
Authors:
Tomasz POLACIK
Title:AntiChains, Focuses and Projective Formulas
Pages:112
File:bibtex
Abstract ( + )
We characterize projective formulas in intuitionistic propositional logic in terms of~properties of~subsets of~universal Kripke models they define. The characterization allows us to prove some properties of~the formulas in question.

Authors:
E. CALARADO and Vladimir V.RYBAKOV
Title:Combining Time and Knowledge, Semantic Approach
Pages:1321
File:bibtex
Abstract ( + )
The paper investigates a semantic approach for combining knowledge and time. We introduce a multimodal logic LF containing modalities for knowledge and time in a semantic way, as the set of all Fvalid formulae for a class of special frames F. The main result of our paper is the theorem stating that LT_{K} is decidable and giving a resolving algorithm. The result is proven by using standard tools: filtration, bulldozing and contracting pmorphisms.

Authors:
Tarek Sayed AHMED
Title:A Sufficient and Necessary Condition for Omitting Types
Pages:2327
File:bibtex
Abstract ( + )
The Omitting Types Theorem gives a sufficent condition for a type to be omitted. Here we give a sufficient and necessary condition for a a type to be omitted. Our proof is algebraic via cylindric algebras.

Authors:
Tarek Sayed AHMED
Title:An Independence Result in Algebraic Logic
Pages:2936
File:bibtex
Abstract ( + )
We formulate a statement in Algebraic Logic that turns out to be independent of ZFC. We relate this statement to omitting types for first order logic and variants thereof.

Authors:
A. FIGALLO JR. and A. ZILIANI
Title:Remarks on Hertz Algebras and Implicative Semilattices
Pages:3742
File:bibtex
Abstract ( + )
It is a fact that several authors have accepted as evident that the class of Hilbert algebras with the property that for each pair of elements there exists its infimum are the same as H. Porta's Hertz algebras, H. Curry's implicative semilattices or P. Koehler's Brouwerian semilattices. J. Cirulis pointed out that in some cases this statement has led to incorrect conclusions. After having analyzed such irregularities, we aim to point out that such confusions and inaccuracies are minor and remediable ones and they do not invalidate the importance of the interesting papers they appear in. Besides, we show how such "mistakes" may be simply eliminated.

Authors:
Joao MARCOS
Title:Logics of Essence and Accident
Pages:4356
File:bibtex
Abstract ( + )
We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the nonnormal modal operators of essence and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration.