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 Author, Editor(s)
 Author(s): Blackburn, Patrick Tzakova, Miroslava dblp dblp
 BibTeX cite key*: Tzakova98b

 Title
 Title*: Hybrid Completeness

 Journal
 Journal Title*: Logic Journal of the IGPL Journal's URL: Download URL 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: 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: Personal Comments: Download Access Level:

 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},
}