Journal of Logic, Language and Information

, Volume 24, Issue 3, pp 323–355 | Cite as

Weak Negation in Inquisitive Semantics

  • Vít Punčochář


This paper introduces and explores a conservative extension of inquisitive logic. In particular, weak negation is added to the standard propositional language of inquisitive semantics, and it is shown that, although we lose some general semantic properties of the original framework, such an enrichment enables us to model some previously inexpressible speech acts such as weak denial and ‘might’-assertions. As a result, a new modal logic emerges. For this logic, a Fitch-style system of natural deduction is formulated. The main result of this paper is a theorem establishing the completeness of the system with respect to inquisitive semantics with weak negation. At the conclusion of the paper, the possibility of extending the framework to the level of first order logic is briefly discussed.


Inquisitive semantics Negation Possible worlds   Fitch-style natural deduction Denial 



The work on this paper was supported by grant no. 13-21076S of the Czech Science Foundation.


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© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of Logic, Institute of PhilosophyCzech Academy of SciencesPragueCzech Republic

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