Logics for rough concept analysis

Conference paper (2019)

Authors

Giuseppe Greco Universiteit Utrecht
Peter Jipsen Chapman University
Krishna Manoorkar Indian Institute of Technology Kanpur
A. Palmigiano Ethics & Philosophy of Technology - TPM , University of Johannesburg
Apostolos Tzimoulis Chapman University
Research Group
Ethics & Philosophy of Technology (TPM) (TU Delft)
Modal logic Proper display calculi Algebras for rough sets Formal Concept Analysis Lattice-based logics Rough set theory
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Published Date

2019

Language

English

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Faculty

Technology, Policy and Management

Department

Values Technology and Innovation

Research Group

Ethics & Philosophy of Technology

Abstract

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.