Rational Agency from a Truth-Functional Perspective

• Authors: Kubyshkina Ekaterina , Zaitsev Dmitry V.
• Languages of publication: EN

Abstracts

EN

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 (an “ontological” and an “epistemic” one) 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

EN

many-valued logics; generalized truth values; Church-Fitch’s paradox

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2016
• Volume: 25
• Issue: 4
• Pages: 499-520

Dates

online

2016-07-15

Contributors

author

Kubyshkina Ekaterina

• Department of Philosophy, University of Paris 1 Panthéon – Sorbonne, Institute for History and Philosophy of Sciences and Technology, 13, rue du Four, 75006 Paris, France

author

Zaitsev Dmitry V.

• Department of Philosophy, Lomonosov Moscow State University, “Shuvalovskiy” bldg, MSU, Leninskiye gory, 119991, Moscow, Russia

References

• Beall, J.C., “Fitch’s proof, verificationism, and the knower paradox”, Australasian Journal of Philosophy, 78 (2000): 241–247. DOI: 10.1080/00048400012349521
• Beall, J.C., “Knowability and possible epistemic oddities”, pages 105–125, in [27], 2009. DOI: 10.1093/acprof:oso/9780199285495.003.0009
• Belnap, N.D., “How a computer should think”, pages 30–55 in Contemporary aspects of philosophy, G. Ryle (ed.), Oriel Press Ltd, Stocksfield, 1977.
• Belnap, N.D., “A useful four-valued logic”, pages 5–37 in Modern Uses of Multiple-valued Logic, M. Dunn and G. Epstein (eds.), volume 2 of the series “Episteme”, D. Reidel Publishing Company, Dordrecht, 1977. DOI: 10.1007/978-94-010-1161-7_2
• Burgess, J., 2009, “Can truth out?”, pages 147–162 in [27], 2009. DOI: 10.1017/CBO9780511487347.012
• Duc, H.N., “Reasoning about rational, but not logically omniscient, agents”, Journal of Logic and Computation, 7, 5 (1997): 633–648. DOI: 10.1093/logcom/7.5.633
• Dunn, J.M., “Intuitive semantics for first-degree entailments and ‘coupled trees’ ”, Philosophical Studies, 29 (1976): 149–168. DOI: 10.1007/BF00373152
• Dunn, J.M., “Partiality and its dual”, Studia Logica, 66 (2000): 5–40. DOI: 10.1023/A:1026740726955
• Dummett, M., “Victor’s error”, Analysis, 61 (2001): 1–2. DOI: 10.1093/analys/61.1.1
• Dummett, M., “Fitch’s paradox of knowability”, pages 51–52 in [27], Oxford University Press, Oxford, 2009. DOI: 10.1093/acprof:oso/9780199285495.003.0005
• Edington, D., “The paradox of knowability”, Mind, 94 (1985): 557–568. DOI: 10.1093/mind/XCIV.376.557
• Gottwald, S., A treatise on many-valued logic, Baldock, Research Studies Press, 2001.
• Hintikka, J., Knowledge and Belief, Cornell University Press, Ithaca, N.Y., 1962.
• Kleene, S.C., “On a notation for ordinal numbers”, Journal of Symbolic Logic, 3 (1938): 150–155. DOI: 10.2307/2267778
• Kleene, S.C., Introduction to Metamathematics, Van Nostrand, Amsterdam and Princeton, 1952.
• Łukasiewicz, J., “Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls”, Comptes rendus de la Société des Sciences et des Lettres de Varsovie, 23 (1930): 1–21. English translation in [18].
• Łukasiewicz, J., and A. Tarski, “Untersuchungen über den Aussagenkalküls”, Comptes rendus de la Société des Sciences et des Lettres de Varsovie, 23 (1930): 1–21. English translation in [18].
• Łukasiewicz, J., Selected Works, L. Borkowski (ed.), North-Holland, Amsterdam, 1970.
• Maffezioli, P., A. Naibo, A., and S. Negri, “The Church–Fitch knowability paradox in the light of structural proof theory”, Synthese, 190, 14 (2013):2677–2716. DOI: 10.1007/s11229-012-0061-7
• Nozick, R., Philosophical Explanations (Chapter 3), Harvard University Press, Cambridge, MA, 1981.
• Martin-Löf, P., “Truth and knowability: On the principles C and K of Michael Dummett”, pages 105–114 in Truth in mathematics, G. Dales and G. Oliveri (eds.), Oxford University Press, Oxford, 1998.
• Odintsov, S.P., and H. Wansing, “The logic of generalized truth values and the logic of bilattices”, Studia Logica, 103, 1 (2015): 91–112. DOI: 10.1007/s11225-014-9546-3
• Post, E., “Introduction to a general theory of elementary propositions”, American Journal of Mathematics, 43 (1921): 163–185. DOI: 10.2307/2370324
• Priest, G., “Beyond the limits of knowledge”, pages 93–104 in [27], 2009. DOI: 10.1093/acprof:oso/9780199285495.003.0008
• Proietti C., and G. Sandu, “Fitch’s paradox and ceteris paribus modalities”, Synthese,173,1,(2010):75–87. DOI: 10.1007/s11229-009-9677-7
• Restall G., “Not every truth can be known (at least, not all at once)”, pages 339–354, in [27], 2009. DOI: 10.1093/acprof:oso/9780199285495.003.0022
• Salerno J., New Essays on the Knowability Paradox, Oxford University Press, 2009.
• Shramko, Y., J.M. Dunn, and T. Takenaka, “The trilatice of constructive truth values”, Journal of Logic and Computation, 11 (2001): 761–788. DOI: 10.1093/logcom/11.6.761
• Shramko, Y., and H. Wansing, “Some useful 16-valued logics: How a computer network should think”, Journal of Philosophical Logic, 34, 2 (2005): 121–153. DOI: 10.1007/s10992-005-0556-5
• Shramko, Y., and H. Wansing, “Hyper-contradictions, generalized truth-values and logics of truth and falsehood”, Journal of Logic, Language and Information, 15, 4 (2006): 403–424. DOI: 10.1007/s10849-006-9015-0
• Shramko, Y., and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values, Springer, 2011.
• Tennant, N., The Taming of the True, Oxford University Press, Oxford, 1997.
• Tennant, N., “Revamping the restriction strategy”, pages 223–238 in [27], 2009. DOI: 10.1093/acprof:oso/9780199285495.003.0015
• Wansing H., “Diamonds are a philosopher’s best friends”, Journal of Philosophical Logic, 31, 6 (2002): 591–612. DOI: 10.1023/A:1021256513220
• Williamson, T., “Intuitionism disproved?”, Analysis, 42 (1982): 203–207. DOI: 10.1093/analys/42.4.203
• Williamson, T., “Verificationism and non-distributive knowledge”, Australasian Journal of Philosophy, 71 (1993): 78–86. DOI: 10.1080/00048409312345072
• Wintein, S., and R.A. Muskens, “From bi-facial truth to bi-facial proofs”, Studia Logica, 103, 3, (2015): 545–558. DOI: 10.1007/s11225-014-9578-8
• Zaitsev, D.V., “A few more useful 8-valued logics for reasoning with tetralattice EIGHT4”, Studia Logica, 92, 2 (2009): 265–280. DOI: 10.1007/s11225-009-9198-x
• Zaitsev, D.V., and Y. Shramko, “Bi-facial truth: A case for generalized truth values”, Studia Logica, 101, 6 (2013): 299–318. DOI: 10.1007/s11225-013-9534-z
• Zaitsev D., “Logics of generalized classical truth values”, pages 331–341 in The Logica Yearbook 2014, P. Arazim and M. Peliš (eds.), College Publications London, 2015.

Identifiers

DOI

10.12775/LLP.2016.016