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AUTOMATED CORRESPONDENCE ANALYSIS FOR THE BINARY EXTENSIONS OF THE LOGIC OF PARADOX

Published online by Cambridge University Press:  03 July 2017

YAROSLAV PETRUKHIN  and
VASILY SHANGIN
YAROSLAV PETRUKHIN*
Affiliation:
Faculty of Philosophy, Department of Logic, Lomonosov Moscow State University
VASILY SHANGIN*
Affiliation:
Faculty of Philosophy, Department of Logic, Lomonosov Moscow State University
*
*FACULTY OF PHILOSOPHY DEPARTMENT OF LOGIC LOMONOSOV MOSCOW STATE UNIVERSITY LOMONOSOVSKY PROSPEKT, 27-4, GSP-1 MOSCOW 119991, RUSSIAE-mail: [email protected]
†FACULTY OF PHILOSOPHY DEPARTMENT OF LOGIC LOMONOSOV MOSCOW STATE UNIVERSITY LOMONOSOVSKY PROSPEKT, 27-4, GSP-1 MOSCOW 119991, RUSSIAE-mail: [email protected]
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Abstract

B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.

Keywords

03B3568T1503B50non-classical logiclogic of paradoxproof theoryproof searchcorrespondence analysisnatural deduction
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 4 , December 2017 , pp. 756 - 781
Copyright
Copyright © Association for Symbolic Logic 2017 

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References

BIBLIOGRAPHY

Anderson, A. R. & Belnap, N. D. (1975). Entailment. The Logic of Relevance and Necessity, Vol. 1. Princeton, NJ: Princeton University Press.Google Scholar
Anderson, A. R. & Belnap, N. D. (1992). Entailment. The Logic of Relevance and Necessity, Vol. 2. Princeton, NJ: Princeton University Press.Google Scholar
Asenjo, F. G. (1954). La Idea de un Calculo de Antinomias. Seminario Matematico. Universidad Nacional de La Plata.Google Scholar
Asenjo, F. G. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 7(1), 103–105.CrossRefGoogle Scholar
Asenjo, F. G. & Tamburino, J. (1975). Logic of antinomies. Notre Dame Journal of Formal Logic, 16(1), 17–44.Google Scholar
Avron, A. (1991). Natural 3-valued logics—Characterization and proof theory. The Journal of Symbolic Logic, 56(1), 276–294.CrossRefGoogle Scholar
Avron, A. (1986). On an implicational connective of RM. Notre Dame Journal of Formal Logic, 27(2), 201–209.CrossRefGoogle Scholar
Batens, D. (1980). Paraconsistent extensional propositional logics. Logique et Analyse, 23(90–91), 195–234.Google Scholar
Batens, D. (1989). Dynamic dialectical logic. In Priest, G., Routley, R., and Norman, J., editors. Paraconsistent Logic Essays on the Inconsistent. Munich: Philosophia Verlag, pp. 187–217.Google Scholar
Bolotov, A., Basukoski, A., Grigoriev, O., & Shangin, V. (2006). Natural deduction calculus for linear-time temporal logic. Lecture Notes in Computer Science, 4160, 56–68.Google Scholar
Bolotov, A., Bocharov, V., Gorchakov, A., & Shangin, V. (2005). Automated first order natural deduction. In Prasad, B., editor. Proceedings of the 2nd Indian International Conference on Artificial Intelligence (IICAI-2005). Tumkur: IICAI, pp. 1292–1311.Google Scholar
Bolotov, A. & Shangin, V. (2012). Natural deduction system in paraconsistent setting: Proof search for PCont. Journal of Intelligent Systems, 21(1), 1–24.CrossRefGoogle Scholar
Carnielli, W. A., Marcos, J., & Amo, S. (2000). Formal inconsistency and evolutionary databases. Logic and Logical Philosophy, 8, 115–152.Google Scholar
Copi, I. M., Cohen, C., & McMahon, K. (2011). Introduction to Logic (fourteenth edition). New York: Routledge.Google Scholar
D’Agostino, M. (2005). Classical natural deduction. In Artemov, S., Barringer, H., d’Avila Garcez, A., Lamb, L. C., and Woods, J., editors. We Will Show Them! Essays in Honour of Dov Gabbay, Vol. 1. London: College Publications, pp. 429–468.Google Scholar
Da Costa, N. C. A. & Alves, E. H. (1981). Relations between paraconsistent logic and many-valued logic. Bulletin of the Section of Logic, 10(4), 185–190.Google Scholar
D’Ottaviano, I. M. L. & da Costa, N. C. A. (1970). Sur un probléme de Jaśkowski. Comptes Rendus de l’Académie des Sciences de Paris, 270, 1349–1353.Google Scholar
Epstein, R. L. (1990). The Semantic Foundations of Logic. Vol. 1: Propositional Logic. Dordrecht: Kluwer.CrossRefGoogle Scholar
Epstein, R. L. & D’Ottaviano, I. M. L. (2000). Paraconsistent logic: J3. In Epstein, R. L., editor. Propositional Logics, Second Edition, Chapter 9. Belmont, CA: Wadsworth Publishing Company.Google Scholar
Gabbay, D. M. (1994). What is a logical system? In Gabbay, D. M., editor. What is a Logical System? Oxford: Clarendon Press, pp. 179–216.Google Scholar
Gödel, K. (1932). Zum intuitionistischen Aussgenkalkül. Anzeiger der Akademie der Wissenschaften in Wien, 69, 65–66. English translation: On the intuitionistic propositional calculus. In Gödel, K., editor. Collected Works, Vol. 1. New York, 1986, pp. 300–301.Google Scholar
Heyting, A. (1930). Die Formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Academie der Wissenschaften zu Berlin, Berlin, 42–46. English translation: The Formal Rules of Intuitionistic Logic. In Mancosu, P., editor. From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s. Oxford, 1998, pp. 311–328.Google Scholar
Jaśkowski, S. (1936). Recherches sur le système de la logique intuitioniste. Actes du Congrès International de Philosophie Scientifique, 6, 58–61. English translation: Investigations into the system of intuitionistic logic. Studia Logica, 1975, 34, 117–120.Google Scholar
Jaśkowski, S. (1948). Rachunek zdań dla systemów dedukcyjnych sprzecznych. Studia Societatis Scientiarum Torunensis, Sectio A, Vol. I, No. 5, Toruń, 57–77. English translation: A propositional calculus for inconsistent deductive systems. Logic and Logical Philosophy, 7, 1999, 35–56.Google Scholar
Karpenko, A. & Tomova, N. (2017). Bochvar’s three-valued logic and literal paralogics: Their lattice and functional equivalence. Logic and Logical Philosophy, 26(2), 207–235.Google Scholar
Kleene, S. C. (1938). On a notation for ordinal numbers. The Journal of Symbolic Logic, 3(4), 150–155.CrossRefGoogle Scholar
Kleene, S. C. (1952). Introduction to Metamathematics. New York & Toronto: D. van Nostrand Company, Inc.Google Scholar
Kooi, B. & Tamminga, A. (2012). Completeness via correspondence for extensions of the logic of paradox. The Review of Symbolic Logic, 5(4), 720–730.Google Scholar
Łukasiewicz, J. & Tarski, A. (1930). Untersuchungen über den Aussagenkalkul. Comptes Rendus des Séances de la Société des Sciences et des Letters de Varsovie, 3(23), 1–21. English translation: Investigations into the sentential calculus. In Łukasiewicz, J., editor. Selected Works. Amsterdam & Warszawa: North-Holland & PWN, 1970, pp. 131–152.Google Scholar
Marcos, J. (2005). On a problem of da Costa. In Sica, G., editor. Essays of the Foundations of Mathematics and Logic. Monza, Italy: Polimetrica International Scientific Publisher, pp. 53–69.Google Scholar
Martin, J. N. (1975). A syntactic characterization of Kleene’s strong connectives with two designated values. Mathematical Logic Quarterly, 21(1), 181–184.Google Scholar
Mortenson, C. (1989). Paraconsistency and C1 . In Priest, G., Routley, R., and Norman, J., editors. Paraconsistent Logic Essays on the Inconsistent. Munich: Philosophia Verlag, pp. 289–305.Google Scholar
Petrukhin, Y. (2016). Correspondence analysis for first degree entailment. Logical Investigations, 22(1), 108–124.Google Scholar
Popov, V. M. (1999). On the logics related to Arruda’s system V1. Logic and Logical Philosophy, 7, 87–90.Google Scholar
Prawitz, D. (1965). Natural Deduction. Stockholm: Almqvist & Wiksell.Google Scholar
Priest, G. (1979). The logic of paradox. Journal of Philosophical Logic, 8(1), 219–241.Google Scholar
Priest, G. (1984). Logic of paradox revisited. Journal of Philosophical Logic, 13(2), 153–179.Google Scholar
Priest, G. (2002). Paraconsistent logic. In Gabbay, D. M. and Guenthner, F., editors. Handbook of Philosophical Logic, Second Edition, Vol. 6. Dordrecht, The Netherlands: Kluwer Academic Publishers, pp. 287–393.Google Scholar
Resher, N. (1969). Many-Valued Logic. New York: McGraw Hill.Google Scholar
Roy, T. (2006). Natural derivations for priest, an introduction to non-classical logic. Australasian Journal of Logic, 5, 47–192.Google Scholar
Rozonoer, L. (1983a). On finding contradictions in formal theories. I. Automatica and Telemekhanica, 6, 113–124 (in Russian).Google Scholar
Rozonoer, L. (1983b). On finding contradictions in formal theories. II. Automatica and Telemekhanica, 7, 97–104 (in Russian).Google Scholar
Sahlqvist, H. (1975). Completeness and correspondence in the first and second order semantics for modal logic. In Kanger, S., editor. Proceeding of the Third Scandinavian Logic Symposium. Amsterdam: North-Holland Publishing Company, pp. 110–143.CrossRefGoogle Scholar
Sette, A. (1973). On propositional calculus P1 . Mathematica Japonica, 18, 173–180.Google Scholar
Sieg, W. & Pfenning, F. (guest editors) (1998). Note by the guest editors. Studia Logia, 60(1), 1.CrossRefGoogle Scholar
Sobociński, B. (1952). Axiomatization of a partial system of three-valued calculus of propositions. The Journal of Computing Systems, 1, 23–55.Google Scholar
Tamminga, A. (2014). Correspondence analysis for strong three-valued logic. Logical Investigations, 20, 255–268.Google Scholar
Tamminga, A. (2016). Sequent calculi for four-valued logic. Proceedings of the 7th International Conference “Teaching Logic and Prospects of its Development”, Taras Shevchenko National University of Kyiv (May 12–15, 2016), pp. 3–4.Google Scholar
Thomas, N. (2013). LP⇒: Extending LP with a strong conditional. Mathematics. Unpublished manuscript,https://arxiv.org/abs/1304.6467.Google Scholar
Tomova, N. E. (2012). A lattice of implicative extensions of regular Kleene’s logics. Reports on Mathematical Logic, 47, 173–182.Google Scholar
Tomova, N. E. (2015a). Erratum to: Natural implication and modus ponens principle. Logical Investigations, 21(2), 186–187.Google Scholar
Tomova, N. E. (2015b). Natural implication and modus ponens principle. Logical Investigations, 21(1), 138–143.Google Scholar
van Benthem, J. (1976). Modal correspondence theory. Ph.D. Thesis, Universiteit van Amsterdam, Amsterdam.Google Scholar
van Benthem, J. (2001). Correspondence theory. In Gabbay, D. M. and Guenthner, F., editors. Handbook of Philosophical Logic, Second Edition, Vol. 3. Dordrecht, The Netherlands: Kluwer Academic Publishers, pp. 325–408.Google Scholar