| 1. Julia V. BEZGACHEVA, Admissible rules for temporal logic LinTGrz | 60 [Abstract] [PDF] |
| 2. Anna WOJTOWICZ, The interpolation, Hallden-completeness, Robinson and Beth properties in modal logics | 67 [Abstract] [PDF] |
| 3. Stephane DEMRI, Extensions of modal logic S5 preserving NP-completeness | 73 [Abstract] [PDF] |
| 4. Ivan CHAJDA and Ewa GRACZYNSKA, Jonsson's lemma for regular and nilpotent shifts of pseudovarieties | 85 [Abstract] [PDF] |
| 5. Zbigniew STACHNIAK, On minimal resolution proof for resolution logics | 94 [Abstract] [PDF] |
| 6. Marek NOWAK, A general approach to the algebras of unary functions in a Boolean semantics for natural language | 102 [Abstract] [PDF] |
1. Julia V. BEZGACHEVA, Admissible rules for
temporal logic LinTGrz
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.
2. Anna WOJTOWICZ, The interpolation,
Hallden-completeness, Robinson and Beth properties in modal logics
In this article the connections between the interpolation, Hallden-completeness,
Robinson and Beth properties for sentential and corresponding first-order 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
first-order modal logics is false.
3. Stephane DEMRI, Extensions of modal
logic S5 preserving NP-completeness
We present a family of multi-modal logics having NP-complete satisfiability problems
and admitting in the language S5-like 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.
4. Ivan CHAJDA and Ewa GRACZYNSKA, Jonsson's
lemma for regular and nilpotent shifts of pseudovarieties
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).
5. Zbigniew STACHNIAK, On minimal resolution
proof for resolution logics
In this paper we describe a class of resolution logics P of v-degrees
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 finitely-valued logics of Lukasiewicz and Post. Only
propositional logics are discussed in this paper. Some familiarity with
matrix semantics is assumed.
6. Marek NOWAK, A general approach to the algebras
of unary functions in a Boolean semantics for natural language
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.