
Authors:
Marek NOWAK
Title:Quasiorders, Tolerance Relations and Corresponding "Partitions"
Pages:6578
File:bibtex
Abstract ( + )
The paper deals with a generalization of the notion of partition for wider classes of binary relations than equivalences: for quasiorders and tolerance relations. The counterpart of partition for the quasiorders is based on a generalization of the notion of equivalence class while it is shown that such a generalization does not work in case of tolerances. Some results from [5] are proved in a much more simple way. The third kind of ``partition" corresponding to tolerances, not occurring in [5], is introduced.

Authors:
Mitio TAKANO
Title:Axiomatization of a Basic Logic of Logical Bilattices
Pages:7992
File:bibtex
Abstract ( + )
A sequential axiomatization is given for the 16valued logic that has been proposed by ShramkoWansing~(J Philos Logic 34:121153, 2005) as a candidate for the basic logic of logical bilattices.

Authors:
Gemma ROBLES, S. M. L OPEZ, J. M. BLANCO, and M. M. RECIO, J. R. PARADELA
Title:A 2setup RoutleyMeyer Semantics for the 4valued Relevant Logic E4
Pages:93110
File:bibtex
Abstract ( + )
The logic BN4 can be considered as the 4valued logic of the relevant conditional and the logic E4, as the 4valued logic of (relevant) entailment. The aim of this paper is to endow E4 with a 2setup RoutleyMeyer semantics. It is proved that E4 is strongly sound and complete w.r.t. this semantics.

Authors:
George VOUTSADAKIS
Title:Categorical Abstract Algebraic Logic: Hidden MultiSorted Logics as MultiTerm πInstitutions
Pages:111124
File:bibtex
Abstract ( + )
Babenyshev and Martins proved that two hidden multisorted 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 πinstitutions corresponding to the hidden multisorted deductive systems studied by Babenyshev and Martins satisfy the multiterm condition of GilFérez. This provides a proof of the result of Babenyshev and Martins by appealing to the general result of GilFérez pertaining to arbitrary multiterm πinstitutions. The approach places hidden multisorted deductive systems in a~more general framework and bypasses the laborious reuse of wellknown proof techniques from traditional abstract algebraic logic by using "off the shelf" tools.

Authors:
Andrzej INDRZEJCZAK
Title:Simple Decision Procedure for S5 in Standard CutFree Sequent Calculus
Pages:125140
File:bibtex
Abstract ( + )
In the paper a decision procedure for S5 is presented which uses a cutfree 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 1degree formula, i.e. a modallyflat 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 process of saturation of sequents with reduction of their elements to some normal modal form.