
Authors:
Julia V. BEZGACHEVA
Title:Admissible rules for temporal logic LinTGrz
Pages:6066
File:bibtex
Abstract ( + )
Now temporal logics are working inside different well known formal systems and also are in stage of developing for certain new temporal systems. This temporal systems have to satisfy following properties: to be directed, to be uniform, to be linear, to be infinite (in a sense). We deal with modal temporal logic which has two modalities and correspondently two binary accessibility relations L and R. The temporal configuration consists of two basic components. The first one is a linear temporal frame (W,<) whose points are treated as some temporal events. The second one is a valuation, namely, we associate a set of assertions with each point of this frame, representing what is true at that point. Our research concerns questions of recognizing admissible inference rules for the given temporal logic. The question of admissibility for inference rules is studied for different modal systems.

Authors:
Anna WOJTOWICZ
Title:The interpolation, Halldencompleteness, Robinson and Beth properties in modal logics
Pages:6772
File:bibtex
Abstract ( + )
Halldencompleteness, Robinson and Beth properties in modal logics In this article the connections between the interpolation, Halldencompleteness, Robinson and Beth properties for sentential and corresponding firstorder logics are considered. In particular it will be shown that Gabbay's corollary (formulated in Craig's interpolation theorem for modal logic, Lecture Notes in Mathematics 255 (1972)) about the interpolation property in certain firstorder modal logics is false.

Authors:
Stephane DEMRI
Title:Extensions of modal logic S5 preserving NPcompleteness
Pages:7384
File:bibtex
Abstract ( + )
We present a family of multimodal logics having NPcomplete satisfiability problems and admitting in the language S5like modal operators, common knowledge and distributed knowledge operators. Our motivation is to find out interaction conditions between the modal operators that affect the computational complexity of the logics.

Authors:
Ivan CHAJDA and Ewa GRACZYNSKA
Title:Jonsson's lemma for regular and nilpotent shifts of pseudovarieties
Pages:8593
File:bibtex
Abstract ( + )
We deal with varieties and pseudovarieties of universal algebras, in the sense of B. Birkhoff as well as S. Eilenberg i.e. classes of (finite) algebras closed under the formation of subalgebras, homomorphic images and (finite) direct products. Our aim is to present a variation on Jonsson's Lemma for normal and regular shifts of varieties (pseudovarieties).

Authors:
Zbigniew STACHNIAK
Title:On minimal resolution proof for resolution logics
Pages:94101
File:bibtex
Abstract ( + )
In this paper we describe a class of resolution logics P of vdegrees bounded by the cardinality of a smallest matrix that defines the same inconsistent sets of formulas as P. This class includes, among other logical calculi, all finitelyvalued logics of Lukasiewicz and Post. Only propositional logics are discussed in this paper. Some familiarity with matrix semantics is assumed.

Authors:
Marek NOWAK
Title:A general approach to the algebras of unary functions in a Boolean semantics for natural language
Pages:102108
File:bibtex
Abstract ( + )
The aim of this note is to show that most of the algebraic results (including the most important ones) concerning the restricting as well as negatively restricting functions follows from a general method based on some application of Birkhoff theorem on isomorphism of an algebra and a subdirect product of its quotient algebras.