LiU Electronic Press
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Author:
Szalas, Andrzej (Institute of Informatics, Warsaw University)
Holenderski, Leszek (Institute of Informatics, Warsaw University)
Title:
Incompleteness of First-Order Temporal Logic with Until
Publication type:
Article in journal (Refereed)
Language:
English
Publisher: Elsevier
Status:
Published
In:
Theoretical Computer Science(ISSN 0304-3975)
Volume:
57
Issue:
2-3
Pages:
317-325
Year of publ.:
1988
URI:
urn:nbn:se:liu:diva-74991
Permanent link:
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-74991
Subject category:
Engineering and Technology
Abstract(en) :

The results presented in this paper concern the axiomatizability problem of first-order temporal logic with linear and discrete time. We show that the logic is incomplete, i.e., it cannot be provided with a finitistic and complete proof system. We show two incompleteness theorems. Although the first one is weaker (it assumes some first-order signature), we decided to present it, for its proof is much simpler and contains an interesting fact that finite sets are characterizable by means of temporal formulas. The second theorem shows that the logic is incomplete independently of any particular signature.

Available from:
2012-02-13
Created:
2012-02-13
Last updated:
2012-02-21
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