On the decision problem for two-variable first-order logic

Bulletin of Symbolic Logic 3 (1):53-69 (1997)
Abstract
We identify the computational complexity of the satisfiability problem for FO 2 , the fragment of first-order logic consisting of all relational first-order sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity of its decision problem has not been pinpointed so far. In 1975 Mortimer proved that FO 2 has the finite-model property, which means that if an FO 2 -sentence is satisfiable, then it has a finite model. Moreover, Mortimer showed that every satisfiable FO 2 -sentence has a model whose size is at most doubly exponential in the size of the sentence. In this paper, we improve Mortimer's bound by one exponential and show that every satisfiable FO 2 -sentence has a model whose size is at most exponential in the size of the sentence. As a consequence, we establish that the satisfiability problem for FO 2 is NEXPTIME-complete
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/421196
Options
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 30,798
Through your library
References found in this work BETA
On Languages with Two Variables.Michael Mortimer - 1975 - Mathematical Logic Quarterly 21 (1):135-140.
The Unsolvability of the Gödel Class with Identity.Warren D. Goldfarb - 1984 - Journal of Symbolic Logic 49 (4):1237-1252.
Correction to a Note on the Entscheidungsproblem.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (3):101-102.

Add more references

Citations of this work BETA
Logics for the Relational Syllogistic.Ian Pratt-hartmann & Lawrence S. Moss - 2009 - Review of Symbolic Logic 2 (4):647-683.
On the Restraining Power of Guards.Erich Grädel - 1999 - Journal of Symbolic Logic 64 (4):1719-1742.
Deciding Regular Grammar Logics with Converse Through First-Order Logic.Stéphane Demri & Hans De Nivelle - 2005 - Journal of Logic, Language and Information 14 (3):289-329.
On Preservation Theorems for Two-Variable Logic.Erich Gradel & Eric Rosen - 1999 - Mathematical Logic Quarterly 45 (3):315-325.

View all 14 citations / Add more citations

Similar books and articles
Added to PP index
2009-01-28

Total downloads
29 ( #183,248 of 2,202,702 )

Recent downloads (6 months)
3 ( #97,530 of 2,202,702 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature