Abstract
In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.
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References
Asenjo, F.G.: A calculus of antinomies. Notre Dame J. Formal Log. 7, 103–105 (1966)
Belikov, A.A.: Axiomatization of Dunn–Belnap’s logic with the sole designated value (in Russian). In: The Proceeding of the 9th Smirnov Readings in Logic. Moscow: Contemporary Notebooks, pp. 53–55 (2015)
Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-valued Logic. Reidel Publishing Company, Boston, pp. 7–37 (1977)
Belnap, N.D.: How a computer should think. In: Rule, G. (ed.) Contemporary Aspects of Philosophy. Oriel Press Ltd, Stocksfield, pp. 30–56 (1977)
Bochvar, D.A.: On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus. Hist. Philos. Log. 2, 87–112 (1981). F
Bonzio, S., Gil-Férez, J., Paoli, F., Peruzzi, L.: On paraconsistent weak kleene logic: axiomatisation and algebraic analysis. Stud. Log. 105, 253–297 (2017)
Bolotov, A., Shangin, V.: Natural deduction system in paraconsistent setting: proof search for PCont. J. Intell. Syst. 21, 1–24 (2012)
Dunn, J.M.: Intuitive semantics for first-degree entailment and coupled trees. Philos. Stud. 29, 149–168 (1976)
Fitting, M.: Kleene’s logic, generalized. J. Log. Comput. 1, 797–810 (1991)
Fitting, M.: Kleene’s three valued logics and their children. Fundam. Inform. 20, 113–131 (1994)
Fitting, M.: Negation as refutation. In: Parikh, R. (ed.) Proceedings of the Fourth Annual Symposium on Logic in Computer Science, IEEE, pp. 63–70 (1989)
Halldén, S.: The Logic of Nonsense. Lundequista Bokhandeln, Uppsala (1949)
Kleene, S.C.: Introduction to metamathematics. Sixth Reprint, Wolters-Noordhoff Publishing and North-Holland Publishing Company (1971)
Kleene, S.C.: On a notation for ordinal numbers. J. Symb. Log. 3(1), 150–155 (1938)
Komendantskaya, E.Y.: Functional expressibility of regular Kleene’s logics (in Russian). Log. Investig. 15, 116–128 (2009)
Kooi, B., Tamminga, A.: Completeness via correspondence for extensions of the logic of paradox. Rev. Symb. Log. 5(4), 720–730 (2012)
Łukasiewicz, J.: On three-valued logic. In: Borkowski, L. (ed.) Jan Łukasiewicz: Selected Works, Amsterdam, North-Holland Publishing Company, pp. 87–88 (1997). English translation of Łukasiewicz’s paper of 1920
Petrukhin, Y.I.: Correspondence analysis for first degree entailment. Log. Investig. 22(1), 108–124 (2016)
Petrukhin, Y.: Natural deduction for three-valued regular logics. Log. Log. Philos. Online first article, pp. 1–10 (2016). doi:10.12775/LLP.2016.025
Petrukhin, Y.: Natural deduction for four-valued both regular and monotonic logics. Log. Log. Philos. Online first article, pp. 1–14 (2017). doi:10.12775/LLP.2017.001
Pietz, A., Rivieccio, U.: Nothing but the truth. J. Philos. Log. 42, 125–135 (2013)
Priest, G.: Paraconsistent logic. In: Gabbay, M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 6, 2nd edn, pp. 287–393. Kluwer, Dordrecht (2002)
Priest, G.: The logic of paradox. J. Philos. Log. 8, 219–241 (1979)
Tamminga, A.: Correspondence analysis for strong three-valued logic. Log. Investig. 20, 255–268 (2014)
Tomova, N.E.: About four-valued regular logics (in Russian). Log. Investig. 15, 223–228 (2009)
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Petrukhin, Y.I. Natural Deduction for Fitting’s Four-Valued Generalizations of Kleene’s Logics. Log. Univers. 11, 525–532 (2017). https://doi.org/10.1007/s11787-017-0169-0
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DOI: https://doi.org/10.1007/s11787-017-0169-0