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  1. 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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  • Henkin Quantifiers and Complete Problems.Andreas Blass & Yuri Gurevich - 1986 - Annals of Pure and Applied Logic 32:1--16.
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  • Generalized Quantifiers in Dependence Logic.Fredrik Engström - 2012 - Journal of Logic, Language and Information 21 (3):299-324.
    We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics whose semantics is based on teams instead of assignments, e.g., IF-logic and Dependence logic. Both the monotone and the non-monotone case is considered. It is argued that to handle quantifier scope dependencies of generalized quantifiers in a satisfying way the dependence atom in Dependence logic is not well suited and that the multivalued dependence atom is a better choice. This atom is in fact definably equivalent (...)
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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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  • On branching quantifiers in English.Jon Barwise - 1979 - Journal of Philosophical Logic 8 (1):47 - 80.
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  • Finite Partially‐Ordered Quantifiers.Herbert B. Enderton - 1970 - Mathematical Logic Quarterly 16 (8):393-397.
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  • On the logic of informational independence and its applications.Gabriel Sandu - 1993 - Journal of Philosophical Logic 22 (1):29 - 60.
    We shall introduce in this paper a language whose formulas will be interpreted by games of imperfect information. Such games will be defined in the same way as the games for first-order formulas except that the players do not have complete information of the earlier course of the game. Some simple logical properties of these games will be stated together with the relation of such games of imperfect information to higher-order logic. Finally, a set of applications will be outlined.
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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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