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Intuitionistic epistemology and modal logics of verification. (English) Zbl 06521586
van der Hoek, Wiebe (ed.) et al., Logic, rationality, and interaction. 5th international workshop, LORI 2015, Taipei, Taiwan, October 28–30, 2015. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 9394, 295-307 (2015).
Summary: The language of intuitionistic epistemic logic, IEL [3], captures basic reasoning about intuitionistic knowledge and belief, but its language has expressive limitations. Following Gödel’s explication of IPC as a fragment of the more expressive system of classical modal logic S4 we present a faithful embedding of IEL into S4V – S4 extended with a verification modality. The classical modal framework is finer-grained and more flexible, allowing us to make explicit various properties of verification.
For the entire collection see [Zbl 1325.68024].

68T27 Logic in artificial intelligence
Full Text: DOI
[1] Artemov, S.: Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7(1), 1–36 (2001) · Zbl 0980.03059
[2] Artemov, S., Protopopescu, T.: Discovering Knowability: A Semantical Analysis. Synthese 190(16), 3349–3376 (2013) · Zbl 1284.03024
[3] Artemov, S., Protopopescu, T.: Intuitionistic Epistemic Logic. Tech. rep. [math LO] (December 2014), http://arxiv.org/abs/1406.1582v2 · Zbl 1408.03004
[4] Blackburn, P., de Rijke, M., Vedema, Y.: Modal Logic. Cambridge University Press (2002)
[5] Chagrov, A., Zakharyaschev, M.: Modal Logic. Clarendon Press (1997)
[6] Constable, R.: Types in Logic, Mathematics and Programming. In: Buss, S. (ed.) Handbook of Proof Theory, pp. 683–786. Elsevier (1998) · Zbl 0914.03056
[7] Došen, K., Božić, M.: Models for Normal Intuitionistic Modal Logics. Studia Logica 43(3), 217–245 (1984) · Zbl 0634.03014
[8] Došen, K.: Models for Stronger Normal Intuitionistic Modal Logics 44(1) · Zbl 0634.03015
[9] Došen, K.: Intuitionistic Double Negation as a Necessity Operator. Publications de L’Institute Mathématique (Beograd)(NS) 35(49), 15–20 (1984) · Zbl 0555.03012
[10] Dummett, M.A.E.: Elements of Intuitionism. Clarendon Press (1977) · Zbl 0358.02032
[11] Fitting, M., Mendelsohn, R.: First-Order Modal Logic. Kluwer Academic Publishers (1998) · Zbl 1025.03001
[12] Gödel, K.: An Interpretation of the Intuitionistic Propositional Calculus. In: Feferman, S., Dawson, J.W., Goldfarb, W., Parsons, C., Solovay, R.M. (eds.) Collected Works, vol. 1, pp. 301–303. Oxford Univeristy Press (1933)
[13] Hendricks, V.F.: Formal and Mainstream Epistemology. Cambridge University Press (2006)
[14] Hirai, Y.: An Intuitionistic Epistemic Logic for Sequential Consistency on Shared Memory. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 272–289. Springer, Heidelberg (2010) · Zbl 1311.03060
[15] Leite, A.: Fallibilism. In: Dancy, J., Sosa, E., Steup, M. (eds.) A Companion to Epistemology, 2nd edn., pp. 370–375. Blackwell (2010)
[16] McKinsey, J.C.C., Tarski, A.: Some Theorems About the Sentential Calculi of Lewis and Heyting 13(1), 1–15 (1948) · Zbl 0037.29409
[17] Proietti, C.: Intuitionistic Epistemic Logic, Kripke Models and Fitch’s Paradox. Journal of Philosophical Logic 41(5), 877–900 (2012) · Zbl 1280.03020
[18] Troelstra, A., Schwichtenberg, H.: Basic Proof Theory. Cambridge University Press (2000) · Zbl 0957.03053
[19] Univalent Foundations Program: Homotopy Type Theory. Univalent Foundations Program (2013)
[20] Williamson, T.: On Intuitionistic Modal Epistemic Logic. Journal of Philosophical Logic 21(1), 63–89 (1992) · Zbl 0746.03014
[21] Wolter, F., Zakharyaschev, M.: Intuitionistic Modal Logics as Fragments of Classical Bimodal Logics. In: Orlowska, E. (ed.) Logic at Work, pp. 168–186. Springer (1999) · Zbl 0922.03023
[22] Wolter, F., Zakharyaschev, M.: Intuitionistic Modal Logic. In: Casari, E., Cantini, A., Minari, P. (eds.) Logic and Foundations of Mathematics, pp. 227–238. Kluwer Academic Publishers (1999) · Zbl 0955.03029
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