Vortrag - Termin HEUTE

[Maria Cherry]

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Date: Wed, 09 Dec 1998 12:24:42 +0100
From: Elfriede Nedoma <elfi@kr.tuwien.ac.at>
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Subject: Vortrag - Termin HEUTE
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Sehr geehrte Damen und Herren,

bitte beachten Sie, dass der fuer 16.12.1998 angekuendigte Vortrag von
Dr. Costas Koutras bereits HEUTE um 17:00h im Seminarraum 184/3,
Treitlstrasse 3, 4. Stock
stattfindet.

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Dr. Costas Koutras, National Technical University Athens
MODAL NON-MONOTONIC REASONING IN FITTING'S MANY-VALUED LOGICS

In the early '90s, M. Fitting introduced a mathematically
interesting family of normal many-valued modal logics
(Fund. Inf. 15(2) & 17(1,2), Studia Logica 55(1)).
These logics generalize the classical two-valued paradigm,
employ finite Heyting Algebras for the space of truth values
and correspond to Kripke possible-worlds models with
many-valued accessibility relations. In a subsequents paper
(LFCS-92), M. Fitting proposed a non-monotonic extension of
these logics in the McDermott-Doyle fashion, employing sets of
sequents as epistemic states. Also, a family of autoepistemic
logics in R. Moore's style can be naturally defined this way,
and the same holds for Schwarz's reflexive autoepistemic logic.

In this talk, I will present a series of results in this formal
framework for modal non-monotonic reasoning. Firstly, I will
discuss MV-stable sets, which emerge as a sequential many-valued
analog of Stalnaker-Moore stable sets, with an emphasis on their
epistemic properties. It will be shown that the choice of
sequential belief sets allows us to retain some attractive
classical properties but leads also to a partial failure of
their relation to universal Kripke models. Further, the issue
of their closure under modal consequence will be discussed,
as this issue is associated to important philosophical
aspects of modal NM logics. It will be shown that MV-stable sets
are closed under S4 consequence. Beyond S4,  three conditions
will be given for capturing axioms of negative introspection,
either by placing conditions on the epistemic state or by
restricting the underlying space of truth values.

Finally, I will show that in the class of logics based on linear
Heyting algebras, the situation is surprisingly similar to the
machinery devised by Marek, Schwarz & Truszczynski.  In
particular,  the normal fragments of the two important classical
ranges of modal NML remain intact : many-valued autoepistemic
logic is captured by any non-monotonic logic in K5-KD45  and
many-valued reflexive autoepistemic logic corresponds to KTw5-Sw5.

The results that I will present in this talk are jointly worked
with G. Koletsos (NTUA) and S. Zachos (CUNY).


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Elfriede Nedoma
Technische Universitaet Wien
Institut fuer Informationssysteme       Tel.: 0043-1-58801 18405
Abt. Wissensbasierte Systeme 184/3      Fax.: 0043-1-58801 18493
Treitlstrasse 3, A-1040 Wien            e-mail:elfi@kr.tuwien.ac.at
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