Rough Sets Through Algebraic Logic

Banerjee, Mohua; Chakraborty, Mihir K.

doi:10.3233/fi-1996-283401

Cited by 120 publications

(98 citation statements)

References 10 publications

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“…e.g. [1,18,4,23,24]). Sound and complete sequent calculi have been introduced for the logics naturally associated with some of these classes of algebras [23,24].…”

Section: Introductionmentioning

confidence: 99%

Proper Multi-Type Display Calculi for Rough Algebras

Greco

Liang

Manoorkar

et al. 2019

Electronic Notes in Theoretical Computer Science

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In the present paper, we endow the logics of topological quasi Boolean algebras, topological quasi Boolean algebras 5, intermediate algebras of types 1-3, and pre-rough algebras with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis and applies the principles of the multi-type methodology in the design of display calculi.

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“…e.g. [1,18,4,23,24]). Sound and complete sequent calculi have been introduced for the logics naturally associated with some of these classes of algebras [23,24].…”

Section: Introductionmentioning

confidence: 99%

Proper Multi-Type Display Calculi for Rough Algebras

Greco

Liang

Manoorkar

et al. 2019

Electronic Notes in Theoretical Computer Science

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“…This paper continues a line of investigation started in [9] and aimed at introducing sequent calculi for the logics of varieties of 'rough algebras', introduced and discussed in [1,19]. The 'rough algebras' considered in the present paper are nondistributive (i.e.…”

Section: Introductionmentioning

confidence: 87%

“…(Birkhoff's theorem, main theorem of FCA) Any complete lattice L is isomorphic to the concept lattice P + of some formal context P. An enriched formal context is a tuple F = (P, R , R ) such that P = (A, X, I) is a formal context, and R ⊆ A × X and R ⊆ X × A are I-compatible relations, that is,R (0) [x] (resp. R (0) [a]) and R(1) [a] (resp. R(1) [x]) are Galois-stable for all x ∈ X and a ∈ A.…”

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confidence: 99%

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Logics for Rough Concept Analysis

Greco

Jipsen

Manoorkar

et al. 2019

Logic and Its Applications

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Taking an algebraic perspective on the basic structures of Rough Concept Analysis as the starting point, in this paper we introduce some varieties of lattices expanded with normal modal operators which can be regarded as the natural rough algebra counterparts of certain subclasses of rough formal contexts, and introduce proper display calculi for the logics associated with these varieties which are sound, complete, conservative and with uniform cut elimination and subformula property. These calculi modularly extend the multi-type calculi for rough algebras to a 'nondistributive' (i.e. general lattice-based) setting.

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“…Lower and upper approximations, rough equalities are defined over it and topological algebraic semantics can be formulated over roughly equivalent objects (or subsets of attributes) through extra operations. Duality theorems, proved for pre-rough algebras defined in [14], are specifically for structures relation isomorphic to the approximation space (O, σ). This is also true of the representation results in [15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Generalized Ideals and Co-granular Rough Sets

Mani

2017

Rough Sets

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Abstract. Lattice-theoretic ideals have been used to define and generate non granular rough approximations over general approximation spaces over the last few years by few authors. The goal of these studies, in relation based rough sets, have been to obtain nice properties comparable to those of classical rough approximations. In this research paper, these ideas are generalized in a severe way by the present author and associated semantic features are investigated by her. Granules are used in the construction of approximations in implicit ways and so a concept of co-granularity is introduced. Knowledge interpretation associable with the approaches is also investigated. This research will be of relevance for a number of logico-algebraic approaches to rough sets that proceed from point-wise definitions of approximations and also for using alternative approximations in spatial mereological contexts involving actual contact relations. The antichain based semantics invented in earlier papers by the present author also applies to the contexts considered.

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Rough Sets Through Algebraic Logic

Cited by 120 publications

References 10 publications

Proper Multi-Type Display Calculi for Rough Algebras

Proper Multi-Type Display Calculi for Rough Algebras

Logics for Rough Concept Analysis

Generalized Ideals and Co-granular Rough Sets

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