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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.
Rough set theory, Formal Concept Analysis, Modal logic, Lattice-based logics, Algebras for rough sets, Proper display calculi
Greco, G., Jipsen, P., Manoorkar, K., Palmigiano, A., Tzimoulis, A. (2019). Logics for Rough Concept Analysis. In: Khan, M., Manuel, A. (eds) Logic and Its Applications. ICLA 2019. Lecture Notes in Computer Science(), vol 11600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58771-3_14
This is a pre-copy-editing, author-produced PDF of a chapter accepted for publication in Md. Aquil Khan and Amaldev Manuel (Eds.), Logic and Its Applications (Lecture Notes in Computer Science series), 8th Indian Conference, ICLA 2019, Delhi, India, March 1-5, 2019, Proceedings. The final publication may differ and is available at Springer via https://doi.org/10.1007/978-3-662-58771-3_14.