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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-E xp T ime -complete. This contrasts with an earlier result that the corresponding problems for the full two-variable logic with equivalence closures of two binary predicates are 2-NE xp T ime -complete.

Equivalence closure in the two-variable guarded fragment