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Let C 2 p denote the class of rst order sentences with two variables and with additional quantiiers \there exists exactly (at most, at least) i", for i p, and let C 2 be the union of C 2 p taken over all integers p. We prove that the satissability problem for C 2 1 sentences is NEXPTIME-complete. This strengthens the results by E. Grr adel, Ph. Kolaitis and… (More)

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… (More)

The guarded fragment with transitive guards, [GF+TG], is an extension of the guarded fragment of ÿrst-order logic, GF, in which certain predicates are required to be transitive, transitive predicate letters appear only in guards of the quantiÿers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable.… (More)