This is the programme of the Session of the Polish Association for Logic and
Philosophy of Science, held in Warszawa (Warsaw, PL), November 14, 1997.

Each item of the programme is accopmanied by the corresponding abstract.

=======================================================================

Wendy MacCaull, Department of Mathematics, St. Francis Xavier University,
Antigonish, Kanada: Relational tableaux for tree models, language models and
information networks

Abstract: A tableaux-style proof calculus is given for formalisms for finite
tree models, which rests on an Orlowska-style relational semantics for
nonassociative Lambek calculus (see [1]).  By studying such finite tree
models, we work toward finding a proof calculus for Moortgat and Oehrle's
system for categorial grammar which treats the linguistic phenomena of
headedness and discontinuous constituency (see [2]).  This proof system may
be extended to deal with the full spectrum of substructural logics. 
Modifications to provide a deduction method for Barwise's logic of
information flow, a calculus which models perfect reasoning about the flow
of information through an information network, are outlined.  The
relationship of the Orlowska-style relational semantics to other relational
semantics (such as the arrow logics of van Benthem, Venema and Vakarelov,
and the gaggle theory of Dunn) is clarified.  Some comparisons to Gabbay's
labelled deduction method are made.  This work is part of the general
program to find effective, modular proof systems for nonclassical logics,
based on relational semantics.

[1] Wendy MacCaull, Relational tableaux for tree models, language models and
information networks, submitted.

[2] Yde Venema, Tree models and (labeled) categorial grammar, Journal of
Logic Language and Information, 5 (1996) 253-277.

=========================================================================== 

Wojciech Buszkowski, Instytut Matematyki, Uniwersytet Adama Mickiewicza,
Poznan: 
On models of the Lambek calculus: new representation and completeness
theorems. 
Abstract: We discuss different models for the Lambek calculus and its
variants: residuated semigroups and monoids, algebras of relations,
relational frames, powerset frames and others. We describe a general method
of proving representation theorems concerning these frames by means of a
canonical model construction. We also briefly discuss other methods of
proofs for representation and completeness theorems in this area.

=======================================================================

Grzegorz Malinowski, Zaklad Logiki, Uniwersytet Lodzki:
Referential and Inferential Many-Valuedness

Abstract: Within the framework of Tarski's structural consequence and its
matrix characterisation we discern between the two kinds of referential
many-valuedness - tautological and relational. Next, accepting Suszko's
thesis on logical two-valuedness of any logical construction thus received,
we show a way out to get inferential many-valuedness.

======================================================================

Andrzej Szalas, Instytut Informatyki, Uniwersytet Warszawski:
Quantifier Elimination for Second--Order Predicate Logic
(talk based on the paper by A. Nonnengart, H-J. Ohlbach, A. Szalas;
to appear in Logic, Language and Reasoning, Essays in Honor of Dov 
Gabbay, Part I).

Abstract: In 1935 Wilhelm Ackermann published a paper describing two
algorithms for eliminating existentially quantified predicate symbols. If
the algorithm succeeds, the result is a first-order formula equivalent to
the original second-order formula. These algorithms have been improved by
the authors and Dov Gabbay and new approaches have been developed and
implemented. Applications of these algorithms are in particular the
computation of first--order circuscription and the computation of
correspondence properties for Hilbert axioms in non-classical logics. During
the talk we will give an overview over the various approaches and their
applications.

============================================================================ 

John Cantwell, Department of Philosophy, Uppsala University, Sweden:
Resolving conflicting information - a qualitative approach.

Abstract: Different sources of information may supply conflicting
information.  It turns out that even given an order of trustworthiness on
sources, it is a non-trivial exercise to resolve all kinds of conflict that
may arise. In the talk I will propose a method that settles conflicts in the
general case where there are arbitrarily many sources that have supplied
arbitrarily many, possibly conflicting, pieces of information. All that will
be assumed is that there is a very weak ordering on sets of sources. It will
be shown how the method generates structures well-known in the literature on
non-monotonic logic and belief revision.

============================================================================