Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decidable fragments of first-order modal logics with counting
  quantifiers over varying domains   This paper explores the computational complexity of various natural
one-variable fragments of first-order modal logics with the addition of
counting quantifiers, over both constant and varying domains. The addition of
counting quantifiers provides us a rich language with which to succinctly
express statements about the quantity of objects satisfying a given first-order
property, using a single variable.
  Optimal NExpTime upper-bounds are provided for the satisfiability problems of
the one-variable fragment of the minimal first-order modal logic QK, over both
constant and expanding/decreasing domain models, where counting quantifiers are
encoded as binary strings. For the case where the counting quantifiers are
encoded as unary strings, or are restricted to a finite set of quantifiers, it
is shown that the satisfiability problem over expanding domains is
PSpace-complete, whereas over decreasing domains the problem is shown to be
ExpTime-hard.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: math
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org