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  1. Dependence and Independence.Erich Grädel & Jouko Väänänen - 2013 - Studia Logica 101 (2):399-410.
    We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. (...)
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  • On Definability in Dependence Logic.Juha Kontinen & Jouko Väänänen - 2009 - Journal of Logic, Language and Information 18 (3):317-332.
    We study the expressive power of open formulas of dependence logic introduced in Väänänen [Dependence logic (Vol. 70 of London Mathematical Society Student Texts), 2007]. In particular, we answer a question raised by Wilfrid Hodges: how to characterize the sets of teams definable by means of identity only in dependence logic, or equivalently in independence friendly logic.
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  • Ways of Branching Quantifers.Gila Sher - 1990 - Linguistics and Philosophy 13 (4):393 - 422.
    Branching quantifiers were first introduced by L. Henkin in his 1959 paper ‘Some Remarks on Infmitely Long Formulas’. By ‘branching quantifiers’ Henkin meant a new, non-linearly structured quantiiier-prefix whose discovery was triggered by the problem of interpreting infinitistic formulas of a certain form} The branching (or partially-ordered) quantifier-prefix is, however, not essentially infinitistic, and the issues it raises have largely been discussed in the literature in the context of finitistic logic, as they will be here. Our discussion transcends, however, the (...)
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  • On Branching Quantifiers in English.Jon Barwise - 1979 - Journal of Philosophical Logic 8 (1):47 - 80.
  • From If to Bi.Samson Abramsky & Jouko Väänänen - 2009 - Synthese 167 (2):207 - 230.
    We take a fresh look at the logics of informational dependence and independence of Hintikka and Sandu and Väänänen, and their compositional semantics due to Hodges. We show how Hodges’ semantics can be seen as a special case of a general construction, which provides a context for a useful completeness theorem with respect to a wider class of models. We shed some new light on each aspect of the logic. We show that the natural propositional logic carried by the semantics (...)
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  • ‘Two Examiners Marked Six Scripts.’ Interpretations of Numerically Quantified Sentences.Martin Davies - 1989 - Linguistics and Philosophy 12 (3):293 - 323.
  • Branching Quantification V. Two-Way Quantification.Nina Gierasimczuk & Jakub Szymanik - 2009 - Journal of Semantics 26 (4):329-366.
    Next SectionWe discuss the thesis formulated by Hintikka (1973) that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.
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  • Quantifiers in Language and Logic.Stanley Peters & Dag Westerståhl - 2006 - Clarendon Press.
    Quantification is a topic which brings together linguistics, logic, and philosophy. Quantifiers are the essential tools with which, in language or logic, we refer to quantity of things or amount of stuff. In English they include such expressions as no, some, all, both, many. Peters and Westerstahl present the definitive interdisciplinary exploration of how they work - their syntax, semantics, and inferential role.
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  • Inclusion and Exclusion Dependencies in Team Semantics—on Some Logics of Imperfect Information.Pietro Galliani - 2012 - Annals of Pure and Applied Logic 163 (1):68-84.
  • Hierarchies of Partially Ordered Connectives and Quantifiers.Michał Krynicki - 1993 - Mathematical Logic Quarterly 39 (1):287-294.
    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 equation imagewhat is a strengthening of the Walkoe result. MSC: 03C80.
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  • Quantifiers Vs. Quantification Theory.Jaakko Hintikka - 1973 - Dialectica 27 (3‐4):329-358.
  • On a Generalization of Quantifiers.Andrzej Mostowski - 1957 - Fundamenta Mathematicae 44 (2):12--36.
  • English as a Formal Language.Richard Montague - 1970 - In Bruno Visentini (ed.), Linguaggi nella societa e nella tecnica. Edizioni di Communita. pp. 188-221.
    I reject the contention that an important theoretical difference exists between formal and natural languages.
     
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  • Some Remarks on Infinitely Long Formulas.L. Henkin & Carol R. Karp - 1965 - Journal of Symbolic Logic 30 (1):96-97.
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  • Branching Quantification V. Two-Way Quantification: Articles.Nina Gierasimczuk & Jakub Szymanik - 2009 - Journal of Semantics 26 (4):367-392.
    We discuss the thesis formulated by Hintikka that certain natural language sentences require non-linear quantification to express their meaning. We investigate sentences with combinations of quantifiers similar to Hintikka's examples and propose a novel alternative reading expressible by linear formulae. This interpretation is based on linguistic and logical observations. We report on our experiments showing that people tend to interpret sentences similar to Hintikka sentence in a way consistent with our interpretation.
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  • Compositional Semantics for a Language of Imperfect Information.W. Hodges - 1997 - Logic Journal of the IGPL 5 (4):539-563.
    We describe a logic which is the same as first-order logic except that it allows control over the information that passes down from formulas to subformulas. For example the logic is adequate to express branching quantifiers. We describe a compositional semantics for this logic; in particular this gives a compositional meaning to formulas of the 'information-friendly' language of Hintikka and Sandu. For first-order formulas the semantics reduces to Tarski's semantics for first-order logic. We prove that two formulas have the same (...)
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  • Some Remarks on Infinitely Long Formulas.L. Henkin - 1961 - In Journal of Symbolic Logic. Pergamon Press. pp. 167--183.
  • Branching Generalized Quantifiers and Natural Language.Dag Westerståhl - 1987 - In Peter Gärdenfors (ed.), Generalized Quantifiers. Reidel Publishing Company. pp. 269--298.
  • First order predicate logic with generalized quantifiers.Per Lindström - 1966 - Theoria 32 (3):186--195.
  • Quantifiers Vs. Quantificational Theory.Jaakko Hintikka - 1974 - Linguistic Inquiry 5:153--77.
     
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