BULLETIN OF THE SECTION OF LOGIC

37/2, 2008

TABLE OF CONTENTS


1. A.V. FIGALLO and C.A. SANZA, The NSnxm-propositional Calculus 67-80   [Abstract]   [PDF]
2. Janusz CIUCIURA, Frontiers of the Discursive Logic 81-92   [Abstract]   [PDF]
3. Christopher STEINSVOLD, Completeness for Various Logics of Essence and Accident 93-102   [Abstract]   [PDF]
4. Tarek Sayed AHMED, Variations on Martin's Axiom and Omitting Types from Algebraic Logic,
    Lattice Theory and Topology 		103-114   [Abstract]  
5. Tarek Sayed AHMED, Classes of Representable Algebras with the Amalgamation property 115-122   [Abstract]   [PDF]
6. Tarek Sayed AHMED, RaCAn is not elementary, for n>4 123-136   [Abstract]   [PDF]

ABSTRACTS

1. A.V. FIGALLO and C.A. SANZA, The NSnxm-propositional Calculus

2. Janusz CIUCIURA, Frontiers of the Discursive Logic In a discussion, the participants state opinions. There is an additional assumption that each opinion (or view) is consistent in itself, but we cannot exclude the possibility that some opinions might be inconsistent with one another. This is the main idea behind Jaskowski's discursive logic D2.
The year of 1977 was one of the crucial points in the development of D2. It was the year when Da Costa, Dubikajtis and Kotas published their papers on the axiomatization of the discursive logic. The axiomatization was recognized, ever since, as a first real axiomatization of D2.
The aim of this paper is to show that the claim is mistaken and next to introduce a correct axiomatization of Jaskowski's D2. We also present a direct (Kripke-type) semantics for the logic and prove some key metatheorems.

3. Christopher STEINSVOLD, Completeness for Various Logics of Essence and Accident In a paper by Marcos (2005, this bulletin) logics of essence and accident (LEA) were presented with a completeness proof for the minimal logic, KEA, corresponding to the modal logic K. Using a different canonical approach, we establish completeness results for various logics. We answer two questions from that paper (an open question and a conjecture (in the affirmative)), by giving completeness proofs for the LEA of the modal logics K4 and T. Moreover, we show S4EA = K4EA, and KTEA = KEA. Also, there is a sentence of the language whose validity corresponds to a frame being weakly connected; this yields completeness for S4.3EA.

4. Tarek Sayed AHMED, Variations on Martin's Axiom and Omitting Types from Algebraic Logic, Lattice Theory and Topology

5. Tarek Sayed AHMED, Classes of Representable Algebras with the Amalgamation property We introduce an abstract class of algebras that is a proper reduct of both Pinter's substitution algebras and cylindric algebras. We show that the class of representable algebras have the amalgamation property.

6. Tarek Sayed AHMED, RaCAn is not elementary, for n>4 We show that the class RaCAn of relation algebras reducts of cylindric algebras of dimension n is not elementary when n>4. This answers a long standing open question in algebraic logic posed by Nemeti and independently by Maddux.

BULLETIN OF THE SECTION OF LOGIC