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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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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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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
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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: 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 ...
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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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.
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.
A ManyValued Temporal Logic and Reasoning Framework for Decision Making
"... Temporality and uncertainty are important features of real world systems where the state of a system evolves over time and the transition through states depends on uncertain conditions. Examples of such application areas where these concepts matter are smart home systems, disaster management, and ro ..."
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Temporality and uncertainty are important features of real world systems where the state of a system evolves over time and the transition through states depends on uncertain conditions. Examples of such application areas where these concepts matter are smart home systems, disaster management, and robot control etc. Solving problems in such areas usually requires the use of formal mechanisms such as logic systems, statistical methods and other reasoning and decisionmaking methods. In this chapter, we extend a previously proposed temporal reasoning framework to enable the management of uncertainty based on a manyvalued logic. We prove that this new manyvalued temporal propositional logic system is sound and complete. We also provide extended reasoning algorithms that can now handle both temporality and uncertainty in an integrated way. We illustrate the framework through a simple but realistic scenario in a smart home application. Decision making is a process of leading to a selection of a course of action among many alternatives and happening all over the world all the time. People try to collect as much information as they can to help them to perform the most appropriate decision for further
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
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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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...
Nonmonotonic Reasoning Based on Incomplete Logic
"... What characterizes human reasoning is the ability of dealing with incomplete information. Incomplete logic is developed for modeling incomplete knowledge. The most distinctive feature of incomplete logic is its semantics. This is an alternative presentation of partial semantics. In this paper, we wi ..."
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What characterizes human reasoning is the ability of dealing with incomplete information. Incomplete logic is developed for modeling incomplete knowledge. The most distinctive feature of incomplete logic is its semantics. This is an alternative presentation of partial semantics. In this paper, we will introduce the general notion of incomplete logic(ICL), compare it with partial logic, and give the resolution method for it. We will also show how ICL can be applied to nonmonotonic reasoning. We define nonmonotonic derivation as monotonic derivation in ICL from the database and some consistent assumptions. The mechanism of ICL makes it easy to assert the consistency of an assumption without asserting the assumption itself.