Generalization of Rough Sets using Modal Logics

Yao, Yiyu; Lin, Tsau Young

doi:10.1080/10798587.1996.10750660

Cited by 421 publications

(145 citation statements)

References 6 publications

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“…This approach can easily be extended to rough set models based on a relation that is not necessarily an equivalence one [17,18]. These logics remain modal, and use nested modalities.…”

Section: Comparison To Logics Of Rough Setsmentioning

confidence: 99%

Possibilistic vs. Relational Semantics for Logics of Incomplete Information

Banerjee

Dubois

Godo³

2014

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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Abstract. This paper proposes an extension of the MEL logic to a language containing modal formulae of depth 0 or 1 only. MEL is a logic of incomplete information where an agent can express both beliefs and explicitly ignored facts, that only uses modal formulae of depth 1, and no objective ones. The extended logic, called MEL + has the same axioms as, and is in some sense equivalent to, S5 with a restricted language, but with the same expressive power. The semantics is not based on Kripke models with equivalence relations, but on pairs made of an interpretation (representing the real state of facts) and a non-empty set of possible interpretations (representing an epistemic state). Soundness and completeness are established. We provide a rationale for using our approach when an agent reasons about what is known of the epistemic state of another agent and compares it with what is known about the real world. Our approach can be viewed as an alternative to the basic epistemic logic not concerned with introspection. We discuss the difference with S5 used as a logic for rough sets, and the similarity with some previous non-monotonic logics of knowledge is highlighted.

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“…This approach can easily be extended to rough set models based on a relation that is not necessarily an equivalence one [17,18]. These logics remain modal, and use nested modalities.…”

Section: Comparison To Logics Of Rough Setsmentioning

confidence: 99%

Possibilistic vs. Relational Semantics for Logics of Incomplete Information

Banerjee

Dubois

Godo³

2014

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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“…Most of the research in the rough sets field has been focused on the following issues: algebraic characterization and interpretation of rough sets [Pag97]; relations of rough set theory with other theories to represent knowledge, like modal logics [YL96]; integration of rough sets with other techniques like inductive logic programming [MK00] or fuzzy sets [Wyg89,DP92]; extensions to the basic rough set formalism using different types of indiscernibility relations and more general definitions of upper and lower approximations [YL96,SS96,Zia93]; construction of software tools for data mining based on rough sets methods [ØK97]; application of rough set techniques to real problems [KØ99,MK02,ZF02].…”

Section: Problem Formulationmentioning

confidence: 99%

A Framework for Reasoning with Rough Sets

Vitória

2005

Transactions on Rough Sets IV

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Rough sets framework has two appealing aspects. First, it is a mathematical approach to deal with vague concepts. Second, rough set techniques can be used in data analysis to find patterns hidden in the data. The number of applications of rough sets to practical problems in different fields demonstrates the increasing interest in this framework and its applicability.Most of the current rough sets techniques and software systems based on them only consider rough sets defined explicitly by concrete examples given in tabular form. The previous research mostly disregards the following two problems. The first problem is related with how to define rough sets in terms of other rough sets. The second problem is related with how to incorporate domain or expert knowledge.This thesis 1 proposes a language that caters for implicit definitions of rough sets obtained by combining different regions of other rough sets. In this way, concept approximations can be derived by taking into account domain knowledge. A declarative semantics for the language is also discussed. It is then shown that programs in the proposed language can be compiled to extended logic programs under the paraconsistent stable model semantics. The equivalence between the declarative semantics of the language and the declarative semantics of the compiled programs is proved. This transformation provides the computational basis for implementing our ideas. A query language for retrieving information about the concepts represented through the defined rough sets is also defined. Several motivating applications are described. Finally, an extension of the proposed language with numerical measures is discussed. This extension is motivated by the fact that numerical measures are an important aspect in data mining applications.

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“…Singleton lower and upper approximations were studied in [8,9,16,18,19]. Note that similar three definitions of lower and upper approximations, though not for incomplete decision tables, were studied in [10][11][12][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Local and Global Approximations for Incomplete Data

Grzymała-Busse

Rząsa

2006

Lecture Notes in Computer Science

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Abstract. For completely specified decision tables, where lower and upper approximations are unique, the lower approximation is the largest definable set contained in the approximated set X and the upper approximation of X is the smallest definable set containing X. For incomplete decision tables the existing definitions of upper approximations provide sets that, in general, are not minimal definable sets. The same is true for approximations based on relations that are generalizations of the equivalence relation. In this paper we introduce two definitions of approximations, local and global, such that the corresponding upper approximations are minimal. Local approximations are more precise than global approximations. Global lower approximations may be determined by a polynomial algorithm. However, algorithms to find both local approximations and global upper approximations are NP-hard.

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Generalization of Rough Sets using Modal Logics

Cited by 421 publications

References 6 publications

Possibilistic vs. Relational Semantics for Logics of Incomplete Information

Possibilistic vs. Relational Semantics for Logics of Incomplete Information

A Framework for Reasoning with Rough Sets

Local and Global Approximations for Incomplete Data

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