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Author, Editor
Author(s):
Hustadt, Ullrich
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Editor(s):
Bürckert, Hans-Jürgen
Nutt, Werner
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BibTeX cite key*:
Hustadt93b
Title, Booktitle
Title*:
Automated Support for the Development of Non-classical Logics
Booktitle*:
Workshop: Modellierung epistemischer Propositionen, KI '93
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Language:
English
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Event Start Date:
17 September 2019
Event End Date:
17 September 2019
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URL:
Address*:
Berlin
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Volume:
Number:
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Pages:
Year*:
1993
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Note, Abstract, ©
Note:
To appear as Research Report of DFKI
(LaTeX) Abstract:
The most natural means for specifying a non-classical logic is by means of a Hilbert calculus. Usually, the semantics of a non-classical logic is given in terms of possible worlds. Given an axiomatization of a non-classical logics, the {\em correspondence problem} in these logics is to find for every given Hilbert axiom an equivalent property of the accessibility relation (van Benthem (1984)). For mechanizing deduction in non-classical logics it is very important to find these correspondences (Ohlbach (1991)). So far the method for finding the correspondences was mostly by intuition and the verification required complex proofs (van Benthem (1984)). SCAN is an algorithm which offers a method for computing the correspondences fully automatically. Moreover, since SCAN preserves equivalences, the computed correspondence axioms are {\em guaranteed to be complete} in the sense that a formula is derivable in the Hilbert calculus if and only if it is valid in the frames which are models
of the computed correspondence axiom. In this paper we present the SCAN algorithm and an application of it to the problem of collapsing modalities in multi-modal logics: Given a Hilbert calculus for modalities $\Box_{m_1}$ and $\Box_{m_2}$ we have to ensure that $$\Box_{m_1} P \Leftrightarrow \Box_{m_2} P$$ doesn't hold for all formulae $P$, because this is in general an unwanted consequence of the given axiomatization.
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MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Programming Logics Group
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experts only
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BibTeX Entry:
@INPROCEEDINGS
{
Hustadt93b
,
AUTHOR = {Hustadt, Ullrich},
EDITOR = {B{\"u}rckert, Hans-J{\"u}rgen and Nutt, Werner},
TITLE = {Automated Support for the Development of Non-classical Logics},
BOOKTITLE = {Workshop: Modellierung epistemischer Propositionen, KI '93},
YEAR = {1993},
ADDRESS = {Berlin},
NOTE = {To appear as Research Report of DFKI},
}
Entry last modified by Uwe Brahm/MPII/DE, 03/12/2010
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Editor(s)
Uwe Brahm
Created
01/14/1995 06:52:04 PM
Revisions
2.
1.
0.
Editor(s)
Uwe Brahm/MPII/DE
Uwe Brahm/MPII/DE
Uwe Brahm/MPII/DE
Edit Dates
21/01/95 20:52:29
17/01/95 20:44:32
14/01/95 19:00:53