BULLETIN OF THE SECTION OF LOGIC

35/1, 2006

TABLE OF CONTENTS


1. Tarek Sayed AHMED, Algebras of Sentences 1-10   [Abstract]   [PDF]
2. Szymon FRANKOWSKI, General approach to many valued Kripke models 11-26   [Abstract]   [PDF]
3. Szymon FRANKOWSKI, Definable classes of many valued Kripke frames 27-36   [Abstract]   [PDF]
4. Joanna GRYGIEL, Weighted Double Skeletons 37-48   [Abstract]   [PDF]
5. Andrei KHRENNIKOV, Andrew SCHUMANN, Logical Approach to p-adic Probabilities 49-57   [Abstract]   [PDF]

ABSTRACTS

1. Tarek Sayed AHMED, Algebras of Sentences In this note we give an interpretation of cylindric algebras as algebras of sentences (rather than formulas) of first order logic. We show that the isomorphism types of such algebras of sentences coincide with the class of neat reducts of cylindric algebras. Also we show how this interpretation sheds light on some recent results. This is done by likening Henkin's Neat Embedding Theorem to his celebrated completeness proof.

2. Szymon FRANKOWSKI, General approach to many valued Kripke models Main investigations concerning Kripke models refer to two valued case. The papers devoted to many-valued modal logics do not contain even elementary theory of appropriate models. This paper provides very general notion of many valued Kripke model for every standard multimodality, and displays the suitable generalizations of the ideas known from the classical case: disjoint sum of Kripke models, bounded morphism (sometimes called p-morphism), bisimulation.

3. Szymon FRANKOWSKI, Definable classes of many valued Kripke frames This paper is a continuation of the paper BSL 35/1/2 and introduces the counterparts of well known notions as frame definability and first order correspondence.

4. Joanna GRYGIEL, Weighted Double Skeletons We introduce a notion of weighted double skeleton of finite distributive lattices, which provides full characterization of the lattices.

5. Andrei KHRENNIKOV and Andrew SCHUMANN, Logical Approach to p-adic Probabilities In this paper we considered a moving from classical logic and Kolmogorov's probability theory to non-classical p-adic valued logic and p-adic valued probability theory. Namely, we defined p-adic valued logic and further we constructed probability space for some ideals on truth values of p-adic valued logic. We proposed also p-adic valued inductive logic. Such a logic was considered for the first time. The main originality of p-adic valued inductive logic consists in the non-classical interpretation of the negation symbol.

BULLETIN OF THE SECTION OF LOGIC