Logic and Logical Philosophy 25 (4):499-520 (2016)

Ekaterina Kubyshkina
University of Campinas
Dmitry Zaitsev
Lomonosov Moscow State University
The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truth-functionally. In order to obtain this system, we propose a four-valued logic, that we call the logic of rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truth-functional negations is provided. These negations allow us to express the statements about knowing or not knowing something at the syntactic level. Moreover, such a system is applied to the analysis of knowability paradox. In particular, we show that the paradox is not derivable in terms of the logic of rational agent.
Keywords many-valued logics   generalized truth values   Church-Fitch’s paradox
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DOI 10.12775/LLP.2016.016
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References found in this work BETA

The Paradox of Knowability.Dorothy Edgington - 1985 - Mind 94 (376):557-568.
Victor's Error.Michael Dummett - 2001 - Analysis 61 (1):1–2.
"Victor's Error".Michael Dummett - 2001 - Analysis 61 (1):1-2.
Fitch's Paradox of Knowability.Michael Dummett - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press.

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Citations of this work BETA

The Logic of Internal Rational Agent.Yaroslav Petrukhin - 2021 - Australasian Journal of Logic 18 (2).
Many-Valued Logics and Bivalent Modalities.Edson Bezerra & Giorgio Venturi - forthcoming - Logic and Logical Philosophy:1-26.

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