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Author, Editor(s)

Author(s):

Blackburn, Patrick
Tzakova, Miroslava

dblp
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BibTeX cite key*:

Tzakova98b

Title

Title*:

Hybrid Completeness

Journal

Journal Title*:

Logic Journal of the IGPL

Journal's URL:


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for the article:


Language:

English

Publisher

Publisher's
Name:

Oxford University Press

Publisher's URL:


Publisher's
Address:


ISSN:

1368-9894

Vol, No, pp, Date

Volume*:

6

Number:

4

Publishing Date:

July 1998

Pages*:

625-650

Number of
VG Pages:


Page Start:


Page End:


Sequence Number:


DOI:


Note, Abstract, ©

Note:

Revised Version of MPI-I-97-2-007

(LaTeX) Abstract:

In this paper we discuss two {\em hybrid languages\/}, ${\cal
L}(\forall)$ and ${\cal L}(\downarrow)$, and provide them with complete
axiomatizations. Both languages combine features of modal and
classical logic. Like modal languages, they contain modal operators
and have a Kripke semantics. Unlike modal languages, in these systems
it is possible to `label' states by using $\forall$ and $\downarrow$
to bind special {\em state variables\/}.

This paper explores the consequences of hybridization for
completeness. As we shall show, the challenge is to blend the modal
idea of {\em canonical models\/} with the classical idea of {\em
witnessed\/} maximal consistent sets. The languages ${\cal
L}(\forall)$ and ${\cal L}(\downarrow)$ provide us with two extreme examples
of the issues involved. In the case of ${\cal L}(\forall)$, we can
combine these ideas relatively straightforwardly with the aid of
analogs of the {\em Barcan\/} axioms coupled with a {\em modal theory
of labeling\/}. In the case of ${\cal L}(\downarrow)$, on the other hand,
although we can still formulate a theory of labeling, the Barcan
analogs are not valid. We show how to overcome this difficulty by
using $\mbox{{\it COV}}^{ \ \ast}$, an infinite collection of additional rules of proof
which has been used in a number of investigations of extended modal
logic.

URL for the Abstract:


Categories,
Keywords:

Hybrid Languages, Axiomatic Completeness, Modal Logic

HyperLinks / References / URLs:

http://www.oup.co.uk/igpl/Volume_06/Issue_04/

Copyright Message:


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Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Programming Logics Group

Audience:

experts only

Appearance:

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


BibTeX Entry:

@ARTICLE{Tzakova98b,
AUTHOR = {Blackburn, Patrick and Tzakova, Miroslava},
TITLE = {Hybrid Completeness},
JOURNAL = {Logic Journal of the IGPL},
PUBLISHER = {Oxford University Press},
YEAR = {1998},
NUMBER = {4},
VOLUME = {6},
PAGES = {625--650},
MONTH = {July},
ISBN = {1368-9894},
NOTE = {Revised Version of MPI-I-97-2-007},
}


Entry last modified by Uwe Brahm, 03/12/2010
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Editor(s)
Miroslava Tzakova
Created
01/16/1998 02:42:06 PM
Revisions
12.
11.
10.
9.
8.
Editor(s)
Uwe Brahm
Miroslava Tzakova
Miroslava Tzakova
Miroslava Tzakova
Miroslava Tzakova
Edit Dates
30.03.99 22:29:53
10/10/98 16:38:21
06/10/98 15:14:36
06/10/98 15:06:24
28/06/98 17:06:47