A Generalization of Inquisitive Semantics

Abstract

This paper introduces a generalized version of inquisitive semantics, denoted as GIS, and concentrates especially on the role of disjunction in this general framework. Two alternative semantic conditions for disjunction are compared: the first one corresponds to the so-called tensor operator of dependence logic, and the second one is the standard condition for inquisitive disjunction. It is shown that GIS is intimately related to intuitionistic logic and its Kripke semantics. Using this framework, it is shown that the main results concerning inquisitive semantics, especially the axiomatization of inquisitive logic, can be viewed as particular cases of more general phenomena. In this connection, a class of non-standard superintuitionistic logics is introduced and studied. These logics share many interesting features with inquisitive logic, which is the strongest logic of this class.

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Notes

  1. 1.

    The reason why the words “local” and “global” are used in this context will be clarified later.

  2. 2.

    The modal logic of the mentioned semantics from [1] is S4, which is, as is well known, a so-called modal companion of intuitionistic logic (see, e.g., [6]).

  3. 3.

    Medvedev logic is defined at the end of this section.

  4. 4.

    I am grateful to Nick Bezhanishvili for informing me of these two theorems.

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Correspondence to Vít Punčochář.

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The work on this paper was supported by grant no. 13-21076S of the Czech Science Foundation. I am also grateful to Ivano Ciardelli and the anonymous reviewers for their very helpful suggestions.

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Punčochář, V. A Generalization of Inquisitive Semantics. J Philos Logic 45, 399–428 (2016). https://doi.org/10.1007/s10992-015-9379-1

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Keywords

  • Intuitionistic logic
  • Superintuitionistic logics
  • Inquisitive logic
  • Topological semantics
  • Kripke semantics
  • Disjunction