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31Number of Extensions of Non-Fregean LogicsJournal of Philosophical Logic 34 (2): 193-206. 2005.We show that there are continuum many different extensions of SCI (the basic theory of non-Fregean propositional logic) that lie below WF (the Fregean extension) and are closed under substitution. Moreover, continuum many of them are independent from WB (the Boolean extension), continuum many lie above WB and are independent from WH (the Boolean extension with only two values for the equality relation), and only countably many lie between WH and WF
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42Relational dual tableau decision procedure for modal logic KLogic Journal of the IGPL 20 (4): 747-756. 2012.We present a dual tableau system, RLK, which is itself a deterministic decision procedure verifying validity of K-formulas. The system is constructed in the framework of the original methodology of relational proof systems, determined only by axioms and inference rules, without any external techniques. Furthermore, we describe an implementation of the system RLK in Prolog, and we show some of its advantages.
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32Dual tableau for a multimodal logic for order of magnitude qualitative reasoning with bidirectional negligibilityInternational Journal of Computer Mathematics 86 (10-11). 2009.We present a relational proof system in the style of dual tableaux for the relational logic associated with a multimodal propositional logic for order of magnitude qualitative reasoning with a bidirectional relation of negligibility. We study soundness and completeness of the proof system and we show how it can be used for verification of validity of formulas of the logic.