
Authors:
A.N. RUTSKIY
Title:Decidability of Modal Logics S4+α_{N}, S4+ξ_{N+1} w.r.t. Admissible Inference Rules
Pages:181189
File:bibtex
Abstract ( + )
The paper examines hypotheses concerning decidability w.r.t. admissibility for some special modal logics. We prove decidability w.r.t. admissible rules for the logics S4+ξ_{N+1}, generated by all finite, rooted, reflexive and transitive frames, maximal clusters of which have at most N elements. Moreover there is a proof given for decidability w.r.t. admissible rules for modal logics S4+α_{N}. Their characteristic classes are finite, rooted, reflexive, transitive frames, which have at most N maximal clusters.

Authors:
Zachary ERNST, Branden FITELSON, Kenneth HARRIS and Larry WOS
Title:A Concise Axiomatization of RM_{>}
Pages:191195
File:bibtex
Abstract ( + )
A new axiomatization for the implicational fragment of Dunn's system RM is given. The new axiomatization is considerably more concise than the axiomatization that was previously known. Specifically, we show that the two axioms CCpCpqCpq and CCCCCpqqprCCCCCqppqrr may be replaced with either CCCpCCCqprqrr or CCCCCpqrCqprr. Because the implicational fragment of RM coincides with the implicational fragment of Sobocinski's system S, the new axiomatization provides a concise basis for that system as well.

Authors:
Mariusz URBANSKI
Title:Remarks on Synthetic Tableaux for Classical Propositional Calculus
Pages:195205
File:bibtex
Abstract ( + )
The Synthetic Tableaux Method of proof for Classical Propositional Calculus is outlined. Basic definitions and theorems (including completness theorem) are given.

Authors:
Joanna GRYGIEL
Title:Sumrepresentations of Finite Lattices
Pages:205212
File:bibtex
Abstract ( + )
Every finite lattice can be represented as a Wronski sum of its sumirreducible intervals. We prove that the set of terms describing all possible sumrepresentations of a given lattice K determines uniquely this lattice.

Authors:
Vladimir V.RYBAKOV
Title:A View of Logical Omniscience Problem
Pages:213229
File:bibtex
Abstract ( + )
We consider a mathematical approach to study the logical omniscience problem. First, the property of a formula of being a consequence of a set of formulas is analysed (as it seems to give rise to some subtle problems). Next, we study axiomatic logic systems of agents and their knowledge in the light of the logical omniscience problem. We find necessary and sufficient conditions for an agent to rejoice logical omniscience for several distinct cases of models classes and logical consequences, in particular, for first order logic models and Kripkelike models for logics of knowledge. This conditions show, in particular, how to avoid logical omniscience if we are basing on axiomatic approach to knowledge of agents.