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Expressivity of Imperfect Information Logics without Identity

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Abstract

In this article we investigate the family of independence-friendly (IF) logics in the equality-free setting, concentrating on questions related to expressive power. Various natural equality-free fragments of logics in this family translate into existential second-order logic with prenex quantification of function symbols only and with the first-order parts of formulae equality-free. We study this fragment of existential second-order logic. Our principal technical result is that over finite models with a vocabulary consisting of unary relation symbols only, this fragment of second-order logic is weaker in expressive power than first-order logic (with equality). Results about the fragment could turn out useful for example in the study of independence-friendly modal logics. In addition to proving results of a technical nature, we address issues related to a perspective from which IF logic is regarded as a specification framework for games, and also discuss the general significance of understanding fragments of second-order logic in investigations related to non-classical logics.

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  1. SIS, mathematics, University of Tampere, Tampere, Finland

    Antti Kuusisto

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  1. Antti Kuusisto
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Kuusisto, A. Expressivity of Imperfect Information Logics without Identity. Stud Logica 101, 237–265 (2013). https://doi.org/10.1007/s11225-013-9482-7

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