
Authors:
Tarek Sayed AHMED
Title:A Confirmation of a Conjecture of Tarski
Pages:103105
File:bibtex
Abstract ( + )
We confirm a conjecture of Tarski on cylindric algebra.

Authors:
Janis CIRULIS
Title:(H)Hilbert Algebras are not same as Hertz Algebras
Pages:107108
File:bibtex
Abstract ( + )
We show by an counterexample that a popular axiom system for Hertz algebras and the main theorem are not correct.

Authors:
Mladen VUKOVIC
Title:A Note on Semantics of the Interpretability Logic IL(KW1)
Pages:109115
File:bibtex
Abstract ( + )
We define a class of generalized Veltman models and prove soundness of the interpretability logic IL(KW1) with respect that class.

Authors:
Tarek Sayed AHMED
Title:Omitting Types for Finite Variable Fragments of First Order Logic
Pages:117122
File:bibtex
Abstract ( + )
We give yet another novel application of algebraic logic to first order logic. Using a construction of Andreka for relation algebras, we show that the classical HenkinOrey Omitting Types Theorem fails for the finite variable fragments of first order logic in a rather strong sense as long as the number of variables available are >2.

Authors:
Norihiro KAMIDE
Title:A Simplified Semantics for a Fragment of Intuitionistic Linear Logic
Pages:123129
File:bibtex
Abstract ( + )
We introduce a simplified Kripke type semantics for the {I,>,*,!,1}fragment of intuitionistic linear logic, and prove a completeness theorem with respect to the semantics by using a simple and intuitive canonical model.

Authors:
Larry WOS, Dolph ULRICH and Branden FITELSON
Title:XCB, the Last of the Shortest Single Axioms for the Classical Equivalential Calculus
Pages:131136
File:bibtex
Abstract ( + )
It has long been an open question whether the formula CB = EpEEEpqErqr is, with the rules of substitution and detachment, a single axiom for the classical equivalential calculus. This paper answers that question affirmatively, thus completing a search for all such elevensymbol single axioms that began seventy years ago.

Authors:
Alexej P. PYNKO
Title:A Cutfree Gentzen Calculus with Subformula Property for Firstdegree Entailments in LC
Pages:137146
File:bibtex
Abstract ( + )
In this paper, we introduce and study a multipleconclusion cutfree propositional Gentzen calculus with subformula property for firstdegree entailments in Dummett's linear intermediate logic LC that is obtained from Gentzen's propositional calculus LK by restricting the rules of introduction of negation to the right side of sequents by allowing their right side formulas to be negations of formulas alone. By a method that adopts some ideas underlying Schutte's reduction method for the Cutfree version of Gentzen's predicate calculus LK, we prove that a sequent is derivable in the calculus under consideration iff it is valid in the threeelement chain Stone algebra. As a consequence, we show that our calculus does axiomatize firstdegree entailments in Dummett's linear intermediate logic and that Cut is permissible in the calculus involved.

Authors:
Piotr LUKOWSKI
Title:Reductive Techniques in Proofs of the Completeness Theorems for the Normal Bimodal Systems
Pages:147159
File:bibtex
Abstract ( + )
The aim of the paper is to consider the modal systems in which the modalities are not mutually defined. To prove the completeness theorems for such systems one can apply the well known techniques, the proofs herein are standard. We intend to throw a new light on the topic applying techniques typical for reductive logic. They can be considered as a good example for the unity of the deductive and the reductive parts of the logic of truth and of falsehood.