“Reductio ad absurdum” and Łukasiewicz’s modalities

Sergei P. Odintsov

DOI: http://dx.doi.org/10.12775/LLP.2003.008

Abstract


The present article contains part of results from my lecture delivered at II Flemish-Polish workshop on Ontological Foundation of Paraconsistency.

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References


Batens, D., Paraconsistent extensional propositional logics’, Logique et Analyse 23 (1980), 195–234.

Batens, D., K. De Clercq, and N. Kurtonina, ‘Embedding and interpolation for some paralogics. The propositional case’, Rep. on Math. Logic 33 (1999), 29–44.

Bernays, P., ‘Review of [5] and [6]’, J. Symb. Logic 18 (1953), 266–268.

da Costa, N.C.A., ‘On the theory of inconsistent formal systems’, Notre Dame J. Form. Logic 15 (1974), 497–510. Bull. Sect. Logic 23, No. 2 (1994), 98–105.

Curry, H. B., ‘On the definition of negation by a fixed proposition in the inferential calculus’, J. Symb. Logic 17 (1952), 98–104.

Curry, H. B., ‘The system LD’, J. Symb. Logic 17 (1952), 35–42.

Curry, H. B., Foundations of mathematical logic, McGrow-Hill Book Company, New York, 1963.

Dosen, K., ‘Negative modal operators in intuitionistic logic’, Publ. Inst. Math., Nouv. Ser. 35(49), (1984), 15–20.

Dosen, K., ‘Negation as a modal operator’, Rep. Math. Logic 20 (1986), 15–28.

Dosen, K., ‘Negation in the light of modal logic’, in D. Gabbay, H. Wansing (eds.) What is Negation?, Kluwer, Dordrecht, 1999, 77–86.

Font, J.M. and P. Hajek, ‘ Łukasiewicz and modal logic’, Math. Preprint Ser., No. 278, Univ. de Barselona, 2000.

van Heijenoort, J., From Frege to Gödel. A source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge, 1967.

Johansson, I., ‘Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus’, Compositio Mathematika 4 (1937), 119–136.

Karpenko, A. S., ‘Two three-valued isomorphs of classical propositional logic and their combinations’, in First World Congress on Paraconsistency, Abstracts, Ghent, 1997, 92–94.

Kolmogorov, A.N., ‘On the principle of excluded middle’, Matematicheskij sbornik 32 (1925), 646–667 [in Russian]. English translation [12], 414–437.

Łukasiewicz, J., ‘A system of modal logic’, The Journal of Computing Systems 1 (1953), 111–149. Reprinted in [18], 352–390.

Łukasiewicz, J., Aristotle’s syllogistic from the standpoint of modern formal logic, (2nd enlarged edition), Clarendon Press, Oxford, 1957.

Łukasiewicz, J., Selected works, edited by L. Borkowski, Stud. in Logic and the Found. of Math. North-Holland, Amsterdam, 1970.

Odintsov, S. P., ‘Maximal paraconsistent extension of Johansson logic’, Logique et analyse 161–162–163 (1998), 107–120.

Odintsov, S. P., Isomorphs of the logic of classical refutability and their generalizations, Proceedings of the seminar of logical center, Inst. of Philosophy of RAS, Moscow, 1998, 48–61.

Odintsov, S. P., ‘Logic of classical refutability and class of extensions of minimal logic’, Logic and Logical Philosophy 9 (2002), 91–107.

Odintsov, S. P., ‘Algebraic semantics and Kripke semantics for extensions of minimal logic’, Logicheskije issledovaninja, No.2, 1999 [in Russian].

Odintsov, S.P., ‘Negatively equivalent extensions of minimal logic and their logics of contradictions’, Logical investigations 7 (2000), 119–127.

Odintsov, S.P., ‘Representation of j-algebras and Segerberg’s logics’, Logique et analyse 165–166 (1999), 81–106.

Porte, J., ‘The -system and the L-system of modal logic’, Notre Dame J. formal Logic 20 (1979), 915–920.

Porte, J., ‘Lukasiewicz’s L-modal system and classical refutability’, Logique Anal. Now. Ser. 27 (1984), 87–92.

Priest, G., Paraconsistent logic. in: D.Gabbay, H.Guenter (eds.) Handbook of Philosophical Logic, second edition.

Pynko, A. P. ‘Algebraic study of Sette’s maximal paraconsistent logic’, Studia Logica 54 (1995), 89–128.

Rescher, N., Many-valued Logic, N.Y., 1969.

Sette, A.M., ‘On the propositional calculus P1’, Mathematica Japonicae 18, No. 3 (1973), 173–180.

Wojtylak, P., ‘Mutual interpretability of sentential logic I’, Rep. on Math. Logic 11 (1981), 69–89.

Wojtylak, P., ‘Mutual interpretability of sentential logic II’, Rep. on Math. Logic 12 (1981), 51–66.








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Financed by MNiSW on the basis of agreement no. 706/P-DUN/2018 (dated 10/05/18). Project 1: “Preparation of articles in English for eight editions of the journal Logic and Logical Philosophy over the period 2018–19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 64800 zł. Project 4: “Digitalisation of eight editions of the journal Logic and Logical Philosophy over the period 2018-19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 18600 zł.


ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

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