Fuzzy logics based on residuated t-norms provide a robust mathematical formalism for logical deduction under uncertain or vague premises. In this paper, we describe a decision algorithm for the tautology problem of Basic Logic, which is the logic of continuous t-norms and their residua [Háj98, CEGT00]. Our algorithm is a refinement of the semantic method of Baaz, Hájek, Montagna, and Veith [BHM...

In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binary...

An application of so-called perception-based logical deduction in the modeling of an economic analysis given in natural language is presented. Fuzzy IF-THEN rules and theory of evaluating linguistic expressions are used, and possibilities of automated reasoning are outlined.

We consider linguistic data(base) summaries in the sense of Yager [Information Sciences 28 (1982) 69–86], exemplified by ‘‘most employees are young and well paid’’ (with some degree of truth added), for a personnel database, as an intuitive, human consistent and natural language based knowledge discovery tool. We present first an extension of the classic Yager s approach to involve more sophist...

1. GRADED DEDUCTIVE TOOLS FOR GRADED INFORMATION In accordance with Tarski’s point of view, we identify a crisp deductive apparatus with a “deduction operator”, i.e. a closure operator D : P(Å)→ P(Å) where Å is the set of formulas in a logic. Given a set X of formulas, we interpret D(X) as the set of logical consequences of X. Now, we can imagine a "stratified" deduction apparatus, i.e. the ava...

Existing search engines––with Google at the top––have many remarkable capabilities; but what is not among them is deduction capability––the capability to synthesize an answer to a query from bodies of information which reside in various parts of the knowledge base. In recent years, impressive progress has been made in enhancing performance of search engines through the use of methods based on b...

This paper shows an architecture for Deductive Fuzzy RDBMS which integrates two approaches of fuzzy databases: the relational and the logical ones. It uses the first one to represent and manipulate imprecise information and the second one to obtain intensional information. Besides, it shows how it is possible to use the resources offered by a conventional RDBMS together with a deduction module ...

The paper deals with fuzzy logic in narrow sense of Lukasiewicz style, i.e. a special kind of many-valued logic which is aimed at modeling of vagueness phenomenon. This logic is a generalization of Lukasiewicz logic with many interesting properties (for example, generalization of the deduction and completeness theorems hold in it). Our aim is to prepare the background for the resolution in fuzz...

The purpose of this paper is to describe a fuzzy cognitive map based on the random neural network model, and to illustrate its application in the modeling of process. This model is based on the probability of activation of the neurons/concepts in the network. Our model carries out inferences via numerical calculation instead of symbolic deduction. The arcs define dynamic relationships between c...