Topic
Quantifier (logic)
About: Quantifier (logic) is a research topic. Over the lifetime, 359 publications have been published within this topic receiving 7027 citations. The topic is also known as: quantor & logical quantification.
Papers published on a yearly basis
Papers
TL;DR: A language, CTL*, in which a universal or existential path quantifier can prefix an arbitrary linear time assertion, is defined and the expressive power of a number of sublanguages is compared.
Abstract: The differences between and appropriateness of branching versus linear time temporal logic for reasoning about concurrent programs are studied. These issues have been previously considered by Lamport. To facilitate a careful examination of these issues, a language, CTL*, in which a universal or existential path quantifier can prefix an arbitrary linear time assertion, is defined. The expressive power of a number of sublanguages is then compared. CTL* is also related to the logics MPL of Abrahamson and PL of Harel, Kozen, and Parikh. The paper concludes with a comparison of the utility of branching and linear time temporal logics.
1,123 citations
Book•
30 Apr 1983
TL;DR: This book discusses syntax and model-Theoretic Semantics, storage and wh-Phenomena, and the Theory of Grammar.
Abstract: I: Syntax and Model-Theoretic Semantics.- II: A Fragment of English.- III: Quantifier Storage.- IV: Storage and wh-Phenomena.- V: wh-Phenomena and the Theory of Grammar.- VI: Presupposition and Quantification.- VII: Gender Agreement.- Notes.- Answers to Selected Exercises.- Index of Names.- Index of Subjects.
521 citations
1 Jan 1995
TL;DR: In this paper, Bittner, Hale, and Portner discuss the Variability of Impersonal Subjects and Quantifier strength in the context of Dynamic Semantics, and present a typology of natural logic based on natural logic.
Abstract: Preface Introduction A Note on Quantification and Blankets in Haisla E Bach On the Absence of Certain Quantifiers in Mohawk M Baker Quantification in Eskimo: a Challenge for Compositional Semantics M Bittner Remarks on Definiteness in Warlpiri M Bittner, K Hale The Variability of Impersonal Subjects G Chierchia On Quantifier Strength I Comorovski Quantification on Correlatives VS Dayal A-Quantifiers and Scope in Mayali N Evans Towards a Typology of Natural Logic L Faltz Universal Quantifiers and Distributivity D Gil Diachronic Sources of 'All' and 'Every' M Haspelmath Mass and Count Quantifiers J Higginbotham On the Characterization of the Weak--Strong Distinction H de Hoop On the Quantificational Force of English Free Relatives P Jacobson Quantification in Straits Salish E Jelinek Quantificational Structures and Compositionality BH Partee Bare Noun Phrases, Verbs, and Quantification in ASL K Petronio Quantification, Events and Gerunds P Portner Domain Restriction in Dynamic Semantics C Roberts The Expression of Quantificational Notions in Asurini do Trocara M Damasco Vieira
504 citations
TL;DR: The alternating-time temporal logic (ATL) as discussed by the authors is a more general variant of temporal logic that allows selective quantification over those paths that are possible outcomes of games, such as the game in which the system and the environment alternate moves.
450 citations
29 Jun 1997
TL;DR: It is proved that FO/sup 2/ can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", and "s sometime in the past", a logic the authors denote by unary-TL.
Abstract: We investigate the power of first-order logic with only two variables over /spl omega/-words and finite words, a logic denoted by FO/sup 2/. We prove that FO/sup 2/ can express precisely the same properties as linear temporal logic with only the unary temporal operators: "next", "previously", "sometime in the future", and "sometime in the past", a logic we denote by unary-TL. Moreover, our translation from FO/sup 2/ to unary-TL converts every FO/sup 2/ formula to an equivalent unary-TL formula that is at most exponentially larger, and whose operator depth is at most twice the quantifier depth of the first-order formula. We show that this translation is optimal. While satisfiability for full linear temporal logic, as well as for unary-TL, is known to be PSPACE-complete, we prove that satisfiability for FO/sup 2/ is NEXP-complete, in sharp contrast to the fact that satisfiability for FO/sup 3/ has non-elementary computational complexity. Our NEXP time upper bound for FO/sup 2/ satisfiability has the advantage of being in terms of the quantifier depth of the input formula. It is obtained using a small model property for FO/sup 2/ of independent interest, namely: a satisfiable FO/sup 2/ formula has a model whose "size" is at most exponential in the quantifier depth of the formula. Using our translation from FO/sup 2/ to unary-TL we derive this small model property from a corresponding small model property for unary-TL. Our proof of the small model property for unary-TL is based on an analysis of unary-TL types.
216 citations
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 21 |
| 2020 | 13 |
| 2019 | 14 |
| 2018 | 15 |
| 2017 | 15 |
| 2016 | 16 |