Journal of Philosophical Logic

, Volume 45, Issue 4, pp 399–428 | Cite as

A Generalization of Inquisitive Semantics

Article

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.

Keywords

Intuitionistic logic Superintuitionistic logics Inquisitive logic Topological semantics Kripke semantics Disjunction 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of LogicInstitute of Philosophy of the Czech Academy of SciencesPraha 1Czech Republic

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