CONICET | Buscador de Institutos y Recursos Humanos

In classical logics, the meaning of a formula is invariant with respect to the renaming of bound variables. This property, normally taken for granted, has been shown not to hold in the case of Information Friendly (IF) logics. This phenomenon has been studied in the literature and, though it was considered annoying and counterintuitive, it was also accepted as an inherent characteristic of these logics. We argue that, on the contrary, this arises from a defect in the formalization of IF logics or, more precisely, from the way in which the semantics for the regular formulas (i.e. formulas where each variable is bound only once) has been generalized to arbitrary formulas. In this work we propose an alternative formalization, based on a variation of the classical notion of valuation, under which invariance with respect the renaming of bound variables is restored. We show that, when one restricts to the regular fragment, our semantics coincides with Hodges´ semantics. We also prove basic metatheoretical results of the resulting logic, such as compositionality, full abstraction, and truth preserving operations on valuations. We work on Hodges´ slash logic (from which results can be easily transferred to other IF-like logics) and we also consider his attening operator, for which we give a game-theoretical semantics.

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