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  1. Henkin Quantifiers and Complete Problems.Andreas Blass & Yuri Gurevich - 1986 - Annals of Pure and Applied Logic 32:1--16.
  • Independence-Friendly Logic: A Game-Theoretic Approach.Allen L. Mann - 2011 - Cambridge University Press.
    A systematic introduction suitable for readers who have little familiarity with logic. Provides numerous examples and complete proofs.
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  • Convention: A Philosophical Study.Richard E. Grandy - 1977 - Journal of Philosophy 74 (2):129-139.
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  • Convention: A Philosophical Study.David K. Lewis - 1973 - Synthese 26 (1):153-157.
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  • Equivalence and Quantifier Rules for Logic with Imperfect Information.Xavier Caicedo, Francien Dechesne & Theo Janssen - 2008 - Logic Journal of the IGPL 17 (1):91-129.
    In this paper, we present a prenex form theorem for a version of Independence Friendly logic, a logic with imperfect information. Lifting classical results to such logics turns out not to be straightforward, because independence conditions make the formulas sensitive to signalling phenomena. In particular, nested quantification over the same variable is shown to cause problems. For instance, renaming of bound variables may change the interpretations of a formula, there are only restricted quantifier extraction theorems, and slashed connectives cannot be (...)
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  • Falsity Conditions for IF-Sentences.Francien Dechesne - 2005 - Philosophia Scientiae 9 (2):305-322.
    We give a procedure to obtain falsity conditions for IF-sentences, using Skolemization. The expressive power of an IF-sentence can then be strongly captured by a pair of Σ11-sentences1. A result from [Burgess 2003] shows that, conversely, any pair of incompatible Σ11-sentences corresponds with an IF-sentence. In the second part, we reflect on the influence of the order of the steps in the Skolemization procedures for IF-logic. We also reflect on the nature of game theoretical negation.
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  • Independent Choices and the Interpretation of IF Logic.Theo M. V. Janssen - 2002 - Journal of Logic, Language and Information 11 (3):367-387.
    In this paper it is argued that Hintikka's game theoreticalsemantics for Independence Friendly logic does not formalize theintuitions about independent choices; it rather is aformalization of imperfect information. Furthermore it is shownthat the logic has several remarkable properties (e.g.,renaming of bound variables is not allowed). An alternativesemantics is proposed which formalizes intuitions aboutindependence.
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  • On Existential Declarations of Independence in If Logic.Fausto Barbero - 2013 - Review of Symbolic Logic 6 (2):254-280.
    We analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.
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  • Equilibrium Semantics of Languages of Imperfect Information.Merlijn Sevenster & Gabriel Sandu - 2010 - Annals of Pure and Applied Logic 161 (5):618-631.
    In this paper, we introduce a new approach to independent quantifiers, as originally introduced in Informational independence as a semantic phenomenon by Hintikka and Sandu [9] under the header of independence-friendly languages. Unlike other approaches, which rely heavily on compositional methods, we shall analyze independent quantifiers via equilibriums in strategic games. In this approach, coined equilibrium semantics, the value of an IF sentence on a particular structure is determined by the expected utility of the existential player in any of the (...)
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  • Falsity Conditions for IF-Sentences.Francien Dechesne - 2005 - Philosophia Scientae 9:305-322.
  • 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.