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Logic of Knowledge and Utterance and the Liar

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Abstract

We extend the ordinary logic of knowledge based on the operator K and the system of axioms S5 by adding a new operator Uϕ, standing for “the agent utters ϕ”, and certain axioms and a rule for U, forming thus a new system KU. The main advantage of KU is that we can express in it intentions of the speaker concerning the truth or falsehood of the claims he utters and analyze them logically. Specifically we can express in the new language various notions of lying, as well as of telling the truth. Consequently, as long as lying or telling the truth about a fact is an intentional mode of the speaker, we can resolve the Liar paradox, or at least some of its variants, turning it into an ordinary (false or true) sentence. Also, using Kripke structures analogous to those employed by S. Kraus and D. Lehmann in [3] for modelling the logic of knowledge and belief, we offer a sound and complete semantics for KU.

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Authors and Affiliations

  1. Department of Mathematics, University of Thessaloniki, 540 06, Thessaloniki, Greece

    Athanassios Tzouvaras

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  1. Athanassios Tzouvaras
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Tzouvaras, A. Logic of Knowledge and Utterance and the Liar. Journal of Philosophical Logic 27, 85–108 (1998). https://doi.org/10.1023/A:1017946620987

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  • DOI: https://doi.org/10.1023/A:1017946620987

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