Two-Variable First-Order Logic with Equivalence Closure

Kieroński, Emanuel; Michaliszyn, Jakub; Pratt-Hartmann, Ian; Tendera, Lidia

doi:10.1109/lics.2012.53

Cited by 23 publications

(44 citation statements)

References 15 publications

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“…We show that the variant with two variables has the finite model property, is decidable and NEXPTIME-complete (Thm. 17), and with four -undecidable (Thm. 21).…”

Section: Our Contributionmentioning

confidence: 99%

Decidability of weak logics with deterministic transitive closure

Charatonik

Kieroński

Mazowiecki

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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The deterministic transitive closure operator, added to languages containing even only two variables, allows to express many natural properties of a binary relation, including being a linear order, a tree, a forest or a partial function. This makes it a potentially attractive ingredient of computer science formalisms. In this paper we consider the extension of the two-variable fragment of first-order logic by the deterministic transitive closure of a single binary relation, and prove that the satisfiability and finite satisfiability problems for the obtained logic are decidable and EXPSPACE-complete. This contrasts with the undecidability of two-variable logic with the deterministic transitive closures of several binary relations, known before. We also consider the class of universal first-order formulas in prenex form. Its various extensions by deterministic closure operations were earlier considered by other authors, leading to both decidability and undecidability results. We examine this scenario in more details.

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“…We show that the variant with two variables has the finite model property, is decidable and NEXPTIME-complete (Thm. 17), and with four -undecidable (Thm. 21).…”

Section: Our Contributionmentioning

confidence: 99%

Decidability of weak logics with deterministic transitive closure

Charatonik

Kieroński

Mazowiecki

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

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“…The logic L 2 1E retains the finite model property, and its satisfiability problem remains NExpTime-complete [14]. The logic L 2 2E lacks the finite model property, and its satisfiability and finite satisfiability problems are both 2-NExpTime-complete [15]. The satisfiability and finite satisfiability problems for L 2 kE are both undecidable when k ≥ 3 [16].…”

Section: Introductionmentioning

confidence: 99%

The two‐variable fragment with counting and equivalence

Pratt-Hartmann

2015

Mathematical Logic Qtrly

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We consider the two-variable fragment of first-order 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 NExpTime-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.

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“…We say L has the finite model property if these problems coincide. The following facts are known: Lcomplete [11]; the satisfiability and finite satisfiability problems for L 2 kE (k ≥ 3) are both undecidable [9]. In this paper, we investigate C 2 1E-the two variable fragment with counting and one equivalence, and C 2 2E-the two variable fragment with counting and two equivalences.…”

Section: Introductionmentioning

confidence: 99%

Logics with counting and equivalence

Pratt-Hartmann

2014

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Nin

Self Cite

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We consider the two-variable fragment of first-order 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 NEXPTIME-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.

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Two-Variable First-Order Logic with Equivalence Closure

Cited by 23 publications

References 15 publications

Decidability of weak logics with deterministic transitive closure

Decidability of weak logics with deterministic transitive closure

The two‐variable fragment with counting and equivalence

Logics with counting and equivalence

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