
Authors:
Alexander S. KARPENKO and Vladimir M.POPOV
Title:BCKX is the axiomatization of implicational fragment of Lukasiewicz's infinitevalued logic L_{&omega};
Pages:112117
File:bibtex
Abstract ( + )
[Abstract]

Authors:
M.I. GOLOVANOV
Title:Bimodal propositional logic S5_{2}C_{n}
Pages:118125
File:bibtex
Abstract ( + )
In general as a rule case the polymodal logics have more complicate structure comparing tomonomodal logics. Nevertheless sometimes it is possible to obtain rather strong positive results about polymodal logics. For example V. B. Shechtman proved an assertion of general character concerning semantic characterization of polymodal logics, as a corollary, the completeness, finite model property, and decidability of some logics follow. In particular finite model property and decidability for logic S5_{2}C_{1} follows from the mentioned results of V. B. Shechtman. Formerly author studied the inference rules forpolymodal logical system S5_{n}C with commutative modalities. S5_{n}C is the logic with n modalities L1,...,Ln, all of them satisfying the axioms of S5 and the following axioms: LiLj p <=> LjLi p, i,j=1...n. It was proved that the logic S5_{n}C is decidable with respect to admissibility of inference rules, at the same time, among the extensions of S5_{n}C (n>2) there are the logics which are not decidable. The aim of our current paper is to study the family of logics S5_{2}C_{n} which all are contained in S5_{2}C.

Authors:
V.V. RIMATSKIY
Title:Finite bases of admissible inference rules for modal logics of width 2
Pages:126134
File:bibtex
Abstract ( + )
Presented article is devoted to study of inference rules admissible for strong modal logics. We investigate bases for admissible rules. This problem has algebraic analog: if some corresponding quasivariety has finite basis for its quasiidentity. Such basis of inference rules allows to increase deductive ability of logic and solve various connected problems. The main result is the following: Any tabular modal logic of width 2 has finite basis of admissible inference rules.

Authors:
Sergej MARDAEV
Title:Fixed points of modal negative operators
Pages:135138
File:bibtex
Abstract ( + )
In this paper we investigate negative schemes in transitive Kripke models irrespective of the ascending chain condition. We show that not all negative schemes have an unique solution in this case. We present sufficient condition for a negative scheme to have an unique and definable solution in all transitive Kripke models and get an immediate corollary for the modal logic K4.

Authors:
Judit MADARASZ, Istvan NEMETI and Gabor SAGI
Title:On the finitization problem of relation algebras
Pages:139143
File:bibtex
Abstract ( + )
The finitization problem in the title was discussed e.g. by Tarski, Givant, Jonsson, Maddux, Andreka, Biro and others. Roughly, the question is whether we can expand the class RRA of representable relation algebras with new permutation invariant operations such that the expanded version of RRA would become finitely axiomatizable. The problem has an equivalent form which concerns axiomatizability of the nvariable fragment Ln of first order logic. The same question was also formulated for the class RCAn of representable cylindric algebras (of dimension n), n>1. In the present work we present some recent results on the problem.

Authors:
Paulo A.S. VELOSO
Title:Characterisations for fork algebras and their relational reducts
Pages:144155
File:bibtex
Abstract ( + )
We examine some alternative characterisations for fork algebras and their relational reducts. These alternative characterisations come from the consideration of special (pairs of) elements in relational algebras. Their adequacy comes from an analysis of the proof of representability, where it was implicit, as well as from properties of these special pairs of elements. This approach provides interesting insights and leads to (equational) presentations with convenient structures.

Authors:
Greg RESTALL
Title:Paraconsistent logics!
Pages:156163
File:bibtex
Abstract ( + )
Hartley Slater provides an interesting argument against paraconsistent logics. In the paper I will show that Slater's argument need not deter the paraconsistent logician.