Small Substructures and Decidability Issues for First-Order Logic with Two Variables

Kieroński, Emanuel; Otto, Martin

doi:10.1109/lics.2005.49

Cited by 36 publications

(44 citation statements)

References 16 publications

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“…This does not imply anything on the decidability of FO 2 (∼, +1), since the equivalence relation and the two tree successor relations cannot be axiomatized in FO 2 . A recent paper generalized the result of [19] in the presence of one or two equivalence relations [16]. Again this does not apply to our context as we also have two successor relations.…”

Section: Introductionmentioning

confidence: 88%

“…Again this does not apply to our context as we also have two successor relations. However [16] also showed that the twovariable fragment of FO with three equivalence relations, without any other structure, is undecidable. This implies that FO 2 (∼1, ∼2, ∼3, +1) is undecidable and that manipulating more than two different attributes at the same time quickly leads to undecidability.…”

Section: Introductionmentioning

confidence: 99%

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Two-variable logic on data trees and XML reasoning

Bojańczyk

David

Muscholl

et al. 2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

173

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Motivated by reasoning tasks in the context of XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result decidability of satisfiability and containment for a dataaware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Two-variable logic on data trees and XML reasoning

Bojańczyk

David

Muscholl

et al. 2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

173

View full text Add to dashboard Cite

show abstract

“…It was shown in [10] that EQ 2 1 also has the finite model property, with satisfiability again NEXPTIME-complete. However, the same paper showed that the finite model property fails for EQ 2 2 , and that its satisfiability problem is in 3-NEXPTIME.…”

Section: Introductionmentioning

confidence: 99%

“…The best currently known corresponding lower bound for these problems is 2-EXPTIME hard, obtained from the less expressive two-variable guarded fragment with equivalence relations [8]. It was further shown in [10] that the satisfiability and finite satisfiability problems for EQ 2 3 are undecidable. In this paper, we show: (i) EC 2 1 retains the finite model property, and its satisfiability problem remains in NEXPTIME; (ii) the satisfiability and finite satisfiability problems for EC 2 2 are both in 2-NEXPTIME; (iii) the satisfiability and finite satisfiability problems for EQ 2 2 are both 2-NEXPTIME-hard.…”

Section: Introductionmentioning

confidence: 99%

“…, # , representing their respective equivalence closures. We establish a 'Scott-type' normal form for EC 2 2 , allowing us to restrict the nesting of quantifiers to depth two, and we recall a small substructure property for FO 2 [10], allowing us to replace an arbitrary substructure in a model of some FO 2 -formula with one whose size is exponentially bounded in the size of 's signature. Sec.…”

Section: Introductionmentioning

confidence: 99%

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Two-Variable First-Order Logic with Equivalence Closure

Kieroński

Michaliszyn

Pratt-Hartmann

et al. 2012

2012 27th Annual IEEE Symposium on Logic in Computer Science

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We consider the satisfiability and finite satisfiability problems for extensions of the two-variable fragment of firstorder logic in which an equivalence closure operator can be applied to a fixed number of binary predicates. We show that the satisfiability problem for two-variable, first-order logic with equivalence closure applied to two binary predicates is in 2NEXPTIME, and we obtain a matching lower bound by showing that the satisfiability problem for two-variable first-order logic in the presence of two equivalence relations is 2NEXPTIME-hard. The logics in question lack the finite model property; however, we show that the same complexity bounds hold for the corresponding finite satisfiability problems. We further show that the satisfiability (=finite satisfiability) problem for the twovariable fragment of first-order logic with equivalence closure applied to a single binary predicate is NEXPTIME-complete.

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Finite satisfiability for two‐variable, first‐order logic with one transitive relation is decidable

Pratt-Hartmann

2018

Mathematical Logic Qtrly

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Small Substructures and Decidability Issues for First-Order Logic with Two Variables

Cited by 36 publications

References 16 publications

Two-variable logic on data trees and XML reasoning

Two-variable logic on data trees and XML reasoning

Two-Variable First-Order Logic with Equivalence Closure

Finite satisfiability for two‐variable, first‐order logic with one transitive relation is decidable

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