
Authors:
Pilar DELLUNDE i CLAVE
Title:A finitary Iequivalential logic not finitely equivalential
Pages:120122
File:bibtex
Abstract ( + )
In this paper I give a solution to the following problem: Is there a finitary 1equivalential logic that is not finitely equivalential?

Authors:
Josep Maria FONT and Ramon JANSANA
Title:Full models for sentential logic
Pages:123131
File:bibtex
Abstract ( + )
In this note we survey the definition and main properties of the notion of full model of a sentential logic; this notion is a generalization of the wellknown one of matrix model of a sentential logic, and provides us with a novel definition of the algebraic counterpart of a sentential logic which works reasonably well in general, even where the semantics obtained from reduced matrices shows its limitations. The material has been extracted from the monograph: J. M. Font and R. Jansana, A General Algebraic Semantics for Sentential Logics, Manuscript, 1994.

Authors:
Javier Vilanova ARIAS
Title:A possible world semantics for conditional logic based on similarity relations
Pages:132139
File:bibtex
Abstract ( + )
In the paper I present and discuss a development of Lewis comparative similarity semantics for conditional logic based on a material or algorithmic definition of the similarity relation between possible worlds. Four conditionals are defined: conceptual, physical, actual and contingent implication, the first, second and third corresponding to Lewis' VW logic, the last one to Lewis' VC logic.

Authors:
Grzegorz MALINOWSKI
Title:Manyvalued referential matrices
Pages:140146
File:bibtex
Abstract ( + )
The research program iniciated by the possible worlds semantics gave several constructions in which logical values of truth ad falsity are associated with points of reference and sentences. Since the pioneering work by Kripke several attempts have been made to get general rules of producing this kind of semantics. An important step in this direction was made by Wojcicki, who defined matrices having functions from a set of indices into {0,1} as elements. The scope of referential semantics built then in the way accepted in the theory of logical calculi was limited to those structural consequence operations C for which the socalled Cequivalence and Ccongruence coincide, i.e. for selfextensional logics. Referential matrices found applications and were subsequently generalised for the whole class of propositional logics. The recent presentation in Wojcicki's Theory of Logical Calculi shows how referential matrices are related to frames and possible worlds paradigm. In the paper we define some natural manyvalued extension of the concepts of referential matrix and semantics inspired by Rosser and Turquette's formalisation of a class of finitevalued propositional calculi.

Authors:
Judit MADARASZ
Title:The Craig Interpolation Theorem in multimodal logics
Pages:147154
File:bibtex
Abstract ( + )
Interpolation Theorem in multimodal logics Maksimova proved that a normal modal logic (with one unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. (These notions will be recalled below.) In this paper we extend Maksimova's theorem to normal multimodal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multimodal logics with modalities of ranks smaller than 2.

Authors:
Antonio M.SETTE and Elias H.ALVES
Title:On the equivalence between two systems of paraconsistent logic
Pages:155157
File:bibtex
Abstract ( + )
[Abstract]

Authors:
Ildiko SAIN and Istvan NEMETI
Title:Fork algebras in usual and in nonwellfounded set theories. Part I
Pages:158168
File:bibtex
Abstract ( + )
Due to their high expressive power and applicability in computer science, fork algebras have intensively been studied lately. In particular, they have been fruitfully applied e.g. in the theory of programming (specification, semantics etc.). The literature of fork algebras has been alive and active for at least five years by now. Here, among others, we look at various possible choices for the concrete class that could play the role of set or proper fork algebras in a representation theorem.

Authors:
Andrzej INDRZEJCZAK
Title:A note concerning belief logic
Pages:169172
File:bibtex
Abstract ( + )
Professor Tokarz presents four propositional logics of belief operator. Each of them is characterized axiomatically and by algebraic semantics, then proofs of (weak) completeness are provided. However the proofs of soundness are omitted. It should be explained since one of them (LIB) is not in fact sound with respect to its semantics. The aim of this note is to correct this little error. In addition we make some rather obvious remarks concerning the relations of these logics with their alethic modal counterparts.

Authors:
Jacek GEISLER
Title:Classical theories in strong negation logic
Pages:173177
File:bibtex
Abstract ( + )
In the paper a sentential calculus based on Hilbert's positive logic is considered. In the calculus the connective of negation is projected as stronger than the intuitionistic one. Axiomatics and semantics with adequacy theorem are provided. It is shown that every theory of Strong Negation Logic whose axiomatics contains at least one sentence of the form notp is a classical one.

Authors:
Jacek GEISLER
Title:Note on "Conditional negation on the positive logic"
Pages:178178
File:bibtex
Abstract ( + )
[Abstract]