Knowledge vagueness and logic

Rough Sets and Intelligent Systems Paradigms, 2007

The subject-matter of the consideration touches the problem of vagueness. The notion of the rough set, originated by Zdzisław Pawlak, was constructed under the influence of vague information and methods of shaping systems of notions leading to conceptualization and representation of vague knowledge, so also systems of their scopes as some vague sets. This paper outlines some direction of searching for a solution to this problem. In the paper, in connection to the notion of the rough set, the notion of a vague set is introduced. Some operations on these sets and their properties are discussed. The considerations intend to take into account a classical approach to reasoning, based on vague premises, and suggest finding a logic of vague sentences as a non-classical logic in which all counterparts of tautologies of classical logic are laws.

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

In this paper we discuss the multifaceted nature of vagueness, the limits of (standard) set theory in dealing with the foundational aspects that a really innovating theory of vagueness should manifest, and the difficulties in outlining the possible features that such a type of new formalism should exhibit in order to be able to deal with such innovative aspects. We shall highlight some aspects of the role that Fuzzy Set Theory (FST) can play in this process.

2004

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.

Annals of Mathematics and Artificial Intelligence, 2002

The presence of vagueness in scientific theories (in particular, to those related to and connected with the management of information) is briefly analyzed. We consider, firstly, the problem whether vague predicates can be adequately represented by existing formal theories. A negative answer to this question produces, as a by-product, the suggestion that a good semantics for fuzzy sets can be offered by the notion of "distance from idealized items". Secondly, some questions connected with the adequacy of "theories of information" to the multifaceted informal notion of "information" suggest to afford this problem within an enlarged dynamical setting.

2011

Theories, Technologies and Applications

Eprint Arxiv 1006 4551, 2010

In the area of computer science focusing on creating machines that can engage on behaviors that humans consider intelligent. The ability to create intelligent machines has intrigued humans since ancient times and today with the advent of the computer and 50 years of research into various programming techniques, the dream of smart machines is becoming a reality. Researchers are creating systems which can mimic human thought, understand speech, beat the best human chessplayer, and countless other feats never before possible. Ability of the human to estimate the information is most brightly shown in using of natural languages. Using words of a natural language for valuation qualitative attributes, for example, the person pawns uncertainty in form of vagueness in itself estimations. Vague sets, vague judgments, vague conclusions takes place there and then, where and when the reasonable subject exists and also is interested in something. The vague sets theory has arisen as the answer to an illegibility of language the reasonable subject speaks. Language of a reasonable subject is generated by vague events which are created by the reason and which are operated by the mind. The theory of vague sets represents an attempt to find such approximation of vague grouping which would be more convenient, than the classical theory of sets in situations where the natural language plays a significant role. Such theory has been offered by known American mathematician Gau and Buehrer .In our paper we are describing how vagueness of linguistic variables can be solved by using the vague set theory.This paper is mainly designed for one of directions of the eventology (the theory of the random vague events), which has arisen within the limits of the probability theory and which pursue the unique purpose to describe eventologically a movement of reason.

Studies in Fuzziness and Soft Computing, 2009

In spite of its successes as a tool in the field of engineering, fuzzy set theory has yet to achieve the universal footing that probability theory has across the various fields of mathematics, technology, philosophy and psychology. This paper sets out points of critique brought up regarding the fuzzy approach and seeks to analyze them, focusing on the question of whether anything that can be done about these matters. Do these criticisms have any practical relevance or any relevance with respect to the intended fields of usage. Do they or do they not diminish fuzzy logic's suitability as a theory of vagueness?