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55Rasiowa-Sikorski proof system for the non-Fregean sentential logic SCIJournal of Applied Non-Classical Logics 17 (4). 2007.The non-Fregean logic SCI is obtained from the classical sentential calculus by adding a new identity connective = and axioms which say ?a = ß' means ?a is identical to ß'. We present complete and sound proof system for SCI in the style of Rasiowa-Sikorski. It provides a natural deduction-style method of reasoning for the non-Fregean sentential logic SCI
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374Logic. of Descriptions. A New Approach to the Foundations of Mathematics and ScienceStudies in Logic, Grammar and Rhetoric 27 (40): 63-94. 2012.We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems.
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27Relational Logics and Their ApplicationsIn Harrie de Swart, Ewa Orlowska, Gunther Smith & Marc Roubens (eds.), Theory and Applications of Relational Structures as Knowledge Instruments Ii, Springer. pp. 125. 2006.Logics of binary relations corresponding, among others, to the class RRA of representable relation algebras and the class FRA of full relation algebras are presented together with the proof systems in the style of dual tableaux. Next, the logics are extended with relational constants interpreted as point relations. Applications of these logics to reasoning in non-classical logics are recalled. An example is given of a dual tableau proof of an equation which is RRA-valid, while not RA-valid.