Logics with counting and equivalence

Pratt-Hartmann, Ian

doi:10.1145/2603088.2603117

Cited by 8 publications

(7 citation statements)

References 14 publications

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“…In [4] it is shown that finite satisfiability for C 2 interpreted over structures where two binary relations are interpreted as forests of finite trees (which subsumes the case of two successor relations on two linear orders) is NExpTime-complete. [30] shows that the satisfiability and finite satisfiability problems for C 2 with one equivalence relation are both NExpTime-complete. All extensions of C 2 mentioned above allow arbitrary number of other binary relations.…”

Section: Introductionmentioning

confidence: 99%

Two-variable Logic with Counting and a Linear Order

Charatonik¹,

Witkowski²

2016

Logical Methods in Computer Science

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Abstract. We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C 2 ) 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: C 2 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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Section: Introductionmentioning

confidence: 99%

Two-variable Logic with Counting and a Linear Order

Charatonik¹,

Witkowski²

2016

Logical Methods in Computer Science

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“…Our work also gives rise to other questions. We suspect that our results can be extended to ω-languages, and we would like to adapt them to C 2 , which extends FO 2 with counting quantifiers [26,31]. We also plan to explore further the computational power of our automata model, for instance, to establish a pumping lemma that allows us to prove that some context-free languages are not PI languages.…”

Section: Discussionmentioning

confidence: 99%

Pebble-Intervals Automata and FO$$^2$$ with Two Orders

Labai

Kotek

Ortiz

et al. 2020

Language and Automata Theory and Applications

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We introduce a novel automata model, which we call pebble-intervals automata (PIA), and study its power and closure properties. PIAs are tailored for a decidable fragment of FO that is important for reasoning about structures that use data values from infinite domains: the two-variable fragment with one total preorder and its induced successor relation, one linear order, and an arbitrary number of unary relations. We prove that the string projection of every language of data words definable in the logic is accepted by a pebble-intervals automaton A, and obtain as a corollary an automata-theoretic proof of the EXPSPACE upper bound for finite satisfiability due to Schwentick and Zeume.

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“…Finite satisfiability of C 2 with two forests was shown in [10] to be NEXPTIME-complete. Satisfiability and finite satisfiability of C 2 with a single equivalence relation was shown to be NEXPTIME-complete, while C 2 with two equivalence relations is undecidable [26]. Decidability of extensions of F O 2 with successor relations, order relations, and equivalence relations without counting were studied [13], [16], [17], [20], [21], [30].…”

Section: The Two-variable Fragment and Alcqiomentioning

confidence: 99%

Extending ALCQIO with Trees

Kotek

imkus

Veith

et al. 2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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We study the description logic ALCQIO, which extends the standard description logic ALC with nominals, inverses and counting quantifiers. ALCQIO is a fragment of first order logic and thus cannot define trees. We consider the satisfiability problem of ALCQIO over finite structures in which k relations are interpreted as forests of directed trees with unbounded outdegrees.We show that the finite satisfiability problem of ALCQIO with forests is polynomial-time reducible to finite satisfiability of ALCQIO. As a consequence, we get that finite satisfiability is NEXPTIME-complete. Description logics with transitive closure constructors or fixed points have been studied before, but we give the first decidability result of the finite satisfiability problem for a description logic that contains nominals, inverse roles, and counting quantifiers and can define trees.

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Logics with counting and equivalence

Cited by 8 publications

References 14 publications

Two-variable Logic with Counting and a Linear Order

Two-variable Logic with Counting and a Linear Order

Pebble-Intervals Automata and FO$$^2$$ with Two Orders

Extending ALCQIO with Trees

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