Complexity of the Guarded Two-Variable Fragment with Counting Quantifiers

We show that the finite satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME. The method employed also yields a simple proof of a result recently obtained by Y. Kazakov, that the satisfiability problem for the guarded two-variable fragment with counting quantifiers is in EXPTIME.Comment: 20 pages, 3 figure

Data-Complexity of the Two-Variable Fragment with Counting Quantifiers

The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment with counting is co-NP-complete

The two-variable fragment with counting and equivalence

We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a sin-gle distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIME-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable. Copyright line will be provided by the publisher

Fluted Logic with Counting

The fluted fragment is a fragment of first-order logic in which the order of quantification of variables coincides with the order in which those variables appear as arguments of predicates. It is known that the fluted fragment possesses the finite model property. In this paper, we extend the fluted fragment by the addition of counting quantifiers. We show that the resulting logic retains the finite model property, and that the satisfiability problem for its (m+1)-variable sub-fragment is in m-NExpTime for all positive m. We also consider the satisfiability and finite satisfiability problems for the extension of any of these fragments in which the fluting requirement applies only to sub-formulas having at least three free variables

A Note on the Complexity of the Satisfiability Problem for Graded Modal Logics

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive interpretations such as "It is true at no fewer than 15 accessible worlds that...", or "It is true at no more than 2 accessible worlds that...". We investigate the complexity of satisfiability for this language over some familiar classes of frames. This problem is more challenging than its ordinary modal logic counterpart--especially in the case of transitive frames, where graded modal logic lacks the tree-model property. We obtain tight complexity bounds for the problem of determining the satisfiability of a given graded modal logic formula over the classes of frames characterized by any combination of reflexivity, seriality, symmetry, transitivity and the Euclidean property.Comment: Full proofs for paper presented at the IEEE Conference on Logic in Computer Science, 200