Deductive systems with unified multiple-conclusion rules
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Опубликован:
13.12.2020
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Аннотация
Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and are being treated in the same way. The suggested approach is based on the ideas of Ƚukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. A special attention is paid to the logics in which each proposition is either accepted or rejected.
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Как цитировать
Citkin A. Deductive systems with unified multiple-conclusion rules // Логические исследования / Logical Investigations. 2020. Т. 26. № 2. C. 87-105.
Выпуск
Раздел
Философия и логика
Copyright (c) 2020 Alex Citkin
Это произведение доступно по лицензии Creative Commons «Attribution-NonCommercial» («Атрибуция — Некоммерческое использование») 4.0 Всемирная.
Литература
Bochvar, 1939 – Bochvar, D.A. “On a three valued calculus and its application to the analysis of contradictories”, Matematicheskii Sbornik, 1939, Vol. 4, No. 2, pp. 287–308.
Carnap, 1942 – Carnap, R. Introduction to Semantics. Harvard University Press, Cambridge, Mass, 1942.
Carnap, 1943 – Carnap, R. Formalization of Logic. Harvard University Press, Cambridge, Mass, 1943.
Citkin, 2015 – Citkin, A. “A meta-logic of inference rules: syntax”, Log. Log. Philos., 2015, Vol. 24, No. 3, pp. 313–337.
Goranko, 2019 – Goranko, V. “Hybrid deduction-refutation systems”, Axioms, 2019, Vol. 8, No. 4, p. 118.
Goranko et al., 2020 – Goranko, V., Pulcini, G., and Skura, T. “Refutation systems: An overview and some applications to philosophical logics”, in: Liu, F., Ono, H., and Yu, J. (eds.) Knowledge, Proof and Dynamics, Logic in Asia. Springer, Singapore, 2020, pp. 173–197.
Kracht, 2010 – Kracht, M. “Judgment and consequence relations”, J. Appl. NonClassical Logics, 2010, Vol. 20, No. 4, pp. 423–435.
Ƚukasiewicz, Jan, 1970 – Ƚukasiewicz, J. “Two-valued logic”, in: Borkowski, L., (ed.)
Selected Works, Studies in Logic and the Foundations of Mathematics. North-Holland, 1970, pp. 89–109. Translation of 1921 paper in Polish.
Pavlov, 2004 – Pavlov, S. Logika s operatorami istinnosti i lozhnosti [Logic with truth and falsehood operators]. Institute of Philosophy RAN, 2004. (In Russian)
Pavlov, 2011 – Pavlov, S. “The logic with truth and falsehood operators from a point of view of universal logic”, Log. Univers., 2011, Vol. 5, No. 2, pp. 319–325.
Restall, 2015 – Restall, G. “Assertion, denial, accepting, rejecting, symmetry, and paradox”, in: Carter, C.R. and Hjortland, O.T. (eds.), Foundations of Logical Consequence. Oxford University Press, 2015, pp. 310–321.
Rumfitt, 2000 – Rumfitt, I. “ ‘Yes’ and ‘No’ ”, Mind, 2000, Vol. 109, No. 436, pp. 781823.
Scott, 1974 – Scott, D.S. “Rules and derived rules”, in: Stenlund, S., editor, Logical Theory and Semantic Analysis, Essays dedicated to Stig Kanger. D. Reidel Publishing Company, 1974, pp. 147–161.
Shoesmith and Smiley, 2008 – Shoesmith, D.J. and Smiley, T.J. Multiple-conclusion logic. Cambridge University Press, Cambridge, 2008. Reprint of the 1978 original [MR0500331].
Skura, 2011 – Skura, T. “Refutation systems in propositional logic”, in: Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume 16 of Handbook of Philosophical Logic. Springer Netherlands, 2011, pp. 115–157.
Smiley, 1996 – Smiley, T. “Rejection”, Analysis (Oxford), 1996, Vol. 56, No. 1, pp. 1–9. Staszek, 1971 – Staszek, W. “On proofs of rejection”, Studia Logica, 1971, Vol. 29, pp. 17–25.
Torben, 2011 – Torben, B. Hybrid Logic and its Proof-Theory. Springer, 2011.
von Wright, 1987 – von Wright, G. “Truth-logic”, Logique et Analyse, 1987, Vol. 30, No. 120, pp. 311–334.
Wybraniec-Skardowska, 2018 – Wybraniec-Skardowska, U. “Rejection in Lukasiewicz’s and Slupecki’s sense”, in: The Lvov-Warsaw school. Past and present, Stud. Univers. Log. Birkh¨auser/Springer, Cham, 2018, pp. 575–597.
Carnap, 1942 – Carnap, R. Introduction to Semantics. Harvard University Press, Cambridge, Mass, 1942.
Carnap, 1943 – Carnap, R. Formalization of Logic. Harvard University Press, Cambridge, Mass, 1943.
Citkin, 2015 – Citkin, A. “A meta-logic of inference rules: syntax”, Log. Log. Philos., 2015, Vol. 24, No. 3, pp. 313–337.
Goranko, 2019 – Goranko, V. “Hybrid deduction-refutation systems”, Axioms, 2019, Vol. 8, No. 4, p. 118.
Goranko et al., 2020 – Goranko, V., Pulcini, G., and Skura, T. “Refutation systems: An overview and some applications to philosophical logics”, in: Liu, F., Ono, H., and Yu, J. (eds.) Knowledge, Proof and Dynamics, Logic in Asia. Springer, Singapore, 2020, pp. 173–197.
Kracht, 2010 – Kracht, M. “Judgment and consequence relations”, J. Appl. NonClassical Logics, 2010, Vol. 20, No. 4, pp. 423–435.
Ƚukasiewicz, Jan, 1970 – Ƚukasiewicz, J. “Two-valued logic”, in: Borkowski, L., (ed.)
Selected Works, Studies in Logic and the Foundations of Mathematics. North-Holland, 1970, pp. 89–109. Translation of 1921 paper in Polish.
Pavlov, 2004 – Pavlov, S. Logika s operatorami istinnosti i lozhnosti [Logic with truth and falsehood operators]. Institute of Philosophy RAN, 2004. (In Russian)
Pavlov, 2011 – Pavlov, S. “The logic with truth and falsehood operators from a point of view of universal logic”, Log. Univers., 2011, Vol. 5, No. 2, pp. 319–325.
Restall, 2015 – Restall, G. “Assertion, denial, accepting, rejecting, symmetry, and paradox”, in: Carter, C.R. and Hjortland, O.T. (eds.), Foundations of Logical Consequence. Oxford University Press, 2015, pp. 310–321.
Rumfitt, 2000 – Rumfitt, I. “ ‘Yes’ and ‘No’ ”, Mind, 2000, Vol. 109, No. 436, pp. 781823.
Scott, 1974 – Scott, D.S. “Rules and derived rules”, in: Stenlund, S., editor, Logical Theory and Semantic Analysis, Essays dedicated to Stig Kanger. D. Reidel Publishing Company, 1974, pp. 147–161.
Shoesmith and Smiley, 2008 – Shoesmith, D.J. and Smiley, T.J. Multiple-conclusion logic. Cambridge University Press, Cambridge, 2008. Reprint of the 1978 original [MR0500331].
Skura, 2011 – Skura, T. “Refutation systems in propositional logic”, in: Gabbay, D. M. and Guenthner, F., editors, Handbook of Philosophical Logic, volume 16 of Handbook of Philosophical Logic. Springer Netherlands, 2011, pp. 115–157.
Smiley, 1996 – Smiley, T. “Rejection”, Analysis (Oxford), 1996, Vol. 56, No. 1, pp. 1–9. Staszek, 1971 – Staszek, W. “On proofs of rejection”, Studia Logica, 1971, Vol. 29, pp. 17–25.
Torben, 2011 – Torben, B. Hybrid Logic and its Proof-Theory. Springer, 2011.
von Wright, 1987 – von Wright, G. “Truth-logic”, Logique et Analyse, 1987, Vol. 30, No. 120, pp. 311–334.
Wybraniec-Skardowska, 2018 – Wybraniec-Skardowska, U. “Rejection in Lukasiewicz’s and Slupecki’s sense”, in: The Lvov-Warsaw school. Past and present, Stud. Univers. Log. Birkh¨auser/Springer, Cham, 2018, pp. 575–597.