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FO^2 with one transitive relation is decidable
- Publication Year :
- 2013
-
Abstract
- We show that the satisfiability problem for the two-variable first-order logic, FO^2, over transitive structures when only one relation is required to be transitive, is decidable. The result is optimal, as FO^2 over structures with two transitive relations, or with one transitive and one equivalence relation, are known to be undecidable, so in fact, our result completes the classification of FO^2-logics over transitive structures with respect to decidability. We show that the satisfiability problem is in 2-NExpTime. Decidability of the finite satisfiability problem remains open.
Details
- Database :
- OAIster
- Notes :
- application/pdf, English
- Publication Type :
- Electronic Resource
- Accession number :
- edsoai.on1358719981
- Document Type :
- Electronic Resource
- Full Text :
- https://doi.org/10.4230.LIPIcs.STACS.2013.317