2,196 research outputs found
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
Extending Two-Variable Logic on Trees
The finite satisfiability problem for the two-variable fragment of first-order logic interpreted over trees was recently shown to be ExpSpace-complete. We consider two extensions of this logic. We show that adding either additional binary symbols or counting quantifiers to the logic does not affect the complexity of the finite satisfiability problem. However, combining the two extensions and adding both binary symbols and counting quantifiers leads to an explosion of this complexity. We also compare the expressive power of the two-variable fragment over trees with its extension with counting quantifiers. It turns out that the two logics are equally expressive, although counting quantifiers do add expressive power in the restricted case of unordered trees
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
One-Dimensional Fragment Over Words and Trees
One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a complete classification of the complexity of its satisfiability problem for various navigational signatures and comparing its expressive power with other important formalisms. These include the two-variable fragment with counting and the unary negation fragment.Peer reviewe
One-Dimensional Logic over Trees
A one-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential quantifiers that leave at most one variable free. This fragment contains two-variable logic, and it is known that over words both formalisms have the same complexity and expressive power. Here we investigate the one-dimensional fragment over trees. We consider unranked unordered trees accessible by one or both of the descendant and child relations, as well as ordered trees equipped additionally with sibling relations. We show that over unordered trees the satisfiability problem is ExpSpace-complete when only the descendant relation is available and 2ExpTime-complete with both the descendant and child or with only the child relation. Over ordered trees the problem remains 2ExpTime-complete. Regarding expressivity, we show that over ordered trees and over unordered trees accessible by both the descendant and child the one-dimensional fragment is equivalent to the two-variable fragment with counting quantifiers
A NExpTime-Complete Description Logic Strictly Contained in C²
We examine the complexity and expressivity of the combination of the Description Logic ALCQI with a terminological formalism based on cardinality restrictions on concepts. This combination can naturally be embedded into C², the two variable fragment of predicate logic with counting quantifiers. We prove that ALCQI has the same complexity as C² but does not reach its expressive power.An abriged version of this paper has been submitted to CSL'9
Two-variable Logic with Counting and a Linear Order
We study the finite satisfiability problem for the two-variable fragment of
first-order logic extended with counting quantifiers (C2) and interpreted over
linearly ordered structures. We show that the problem is undecidable in the
case of two linear orders (in the presence of two other binary symbols). In the
case of one linear order it is NEXPTIME-complete, even in the presence of the
successor relation. Surprisingly, the complexity of the problem explodes when
we add one binary symbol more: C2 with one linear order and in the presence of
other binary predicate symbols is equivalent, under elementary reductions, to
the emptiness problem for multicounter automata
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