BULLETIN OF THE SECTION OF LOGIC

26/4, 1997

TABLE OF CONTENTS

1. E. A. SIDORENKO, Relevant semantics with binary relation of accessibility 168   [Abstract]   [PDF]
2. Miklos FERENCZI, On inducing cylindrical homomorphism by point function 179   [Abstract]   [PDF]
3. Vladimir L. VASYUKOV, Implicative logics in categories 188   [Abstract]   [PDF]
4. Marek NASIENIEWSKI and Andrzej PIETRUSZCZAK, An elementary proof of equivalence of the conditions in definition of conditionally distributive lattices 193   [Abstract]   [PDF]
5. Paulo A. S. VELOSO, On the independence of the axioms for fork algebras 197   [Abstract]   [PDF]
6. Ewa GRACZYNSKA, G. Birkhoff's theorems for regular varieties 210   [Abstract]   [PDF]
7. Grzegorz MALINOWSKI, Inferential extensions of Lukasiewicz modal logic 220   [Abstract]   [PDF]

ABSTRACTS

1. E. A. SIDORENKO, Relevant semantics with binary relation of accessibility The introduced relational semantics Sea for relevant logic has as reference points two-storeyed worlds. The ground floor of each such a world consists of propositions or its negations (atomic floor) and the first floor consists of formulae (entailment floor). A distinctive peculiarity of the semantics Sea is that any formula cannot be verified (or falsified) in all worlds. And so a formula A is considered as semantically true, iff A is verified in each world, where A->A is verified. Here the Sea semantics is adopted for both well known systems E, R, NR and for the formulated by the author ENR, which formalises Entailment as Necessary Relevant Implication directly.

2. Miklos FERENCZI, On inducing cylindrical homomorphism by point function

3. Vladimir L. VASYUKOV, Implicative logics in categories

4. Marek NASIENIEWSKI and Andrzej PIETRUSZCZAK, An elementary proof of equivalence of the conditions in definition of conditionally distributive lattices

5. Paulo A. S. VELOSO, On the independence of the axioms for fork algebras We establish the independence of the fork axioms by examining their role and presenting expansions of (simple) algebras of relations that falsify each one of these fork equations while satisfying the other axioms. We aslo examine these algebras to obtain further information about the independence of these axioms.

6. Ewa GRACZYNSKA, G. Birkhoff's theorems for regular varieties Our aim is to present a variation of Birkhoff's type theorems for regular varieties, via a suitable notion of regular congruences. This answers a question posed by Prof. Jerzy Plonka.

7. Grzegorz MALINOWSKI, Inferential extensions of Lukasiewicz modal logic Two inferential extensions of the Lukasiewicz system of modal logic are propositional logics based on the so-called q-consequence operation. The main feature of q-consequence is that its rules lead from non-rejected assumptions to accepted conclusions. We present q-consequence and introduce concepts of extensionality and intensionality indistinguishable within the Tarski paradigm of consequence. The q-consequence operations for L-modal system prove to be good experimental range for expressing unorthodox notions of extensionality and intensionality. They also permit to distinguish between the two "indistinguishable connectives of possibility",

BULLETIN OF THE SECTION OF LOGIC