Partially Ordered Connectives

Sandu, Gabriel; Väänánen, Jouko

doi:10.1002/malq.19920380134

Cited by 23 publications

(23 citation statements)

References 7 publications

(4 reference statements)

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“…Proof. The game is a simple adaption of the one presented in [19]. 2 Fagin [10] showed that the monadic fragments of Σ It remains to be shown that for arbitrary m, k, n, there exist graphs A and B meeting (i) and (ii).…”

Section: Theorem 3 ([7 11]) For Every Integer M the Following Are mentioning

confidence: 99%

“…In this sense ∃α i is a 'restricted' quantifier, hence the name 'Henkin quantifier with restricted quantifiers'. The model theory for Henkin quantifiers with restricted variables was taken up in [19], be it under the name of 'partially ordered connectives' and written in the following format:…”

Section: Introductionmentioning

confidence: 99%

“…The usage of the symbol reflects the fact that the variables i j range over a fixed domain of {0, 1}. Sandu and Väänänen [19,Proposition 2] show that any first-order formula φ prefixed by the partially ordered connective D 2 1 xi can be translated into H 2 1 xy φ , for some first-order φ . Furthermore, they provide an Ehrenfeucht-Fraïssé game for partially ordered connectives and use it to give non-definability results.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we take up the study of Henkin quantifiers with boolean variables [4] also known as partially ordered connectives [19]. We consider first-order formulae prefixed by partially ordered connectives, denoted D, on finite structures.…”

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confidence: 99%

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Partially Ordered Connectives and ∑1 1 on Finite Models

Sevenster

Tulenheimo

2006

Logical Approaches to Computational Barriers

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Abstract. In this paper we take up the study of Henkin quantifiers with boolean variables [4] also known as partially ordered connectives [19]. We consider first-order formulae prefixed by partially ordered connectives, denoted D, on finite structures. We characterize D as a fragment of second-order existential logic Σ 1 1 ♥ whose formulae do not allow for existential variables being argument of predicate variables. We show that Σ 1 1 ♥ harbors a strict hierarchy induced by the arity of predicate variables and that it is not closed under complementation, by means of a game-theoretical argument. Admitting for at most one existential variable to appear as the argument of a predicate variable already yields a logic coinciding with full Σ 1 1 , thus we show.

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Section: Theorem 3 ([7 11]) For Every Integer M the Following Are mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Partially Ordered Connectives and ∑1 1 on Finite Models

Sevenster

Tulenheimo

2006

Logical Approaches to Computational Barriers

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“…To make this connection more clear, we define a syntactic variant of the partially-ordered connectives of Sandu and Väänänen [SV92], closely related to the narrow Henkin quantifier of Blass and Gurevich [BG86]. We show that our definition of partially-ordered connectives is, in a strong sense, equivalent to that of Sandu and Väänänen.…”

Section: Introductionmentioning

confidence: 95%

Boolean Dependence Logic and Partially-Ordered Connectives

Ebbing

Hella

Lohmann

et al. 2013

Logic, Language, Information, and Computation

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We introduce a new variant of dependence logic (D) called Boolean dependence logic (BD). In BD dependence atoms are of the type =(x 1 , . . . , x n , α), where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions.We compare the expressive power of BD to D and first-order logic enriched by partially-ordered connectives, F O(POC). We show that the expressive power of BD and D coincide. We define natural syntactic fragments of BD and show that they coincide with the corresponding fragments of F O(POC) with respect to expressive power. We then show that the fragments form a strict hierarchy.

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Hierarchies of Partially Ordered Connectives and Quantifiers

Krynicki

1993

Mathematical Logic Qtrly

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Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form VZl . . .2n 3y 0 VZl . . . Zk 3t what is a strengthening of the Walkoe result. MSC: 03C80.

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Partially Ordered Connectives

Cited by 23 publications

References 7 publications

Partially Ordered Connectives and ∑1 1 on Finite Models

Partially Ordered Connectives and ∑1 1 on Finite Models

Boolean Dependence Logic and Partially-Ordered Connectives

Hierarchies of Partially Ordered Connectives and Quantifiers

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