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960
The TwoVariable Fragment with Counting Revisited
"... Abstract. The satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting were shown in [5] to be in NExpTime. This paper presents a simplified proof via a result on integer programming due to Eisenbrand and Shmonina [2]. ..."
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Abstract. The satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting were shown in [5] to be in NExpTime. This paper presents a simplified proof via a result on integer programming due to Eisenbrand and Shmonina [2].
The TwoVariable Fragment with Counting and Equivalence.
, 2015
"... We consider the twovariable fragment of firstorder logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIMEcomplete. We furthe ..."
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We consider the twovariable fragment of firstorder logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIMEcomplete. We
Modal logic and the twovariable fragment
 IN ANNUAL CONF. OF THE EUROPEAN ASSOCIATION FOR COMPUTER SCIENCE LOGIC (CSL’01), LNCS
, 2001
"... We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the twovariable fragment F O2 of firstorder logic, bu ..."
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Cited by 20 (6 self)
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We introduce a modal language L which is obtained from standard modal logic by adding the Boolean operators on accessibility relations, the identity relation, and the converse of relations. It is proved that L has the same expressive power as the twovariable fragment F O2 of firstorder logic
Description Logics and the TwoVariable Fragment
 In Proc. DL’01
, 2001
"... We present a description logic L that is as expressive as the twovariable fragment of firstorder logic and differs from other logics with this property in that it encompasses solely standard role and conceptforming operators. The description logic L is obtained from ALC by adding full Boolean ..."
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Cited by 4 (1 self)
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operators on roles, the inverse operator on roles and an identity role. It is proved that L has the same expressive power as the twovariable fragment FO 2 of firstorder logic by presenting a translation from FO 2 formulae into equivalent Lconcepts (and back). Additionally, we discuss
A TwoVariable Fragment of English
, 2001
"... Controlled languages are regimented fragments of natural language designed to make the processing of natural language more efficient and reliable. This paper defines a controlled language, E2V, whose principal grammatical resources include determiners, relative clauses, reflexives and pronouns. We p ..."
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Cited by 20 (5 self)
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provide a formal syntax and semantics for E2V, in which anaphoric ambiguities are resolved in a linguistically natural way. We show that the expressive power of E2V is equal to that of the twovariable fragment of firstorder logic. It follows that the problem of determining the satisfiability of a set
Complexity of the twovariable fragment with counting quantifiers
 Journal of Logic, Language and Information
"... The datacomplexity of both satisfiability and finite satisfiability for the twovariable fragment with counting is NPcomplete; the datacomplexity of both queryanswering and finite queryanswering for the twovariable guarded fragment with counting is coNPcomplete. ..."
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Cited by 71 (6 self)
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The datacomplexity of both satisfiability and finite satisfiability for the twovariable fragment with counting is NPcomplete; the datacomplexity of both queryanswering and finite queryanswering for the twovariable guarded fragment with counting is coNPcomplete.
Complexity of the guarded twovariable fragment with counting quantifiers
 Journal of Logic and Computation
"... We show that the finite satisfiability problem for the guarded twovariable fragment with counting quantifiers is in EXPTIME. The method employed also yields a simple proof of the result obtained in Kazakov [6], that the satisfiability problem for the guarded twovariable fragment with counting quant ..."
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Cited by 7 (3 self)
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We show that the finite satisfiability problem for the guarded twovariable fragment with counting quantifiers is in EXPTIME. The method employed also yields a simple proof of the result obtained in Kazakov [6], that the satisfiability problem for the guarded twovariable fragment with counting
Complexity of the twovariable fragment with (binarycoded) counting quantifiers
 Journal of Logic, Language and Information
, 2005
"... We show that the satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly. 1 ..."
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Cited by 5 (0 self)
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We show that the satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly. 1
Complexity of the Two Variable Fragment with Counting Quantifiers
"... Abstract The satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly. Key words: two variable fragment, counting quantifiers, logic, complexity 1. Backgrou ..."
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Abstract The satisfiability and finite satisfiability problems for the twovariable fragment of firstorder logic with counting quantifiers are both in NEXPTIME, even when counting quantifiers are coded succinctly. Key words: two variable fragment, counting quantifiers, logic, complexity 1
On the TwoVariable Fragment of the Equational Theory of the MaxSum Algebra of the Natural Numbers
, 2000
"... This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the nonexistence of a finite basis ..."
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Cited by 10 (8 self)
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This paper shows that the collection of identities in two variables which hold in the algebra N of the natural numbers with constant zero, and binary operations of sum and maximum does not have a finite equational axiomatization. This gives an alternative proof of the nonexistence of a finite
Results 1  10
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