Abstract
Abstract We consider the guarded two-variable fragment of first-order logic with counting quantifiers, a subfragment of the two-variable fragment with counting quantifiers in which, in addition to the requirement of guarding, individual constants do not appear. We show that this logic lacks the finite model property, but that its satisfiability and finite satisfiability problems are both nevertheless ExpTime-complete. We introduce the concepts of database and data complexity, and show that the satisfiability and finite satisfiability problems for the guarded two-variable fragment of first-order logic with counting quantifiers and databases remain in ExpTime, and are NPTime-complete for data-complexity.
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