BULLETIN OF THE SECTION OF LOGIC

36/3-4, 2007

TABLE OF CONTENTS


Professor Hiroakira Ono In Honorem

edited by Piotr Lukowski


Professor Hiroakira Ono - picture     [JPEG]
1. PROFESSOR HIROAKIRA ONO IN HONOREM, Piotr Lukowski 99     [PDF]
2. Hiroakira Ono's list of selected publications 103     [PDF]
3. Janusz CZELAKOWSKI, Fregean Logics and the Strong Amalgamation Property 105   [Abstract]   [PDF]
4. Josep Maria FONT, On Substructural Logics Preserving Degrees of Truth 117   [Abstract]   [PDF]
5. Yaroslav SHRAMKO and Heinrich WANSING, Entailment Relations and/as Truth Values 131   [Abstract]   [PDF]
6. Tomasz KOWALSKI, Weakly Associative Relation Algebras Hold the Key to the Universe 145   [Abstract]   [PDF]
7. Andrzej INDRZEJCZAK, Labelled Tableau Calculi for Weak Modal Logics 159   [Abstract]   [PDF]
8. Norihiro KAMIDE, Temporalizing Linear Logic 173   [Abstract]   [PDF]
9. Yutaka MIYAZAKI, Normal Forms for Modal Logics KB and KTB 183   [Abstract]   [PDF]
10. Tadeusz LITAK, The Non-reflexive Counterpart of Grz 195   [Abstract]   [PDF]
11. Piotr LUKOWSKI, Epistemicism and Roy Sorensen Arguments 209   [Abstract]   [PDF]

ABSTRACTS

3. Janusz CZELAKOWSKI, Fregean Logics and the Strong Amalgamation Property The note contains general results concerning the equivalence of the amalgamation and strong amalgamation properties in the context of conjunctive Fregean logics.

4. Josep Maria FONT, On Substructural Logics Preserving Degrees of Truth The purpose of this paper is to discuss how some ideas coming from the many-valued logic world can be introduced in a sensible way into the world of substructural logic; namely, the ideas around what does it mean for a logic to say that it preserves degrees of truth. The two mentioned subject areas are by their origin rather far apart. I would like to exemplify how the recent evolution of research in the field of substructural logics, and the application of central techniques from abstract algebraic logic, has revealed such borderline issues and has facilitated their investigation.

5. Yaroslav SHRAMKO and Heinrich WANSING, Entailment Relations and/as Truth Values It has been emphasized by Hiroakira Ono, Petr Hajek, and other logicians that there exists a close relationship between substructural and many-valued logics. This relationship has many aspects, and in the present paper, we take the prominent substructural logic of first-degree entailment as a starting point for making some observations concerning many-valuedness and entailment.

6. Tomasz KOWALSKI, Weakly Associative Relation Algebras Hold the Key to the Universe Maddux observed a tantalisingly close connection between certain relation algebras and relevant logics R RM. He asks whether this connection amounts to full interpretability. Although unable to answer that question, we prove that a version of positive minimal relevant logic B is fully interpretable in the variety of weakly associative relation algebras.

7. Andrzej INDRZEJCZAK, Labelled Tableau Calculi for Weak Modal Logics Many normal and regular modal logics have simple formalizations in terms of labelled tableaux. But these modal logics have direct characterisation in terms of Kripke frames, and labels are naturally modelled on this kind of semantics. It is an interesting question whether this well known method can be extended to some congruent and monotonic modal logics, which are not characterisable by Kripke frames. Fortunately, they are determined by neighbourhood frames, a kind of more general relational semantics. So the main problem is how to apply the method of labels to cover logics with different interpretation of modalities. After short recollection of basic facts concerning respective modal logics and neighbourhood frames, we will offer analytic tableau calculi for some logics axiomatizable by combinations of axioms D, T, 4, 5 and the rule RN (necessitation) over the weakest congruent logic E and monotonic logic M.

8. Norihiro KAMIDE, Temporalizing Linear Logic Completeness theorem with respect to Kripke semantics is shown for an extended intuitionistic linear logic with linear-time temporal operators.

9. Yutaka MIYAZAKI, Normal Forms for Modal Logics KB and KTB Normal forms for propositional modal logics are used to establish the Kripke completeness, the finite model property, and the decidability for modal logics KB and KTB.

10. Tadeusz LITAK, The Non-reflexive Counterpart of Grz The paper studies the weak Grzegorczyk logic (wGrz). In particular, we discuss the relationship between Grz, GL and wGrz as an interesting example of the relationship between an extension of T, its irreflexive counterpart and its non-reflexive counterpart.

11. Piotr LUKOWSKI, Epistemicism and Roy Sorensen Arguments One of the popular approaches to vagueness is epistemicism, according to which vagueness is not real (it does not occur in reality); it is only a special illusion of our imperfect senses. If we had the entire knowledge, we would know exactly where the (always) sharp border lies between tall and not-tall, rich and not-rich, sweet and not-sweet etc. The logical defence of epistimicism is not an easy task. Of great value there would be all proofs for the existence of distinct (clear-cut) borders between positive and negative extensions of a given vague name or predicate. To this aim thought experiments are undertaken. Roy Sorensen has become a real master of thought experiments especially those disguised in the form of sequence of arguments, often called "proofs". The proofs of Sorensen are especially vital in the discussion devoted to vagueness. They are appreciated and thoroughly discussed. It seems, however, that some of them - alas even the most eminent ones - are not free of logical errors; namely it is petitio principi that appears to be the most frequent error in the Sorensen’s thought experiments.

BULLETIN OF THE SECTION OF LOGIC