Syntax and semantics of simple paracomplete logics
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09.04.2013
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Abstract
For an arbitrary fixed element $\beta$ in $\{1; 2; 3; ...; \omega\}$ both a sequent calculus and a natural deduction calculus which axiomatise simple paracomplete logic $I_{2;\beta}$ are built. Additionally, a valuation semantic which is adequate to logic $I_{2;\beta}$ is constructed. For an arbitrary fixed element $\gamma$ in $\{1; 2; 3;...\}$ a cortege semantic which is adequate to logic $I_{2;\gamma}$ is described. A number of results obtainable with the axiomatisations and semantics in question are formulated.
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How to Cite
Popov V., Shangin V. O. Syntax and semantics of simple paracomplete logics // Logicheskie Issledovaniya / Logical Investigations. 2013. VOL. 19. C. 325-333.
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References
Bolotov, A., Grigoryev, O., and Shangin, V., Automated Natural Deduction for Propositional Linear-time Temporal Logic, Proceedings of the 14th International Symposium on Temporal Representation and Reasoning (Time2007), Alicante, Spain, June 28-June 30, pp. 47–58, 2007.
Bolotov, A.E., Shangin, V., Natural Deduction System in Paraconsistent Setting: Proof Search for PCont, Journal of Intelligent Systems, 21(1):1–24, 2012.
Gentzen, G., Investigations into logical deductions, Mathematical theory of logical deduction, Nauka Publishers, M., 1967, pp. 9–74 (in Russian).
Kleene, S.C., Introduction to Metamathematics, Ishi Press International, 1952.
Popov, V.M., On the logic related to A. Arruda’s system V1, Logic and Logical Philosophy, 7:87–90, 1999.
Popov, V.M., Intervals of simple paralogics, Proceedings of the V conference ‘Smirnov Readings in Logic’, June, 20-22, 2007, M., 2007, pp. 35–37 (in Russian).
Popov, V.M., Two sequences of simple paraconsistent logics, Logical investigations, Vol. 14, M., 2007, pp. 257–261 (in Russian).
Popov, V.M., Two sequence of simple paracomplete logics, Logic today: theory, history and applications. The proceedings of X Russian conference, June, 26-28, 2008, St.-Petersburg, SPbU Publishers, 2008, pp. 304–306 (in Russian).
Popov, V.M., Semantical characterization of paracomplete logics $I_{2,1}$, $I_{2,2}$, $I_{2,3}$, ... , Logic, methodology: actual problems and perspectives. The proceedings of conference, Rostov-on-Don, UFU Publishers, 2010, pp. 114–116 (in Russian).
Popov, V.M., Sequential characterization of simple paralogics, Logical investigations, 16:205–220, 2010 (in Russian).
Vasiliev, N.A., Imaginary (non-Aristotelian) logic, Vasiliev N.A. Imaginary logic. Selected works, M., Nauka Publishers, 1989, pp. 53–94. (in Russian).
Bolotov, A.E., Shangin, V., Natural Deduction System in Paraconsistent Setting: Proof Search for PCont, Journal of Intelligent Systems, 21(1):1–24, 2012.
Gentzen, G., Investigations into logical deductions, Mathematical theory of logical deduction, Nauka Publishers, M., 1967, pp. 9–74 (in Russian).
Kleene, S.C., Introduction to Metamathematics, Ishi Press International, 1952.
Popov, V.M., On the logic related to A. Arruda’s system V1, Logic and Logical Philosophy, 7:87–90, 1999.
Popov, V.M., Intervals of simple paralogics, Proceedings of the V conference ‘Smirnov Readings in Logic’, June, 20-22, 2007, M., 2007, pp. 35–37 (in Russian).
Popov, V.M., Two sequences of simple paraconsistent logics, Logical investigations, Vol. 14, M., 2007, pp. 257–261 (in Russian).
Popov, V.M., Two sequence of simple paracomplete logics, Logic today: theory, history and applications. The proceedings of X Russian conference, June, 26-28, 2008, St.-Petersburg, SPbU Publishers, 2008, pp. 304–306 (in Russian).
Popov, V.M., Semantical characterization of paracomplete logics $I_{2,1}$, $I_{2,2}$, $I_{2,3}$, ... , Logic, methodology: actual problems and perspectives. The proceedings of conference, Rostov-on-Don, UFU Publishers, 2010, pp. 114–116 (in Russian).
Popov, V.M., Sequential characterization of simple paralogics, Logical investigations, 16:205–220, 2010 (in Russian).
Vasiliev, N.A., Imaginary (non-Aristotelian) logic, Vasiliev N.A. Imaginary logic. Selected works, M., Nauka Publishers, 1989, pp. 53–94. (in Russian).