Fuzzy Logic in Broader Sense

The Logica Yearbook, 2004

This paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author. Our goal is to think of the state of the art in mathematical fuzzy logic (MFL) and to outline some of the tasks on which, in the author's opinion, MFL should focus in the future. In our discussion, we will mention not only the basic theory, but also its extension called fuzzy logic in broader sense (FLb). The paradigm of the latter is to be the logic of natural human reasoning, whose most essential characteristic is the use of natural language. Besides brief description of FLb, we will also mention some of its applications. On the basis of that, we will ponder on other possible directions for research, namely the possibility of using FLn as a metatheory of fuzzy mathematics, as a proper tool for modeling of the main manifestations of the phenomenon of vagueness, and as a reasonable tool for developing models of linguistic semantics.

1999

ADVANCES IN FUZZY SET THEORY AND APPLICATIONS M.M. Gupta, R.K. Ragade, R.R. Yager (Editors), North-Holland Publishing Company 1979, 1979

L.A. Zadeh and E.H. Mamdani proposed the methods for fuzzy reasoning in which the antecedent involves a fuzzy conditional proposition "If x is A then y is-B" with A and B being fuzzy concepts. This paper points out that the consequences inferred by their methods do not always fit our intuitions, and suggests some new methods which fit our intuitions under several criteria such as modus ponens and modus tollens .

Logic and Logical Philosophy, 2017

In the common man reasoning the presence of vague predicates is pervasive and under the name "fuzzy logic in narrow sense" or "formal fuzzy logic" there are a series of attempts to formalize such a kind of phenomenon. This paper is devoted to discussing the limits of these attempts both from a technical point of view and with respect the original and principal task: to define a mathematical model of the vagueness. For example, one argues that, since vagueness is necessarily connected with the intuition of the continuum, we have to look at the order-based topology of the interval [0,1] and not at the discrete topology of the set {0, 1}. In accordance, in switching from classical logic to a logic for the vague predicates, we cannot avoid the use of the basic notions of real analysis as, for example, the ones of "approximation", "convergence", "continuity". In accordance, instead of defining the compactness of the logical consequence operator and of the deduction operator in terms of finiteness, we have to define it in terms of continuity. Also, the effectiveness of the deduction apparatus has to be defined by using the tools of constructive real analysis and not the one of recursive arithmetic. This means that decidability and semi-decidability have to be defined by involving effective limit processes and not by finite steps stopping processes.

Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 1990

2011

1992

International Journal of Approximate Reasoning, 1989

The generalized modus ponens is a fuzzy logic pattern of reasoning that permits inferences to be made with rules having imprecise information in both their antecedent and consequent parts. Several alternatives are available to represent the meaning one wishes to assign to a given rule. This paper first explores four of the most often encountered possibilities, in the case where a single rule is considered at a time. Second, the behavior of two of them (which seem sufficient for practical use in deduction systems) is investigated in the situation where the dependency between antecedent and consequent variables is described by a collection of rules rather than a single rule. Conjectures are made about what is semantically important in the result yielded by the exact computation of the generalized modus ponens. With these hypotheses it is shown that one can get a meaningful approximation of what is produced by the generalized modus ponens technique and also avoid the well-known inefficiency problem associated with its computation.

1997

In this paper we deal with syntactic aspects of two kinds of fuzzy logic, namely fuzzy logic in narrow (FLn) and that in broader sense (FLb). Fuzzy logic in narrow sense is now quite well established though the work is far from being nished. The goal of this logic is to develop means for modeling of the vagueness phenomenon. One of the partial goals is to formulate analogues of most of the classical logic