Two variable first-order logic over ordered domains

Journal of Symbolic Logic 66 (2):685-702 (2001)
The satisfiability problem for the two-variable fragment of first-order logic is investigated over finite and infinite linearly ordered, respectively wellordered domains, as well as over finite and infinite domains in which one or several designated binary predicates are interpreted as arbitrary wellfounded relations. It is shown that FO 2 over ordered, respectively wellordered, domains or in the presence of one well-founded relation, is decidable for satisfiability as well as for finite satisfiability. Actually the complexity of these decision problems is essentially the same as for plain unconstrained FO 2 , namely non-deterministic exponential time. In contrast FO 2 becomes undecidable for satisfiability and for finite satisfiability, if a sufficiently large number of predicates are required to be interpreted as orderings, wellorderings, or as arbitrary wellfounded relations. This undecidability result also entails the undecidability of the natural common extension of FO 2 and computation tree logic CTL
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2695037
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 25,100
Through your library
References found in this work BETA
On Languages with Two Variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.
Undecidability Results on Two-Variable Logics.Erich Grädel, Martin Otto & Eric Rosen - 1999 - Archive for Mathematical Logic 38 (4-5):313-354.

Add more references

Citations of this work BETA
An Event-Based Fragment of First-Order Logic Over Intervals.Savas Konur - 2010 - Journal of Logic, Language and Information 20 (1):49-68.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

15 ( #300,229 of 2,132,860 )

Recent downloads (6 months)

1 ( #388,048 of 2,132,860 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums