Rational Agency from a Truth-Functional Perspective

Ekaterina Kubyshkina, Dmitry V. Zaitsev

DOI: http://dx.doi.org/10.12775/LLP.2016.016


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.


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

Full Text:



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.

Print ISSN: 1425-3305
Online ISSN: 2300-9802

Partnerzy platformy czasopism