-criteria decision aid community. Formal links between a given relational credibility calculus and associated truth polarization techniques will be ...

Fuzzy set theoretical approach to numerous problems of applied mathematics and, especially, fuzzy logical analysis of those problems become frequent in the modern mathematical modelling of the real world. It is desirable to offer the mathematically oriented reader a summary of the background of the principles of fuzzy logic in a lucid and compact form. The referred book aims to offer such summa...

Logical omniscience states that the knowledge set of ordinary rational agents is closed for its logical consequences. Although epistemic logicians in general judge this principle unrealistic, there no consensus on how it should be restrained. The challenge conceptual: we must find adequate criteria separating obvious consequences (consequences which closure certainly holds) from non-obvious one...

The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by a calculus for the derivation of formulas. Besides this logical approach also a more algebraic a...