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A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 52 (3 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
Deduction in ManyValued Logics: a Survey
 Mathware & Soft Computing, iv(2):6997
, 1997
"... this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of man ..."
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Cited by 8 (1 self)
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this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93]. 2 A classification of manyvalued logics according to their intended application
Decision Logics for Knowledge Representation in Data Mining
 In Proceedings of the 25th Annual International Computer Software and Applications Conference(COMPSAC
, 2001
"... In this paper, the qualitative and quantitative semantics for rules in data tables are investigated from a logical viewpoint. In modern data analysis, knowledge can be discovered from data tables and is usually represented by some rules. However, the knowledge is useful for a human user only when he ..."
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Cited by 5 (5 self)
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In this paper, the qualitative and quantitative semantics for rules in data tables are investigated from a logical viewpoint. In modern data analysis, knowledge can be discovered from data tables and is usually represented by some rules. However, the knowledge is useful for a human user only when he can understand the meaning of the rules. This is called the interpretability problem of intelligent data analysis. The solution of the problem depends on the selection of the rule representation language. A good representation language should have clear semantics so that a rule can be effectively validated with respect to the given data tables. In this regard, logic is one of the best choices. Starting from reviewing the decision logic for data tables, we subsequently generalize it to fuzzy and possibilistic decision logics. The rules are then viewed as the implications between wellformed formulas of these logics and their semantics with respect to precise or uncertain data tables are presented. The validity, support, and confidence of a rule are also rigorously defined in the framework.
On Rough Terminological Logics
"... : In this paper, we incorporate the notion of rough sets into terminological logics. Terminological logics formalize the classical framebased knowledge representation systems in AI and can represent and reason about concepts and roles in the objective worlds. In such logics, a concept is interprete ..."
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Cited by 5 (0 self)
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: In this paper, we incorporate the notion of rough sets into terminological logics. Terminological logics formalize the classical framebased knowledge representation systems in AI and can represent and reason about concepts and roles in the objective worlds. In such logics, a concept is interpreted as a class of individuals, while a role is a binary relations between them. Since the extensions of concepts have rigid boundaries, the systems can not handle rough concepts. By integrating rough set theory with terminological logics, we can model rough concepts and their approximations and reason about the rough subsumption between concepts in the systems. In our framework, two individuals are discernible with respect to a role if they have different relationship with any individual in this role. Thus a variety of indiscernibility relations can be determined and we can represent and reason about data of different granularities in a common language. Keywords: Terminological logics, rough ...
An overview of rough set semantics for modal and quantifier logics
 International Journal of Uncertainty, Fuzziness and Knowledgebased Systems
, 2000
"... In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set o ..."
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Cited by 4 (2 self)
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In this paper, we would like to present some logics with semantics based on rough set theory and related notions. These logics are mainly divided into two classes. One is the class of modal logics and the other is that of quantifier logics. For the former, the approximation space is based on a set of possible worlds, whereas in the latter, we consider the set of variable assignments as the universe of approximation. In addition to surveying some wellknown results about the links between logics and rough set notions, we also develop some new applied logics inspired by rough set theory.
On Rough Quantifiers
 Proceedings of the 14th European Meeting on Cybernetics and Systems Research
, 1998
"... Rough set theory is proposed as the theoretical foundation of information systems and has found rapidly growing applications in intelligent data analysis. An especially interesting problem is its relationship with other knowledge representation formalisms. The most wellknown result is that it can p ..."
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Cited by 1 (1 self)
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Rough set theory is proposed as the theoretical foundation of information systems and has found rapidly growing applications in intelligent data analysis. An especially interesting problem is its relationship with other knowledge representation formalisms. The most wellknown result is that it can provide a semantics for modal logics. Motivated by the strong analogy between quantifiers and modal operators, we would like to consider the generalization of universal and existential quantifiers in first order logic based on rough set notions. By viewing the set of variable assignments as the universe of the approximation space, we can present some quantificational logics based on rough set theory in a uniform way. Keywords: Rough set, first order logic, rough quantifiers, generalized quantifiers, probability quantifiers, neighbourhood systems. 1 Introduction The rough set theory is invented by Pawlak [ Pawlak, 1982; 1991 ] to account for the definability of a concept in terms of some e...
Fourvalued Extension of Rough Sets ⋆
"... Abstract. 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 ..."
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Abstract. 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 similarity relations are fourvalued. A set is fourvalued in the sense that its membership function can have one of the four logical values: unknown (u), false (f), inconsistent (i), or true (t). To this end, a new implication operator and settheoretical operations on fourvalued sets, such as set containment, are introduced. Several properties of lower and upper approximations of fourvalued sets are also presented. 1
A Logic for Reasoning about Fuzzy Truth Values
"... In this paper, we will present a framework for reasoning with vague and uncertain information by fuzzy truthvalued logics. It is shown that possibilistic logic, manyvalued logic, and approximate reasoning can all be embodied in the uniform framework. Keywords Fuzzytruth values, manyvalued lo ..."
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In this paper, we will present a framework for reasoning with vague and uncertain information by fuzzy truthvalued logics. It is shown that possibilistic logic, manyvalued logic, and approximate reasoning can all be embodied in the uniform framework. Keywords Fuzzytruth values, manyvalued logics, possibilistic reasoning, approximate reasoning I. Introduction In the realm of artificial intelligence and knowledgebased systems, one of the central problems is the representation and reasoning of incomplete information. An intelligent agent acting without the full knowledge of the environment would most need the capability of reasoning with incomplete information. It is now commonly believed that there are more than one types of incomplete information so totally different mechanisms would be needed to treat them. An extensive literature has been generated to cope with the problem and various approaches have been proposed. To name some among others, the most notable ones are probabil...
Fuzzy Relevant Logic: What Is It and Why Study It?
"... For any correct argument in scientific reasoning as well as our everyday reasoning, the premises of the argument must be in some way relevant to the conclusion of that argument, and vice versa. On the other hand, in scientific reasoning as well as our everyday reasoning, many arguments may be correc ..."
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For any correct argument in scientific reasoning as well as our everyday reasoning, the premises of the argument must be in some way relevant to the conclusion of that argument, and vice versa. On the other hand, in scientific reasoning as well as our everyday reasoning, many arguments may be correct to some degree, and therefore, a reasoning consisting of such fuzzy arguments is approximate. As a generalization of Boolean classical logic, fuzzy logic was established in order to deal with those fuzzy propositions and to underlie approximate reasoning. However, an approximate reasoning based on fuzzy logic is not necessarily relevant. In this paper, the author intends to call for attentions to such a fundamental research problem: Can we establish a formal logic system to underlie those reasoning that are both relevant and approximate? The paper presents the motivation to study fuzzy relevant logic and discusses possible research directions, problems, and difficulties to establish a form...