Journal of Philosophical Logic 41 (5):877-900 (2012)

Carlo Proietti
University of Amsterdam
The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models
Keywords Intuitionistic logic  Epistemic logic  Fitch’s paradox  Kripke models
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DOI 10.1007/s10992-011-9207-1
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References found in this work BETA

The Taming of the True.Neil Tennant - 1997 - Oxford, England: Oxford University Press.
Intuitionism Disproved?Timothy Williamson - 1982 - Analysis 42 (4):203--7.
Mathematical Modal Logic: A View of its Evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.
What One May Come to Know.J. van Benthem - 2004 - Analysis 64 (2):95-105.

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Citations of this work BETA

Intuitionistic epistemic logic.Sergei Artemov & Tudor Protopopescu - 2016 - Review of Symbolic Logic 9 (2):266-298.
A Canonical Model Construction for Intuitionistic Distributed Knowledge.Gerhard Jäger & Michel Marti - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 420-434.

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