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1
Content available remote On Some Issues in the Foundation of Rough Sets : the Problem of Definition
Chakraborty M. K.
Fundamenta Informaticae
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2016
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Vol. 148, nr 1/2
123--132
EN
This paper is concerned with some issues connected with the foundations of rough set theory. Particularly the problem of definition of a rough set is discussed.
2
Content available remote Graded Consequence with Fuzzy Set of Premises
Dutta S., Chakraborty M. K.
Fundamenta Informaticae
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2014
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Vol. 133, nr 1
1--18
EN
Fuzzy Logic a la Pavelka has been reintroduced here in terms of consequence relation instead of consequence operator. Metalogical notions like, consistency and inconsistency are proposed as graded notions. The relationship between consequence relation and inconsistency, both fuzzy here, is studied. Another metalogical notion viz., equivalence of two sets of formulae that originates from Tarski is defined and investigated in this context when the premise is a fuzzy set.
3
Content available remote Rough Sets : Some Foundational Issues
Chakraborty M.K., Banerjee M.
Fundamenta Informaticae
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2013
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Vol. 127, nr 1-4
1--15
EN
The article analyses prevalent definitions of rough sets from the foundational and mathematical perspectives. In particular, the issue of language dependency in the definitions, and implications of the definitions on the issue of vagueness are discussed in detail.
4
Content available remote Rough Dialogue and Implication Lattices
Chakraborty M.K., Banerjee M.
Fundamenta Informaticae
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2007
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Vol. 75, nr 1-4
123-139
EN
A dialogue is an `activity' by a pair of agents to arrive at some kind of understanding over a concept/belief/piece of information etc. represented by a subset (the extension) in some universe of discourse. The universe is partitioned into two different sets of granules (equivalence classes) representing the perceptions of the agents. So, there are two approximation spaces at the beginning. A third approximation space arises out of superimposition of the two partitions. A dialogue is a finite process of gradual enhancement of the two base subsets of the agents, in their `common' approximation space. Through this process, various kinds of overlap may emerge between the two final subsets. A first introduction of the idea of a dialogue in rough context was made in [6]. This paper further develops the notion and focusses upon the study of the above-mentioned overlaps in a systematic manner. Given two sets A and B in an approximation space, there are nine possible inclusion relations among the sets lo(A), A, up(A), lo(B), B and up(B) where lo and up denote the lower and upper approximation operators respectively. There are five resulting equivalence classes and the quotient set forms a lattice by implication ordering. That is, of the nine relations, only five are independent and they form an implication or entailment lattice. Starting with this basic lattice other implication lattices are formed. Relationship of these lattices with the various overlap conditions between the final pair of sets arrived at after a dialogue is studied. Finally, examples are given, one of which relates dialogues in rough context with rough belief revision [3] - in a line similar to the approach of [5].
5
Content available remote Nonmonotonic Proof Systems : Algebraic Foundations
Ghosh S., Chakraborty M.K.
Fundamenta Informaticae
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2004
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Vol. 59, nr 1
39-65
EN
A general framework for the algebraization of a category of nonmonotonic logics has been suggested. This method has been applied to the systems of Gabbay, and to Cumulative, Preferential and Ranked systems. The minimal logics required to serve as the base logics for the above systems are investigated. MAK triples and KLM triples are formed in ways similar to MAK models and KLM models but now on the algebraic structures for the nonmonotonic systems, thereby a new type of semantics is given to these systems.
6
Content available remote A Study of Interconnections Between Rough and 3-Valued Łukasiewicz Logics
Sen J., Chakraborty M.K.
Fundamenta Informaticae
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2002
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Vol. 51, nr 3
311-324
EN
Sequent calculi for topological quasi-Boolean algebras, topological quasi-Boolean algebras without distributivity, pre-rough algebras and Wajsberg algebras have been presented. It is shown that the calculi for the latter two classes of algebras are equivalent. A connection between some logics for the first class of algebras and the linear logic or linear logic with distributivity has been established.
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