Titlebook: Logic and Its Applications; 10th Indian Conferen Mohua Banerjee,A. V. Sreejith Conference proceedings 2023 The Editor(s) (if applicable) an

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978-3-031-26688-1The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Logic and Its Applications978-3-031-26689-8Series ISSN 0302-9743 Series E-ISSN 1611-3349

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,Relational Semantics for Normal Topological Quasi-Boolean Logic,This work introduces modal logics for varieties of normal topological quasi-Boolean algebras. Relational semantics for these modal logics using involutive frames are established. A discrete duality is given for involutive frames and normal topological quasi-Boolean algebras. Some results on Kripke-completeness and finite model property are given.

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,Modal Logic of Generalized Separated Topological Spaces,nterpret . as the derived set operator in a topological space, the class of all .-spaces is .-defined by the modal formula ., and we show that . is the .-logic of all .-spaces. For ., the class of all .-spaces is not .-definable.

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,Labelled Calculi for the Logics of Rough Concepts,re the labels are atomic formulas of the first order language of ., i.e., relational structures based on formal contexts which provide complete semantics for these logics. We also extend these calculi to provide a proof system for the logic of ..