MPI-INF Logo
Publications

Server    halma.mpi-inf.mpg.de

Proceedings Article, Paper


@InProceedings
Beitrag in Tagungsband, Workshop
Author, Editor
Author(s):
Sofronie-Stokkermans, Vioricadblp
Editor(s):
Ganzinger, Haralddblp
BibTeX cite key*:
Sofronie-Stokkermans1999-cade
Title, Booktitle
Title*:
On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results
cade-99.pdf (248.45 KB)
Booktitle*:
Proceedings of the 16th International Conference on Automated Deduction (CADE-16)
Event, URLs
Conference URL::
http://www.mpi-sb.mpg.de/cade-16/
Downloading URL:
Event Address*:
Trento, Italy
Language:
English
Event Date*
(no longer used):
July 7-10, 1999
Organization:
Event Start Date:
14 May 2024
Event End Date:
14 May 2024
Publisher
Name*:
Springer
URL:
Address*:
Berlin, Germany
Type:
Vol, No, Year, pp.
Series:
Lecture Notes in Artificial Intelligence
Volume:
1632
Number:
Month:
Pages:
157-171
Year*:
1999
VG Wort Pages:
ISBN/ISSN:
Sequence Number:
DOI:
Note, Abstract, ©
(LaTeX) Abstract:
In this paper we give a method for automated theorem proving in the universal theory of certain varieties of distributive lattices with well-behaved operators. For this purpose, we use extensions of Priestley's representation theorem for distributive lattices. We first establish a link between satisfiability of universal sentences with respect to varieties of distributive lattices with operators and satisfiability with respect to certain classes of relational structures. We then use these results for giving a method for translation to clause form of universal sentences in such varieties, and obtain decidability and complexity results for the universal theory of some such varieties. The advantage is that we avoid the explicit use of the full algebraic structure of such lattices, instead using sets endowed with a reflexive and transitive relation and with additional functions and relations. We first studied this type of relationships in the context of finitely-valued logics and then extended the ideas to more

general non-classical logics. This paper shows that the idea is much more general. In particular, the method presented here subsumes both existing methods for translating modal logics to classical logic and methods for automated theorem proving in finitely-valued logics based on distributive lattices with operators.
URL for the Abstract:
http://link.springer.de/link/service/series/0558/bibs/1632/16320157.htm
Keywords:
Theorem Proving, Lattice Theory, Priestley Duality
HyperLinks / References / URLs:
http://link.springer.de/link/service/series/0558/bibs/1632/16320157.pdf
Copyright Message:
Copyright Springer
Download
Access Level:
Public

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:
@INPROCEEDINGS{Sofronie-Stokkermans1999-cade,
AUTHOR = {Sofronie-Stokkermans, Viorica},
 EDITOR = {Ganzinger, Harald},
 TITLE = {On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results},
 BOOKTITLE = {Proceedings of the 16th International Conference on Automated Deduction (CADE-16)},
 PUBLISHER = {Springer},
 YEAR = {1999},
 VOLUME = {1632},
 PAGES = {157--171},
 SERIES = {Lecture Notes in Artificial Intelligence},
 ADDRESS = {Trento, Italy},
}

Entry last modified by Viorica Sofronie-Stokkermans, 03/12/2010
Hide details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)

Editor(s)
Viorica Sofronie-Stokkermans		Created
04/01/1999 09:17:22 PM
Revisions
8.
7.
6.
5.
4.		Editor(s)
Viorica Sofronie-Stokkermans
Viorica Sofronie-Stokkermans
Viorica Sofronie-Stokkermans
Viorica Sofronie-Stokkermans
Viorica Sofronie-Stokkermans		Edit Dates
06/02/2003 11:42:03 AM
06/03/2000 13:58:11
27/05/99 11:07:44
25/05/99 21:18:52
25/05/99 21:17:29

File Attachment Icon
cade-99.pdf