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Author, Editor(s)

Author(s):

Ohlbach, Hans Jürgen
Schmidt, Renate A.

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BibTeX cite key*:

OhlbachSchmidt97

Title

Title*:

Functional Translation and Second-Order Frame Properties of Modal Logics

Journal

Journal Title*:

Journal of Logic and Computation

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Language:

English

Publisher

Publisher's
Name:

Oxford University Press

Publisher's URL:


Publisher's
Address:


ISSN:

0955-792X

Vol, No, pp, Date

Volume*:

7

Number:

5

Publishing Date:

October 1997

Pages*:

581-603

Number of
VG Pages:


Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:

Also available as Research Report MPI-I-95-2-002

(LaTeX) Abstract:

Normal modal logics can be defined axiomatically as Hilbert systems, or semantically in terms of Kripke's possible
worlds and accessibility relations. Unfortunately there are Hilbert axioms which do not have corresponding
first-order properties for the accessibility relation. For these logics the standard semantics-based theorem proving
techniques, in particular, the relational translation into first-order predicate logic, do not work.
There is an alternative translation, the so-called functional translation, in which the accessibility relations are
replaced by certain terms which intuitively can be seen as functions mapping worlds to accessible worlds. In this
paper we show that from a certain point of view this functional language is more expressive than the relational
language, and that certain second-order frame properties can be mapped to first-order formulae expressed in the
functional language. Moreover, we show how these formulae can be computed automatically from the Hilbert
axioms. This extends the applicability of the functional translation method.

URL for the Abstract:


Categories,
Keywords:

modal logic, functional semantics, transformation to many-sorted logic, correspondence problem, quantifier elimination, theorem proving for non-classical logics

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Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Programming Logics Group

Audience:

experts only

Appearance:

MPII WWW Server, MPG publications list, university publications list, working group publication list, Fachbeirat


BibTeX Entry:

@ARTICLE{OhlbachSchmidt97,
AUTHOR = {Ohlbach, Hans J{\"u}rgen and Schmidt, Renate A.},
TITLE = {Functional Translation and Second-Order Frame Properties of Modal Logics},
JOURNAL = {Journal of Logic and Computation},
PUBLISHER = {Oxford University Press},
YEAR = {1997},
NUMBER = {5},
VOLUME = {7},
PAGES = {581--603},
MONTH = {October},
ISBN = {0955-792X},
NOTE = {Also available as Research Report MPI-I-95-2-002},
}


Entry last modified by Christine Kiesel, 03/12/2010
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Editor(s)
Renate A. Schmidt
Created
11/24/1997 04:34:07 PM
Revisions
3.
2.
1.
0.
Editor(s)
Christine Kiesel
Renate A. Schmidt
Renate A. Schmidt
Renate A. Schmidt
Edit Dates
26/04/99 11:46:51
03/12/97 17:13:47
24/11/97 16:51:01
24/11/97 16:39:09