| 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] |
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.