Equivalence closure in the two-variable guarded fragment

Equivalence closure in the two-variable guarded fragment

We consider the satisfiability and finite satisfiability problems for the extension of the two-variable guarded fragment in which an equivalence closure operator can be applied to two distinguished binary predicates. We show that the satisfiability and finite satisfiability problems for this logic are 2-ExpTime-complete. This contrasts with an earlier result that the corresponding problems for ...

A Polynomial Translation from the Two-Variable Guarded Fragment with Number Restrictions to the Guarded Fragment

We consider a two-variable guarded fragment with number restrictions for binary relations and give a satisfiability preserving transformation of formulas in this fragment to the three-variable guarded fragment. The translation can be computed in polynomial time and produces a formula that is linear in the size of the initial formula even for the binary coding of number restrictions. This allows...

Complexity of the Guarded Two-Variable Fragment with Counting Quantifiers

We show that the finite satisfiability problem for the guarded twovariable fragment with counting quantifiers is in EXPTIME. The method employed also yields a simple proof of the result obtained in Kazakov [6], that the satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME.

The Two-Variable Guarded Fragment with Transitive Relations

Decidability of the Guarded Fragment with the Transitive Closure

We consider an extension of the guarded fragment in which one can guard quanti ers using the transitive closure of some binary relations. The obtained logic captures the guarded fragment with transitive guards, and in fact extends its expressive power non-trivially, preserving the complexity: we prove that its satis ability problem is 2Exptime-