http://hdl.handle.net/11089/20688 Sat, 04 Apr 2026 23:33:08 GMT 2026-04-04T23:33:08Z https://dspace.uni.lodz.pl:443/bitstream/id/13b31de3-8551-48f6-b493-8eaafb7a9c69/ http://hdl.handle.net/11089/20688 http://hdl.handle.net/11089/21628 Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus Indrzejczak, Andrzej In the paper a decision procedure for S5 is presented which uses a cut-free sequent calculus with additional rules allowing a reduction to normal modal forms. It utilizes the fact that in S5 every formula is equivalent to some 1-degree formula, i.e. a modally-flat formula with modal functors having only boolean formulas in its scope. In contrast to many sequent calculi (SC) for S5 the presented system does not introduce any extra devices. Thus it is a standard version of SC but with some additional simple rewrite rules. The procedure combines the proces of saturation of sequents with reduction of their elements to some normal modal form. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/11089/21628 2016-01-01T00:00:00Z http://hdl.handle.net/11089/21627 Categorical Abstract Logic: Hidden Multi-Sorted Logics as Multi-Term Institutions Voutsadakis, George Babenyshev and Martins proved that two hidden multi-sorted deductive systems are deductively equivalent if and only if there exists an isomorphism between their corresponding lattices of theories that commutes with substitutions. We show that the -institutions corresponding to the hidden multi-sorted deductive systems studied by Babenyshev and Martins satisfy the multi-term condition of Gil-Férez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of Gil-Férez pertaining to arbitrary multi-term -institutions. The approach places hidden multi-sorted deductive systems in a more general framework and bypasses the laborious reuse of well-known proof techniques from traditional abstract algebraic logic by using “off the shelf” tools. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/11089/21627 2016-01-01T00:00:00Z http://hdl.handle.net/11089/21626 A 2-set-up Routley-Meyer Semantics for the 4-valued Relevant Logic E4 Robles, Gemma; López, Sandra M.; Blanco, José M.; Recio, Marcos M.; Paradela, Jesús R. The logic BN4 can be considered as the 4-valued logic of the relevant conditional and the logic E4, as the 4-valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2-set-up Routley-Meyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/11089/21626 2016-01-01T00:00:00Z http://hdl.handle.net/11089/21625 Axiomatization of a Basic Logic of Logical Bilattices Takano, Mitio A sequential axiomatization is given for the 16-valued logic that has been proposed by Shramko-Wansing (J Philos Logic 34:121–153, 2005) as a candidate for the basic logic of logical bilattices. Fri, 01 Jan 2016 00:00:00 GMT http://hdl.handle.net/11089/21625 2016-01-01T00:00:00Z