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960
The Two-Variable Fragment with Counting Revisited
"... Abstract. The satisfiability and finite satisfiability problems for the two-variable fragment of first-order 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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Cited by 1 (0 self)
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Abstract. The satisfiability and finite satisfiability problems for the two-variable fragment of first-order 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 Two-Variable Fragment with Counting and Equivalence.
, 2015
"... 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 furthe ..."
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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
Modal logic and the two-variable 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 two-variable fragment F O2 of first-order 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 two-variable fragment F O2 of first-order logic
Description Logics and the Two-Variable Fragment
- In Proc. DL’01
, 2001
"... We present a description logic L that is as expressive as the twovariable fragment of first-order 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 two-variable fragment FO 2 of first-order logic by presenting a translation from FO 2 -formulae into equivalent L-concepts (and back). Additionally, we discuss
A Two-Variable 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 two-variable fragment of first-order logic. It follows that the problem of determining the satisfiability of a set
Complexity of the two-variable fragment with counting quantifiers
- Journal of Logic, Language and Information
"... 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. ..."
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Cited by 71 (6 self)
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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.
Complexity of the guarded two-variable 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 two-variable 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 two-variable fragment with counting
Complexity of the two-variable fragment with (binary-coded) counting quantifiers
- Journal of Logic, Language and Information
, 2005
"... We show that the satisfiability and finite satisfiability problems for the two-variable fragment of first-order 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 two-variable fragment of first-order 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 two-variable 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 two-variable 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 Two-Variable Fragment of the Equational Theory of the Max-Sum 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 non-existence 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 non-existence of a finite
Results 1 - 10
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960
