
Authors:
Katsumi SASAKI
Title:The disjunction property of the logics with axioms of only one variable
Pages:4046
File:bibtex
Abstract ( + )
The logics treated here are the intermediate propositional logics of the form LJ+N(i)(a), where N(i)(a)'s are axioms of only one variable studied by Nishimura. As is easily seen, the problem of the disjunction property of LJ+N(i)(a) starts from i=10 and the case of odd i can be trivially neglected. The case of i=10 was solved by Kreisel and Putnam and other cases except i=14 were solved by Anderson. Finally Wronski proved that the logics LJ+N(i)(a) (i=10,12,14,...) have the disjunction property.

Authors:
Kazimierz SWIRYDOWICZ
Title:Regular modal logics inconsistent if LT is added: a contribution to the topography of the lattice of modal logics
Pages:4754
File:bibtex
Abstract ( + )
G.E. Hughes and M.J. Cresswell divided the class of all modal logics into two classes: a class of logics which are closed under the Rule of Necessity (RN) and a class of logics which are not closed under this rule. A special class forms these logics not closed under RN which are inconsistent if LT is added to them. Below we present a preliminary description of regular logics which have this property. We characterize their place in the lattice of all regular modal logics and their connections wit

Authors:
Szabolcs MIKULAS
Title:The completeness of the Lambek calculus with respect to relational semantics
Pages:5566
File:bibtex
Abstract ( + )
Johan van Benthem introduces Relational Semantics (RelSem for short), and states Soundness Theorem for Lambek Calculus w.r.t. RelSem. After doing this, he writes: ``it would be very interesting to have the converse too'', i.e. to have Completeness Theorem. In the following, we state Strong Completeness Theorems for different versions of LC.

Authors:
Richard SYLVAN
Title:Blending semantics for "if" as a oneplace nonassertive with semantics for the conditional
Pages:6771
File:bibtex
Abstract ( + )
[Abstract]

Authors:
Ewa GRACZYNSKA
Title:EIS for nilpotent shifts of varieties
Pages:7278
File:bibtex
Abstract ( + )
In the paper we prove that the operation N preserves the EISproperty for varieties of algebras.