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Inconsistency-tolerant reasoning and paraconsistent logic are of growing importance not only in Knowledge Representation, AI and other areas of Computer Science, but also in Philosophical Logic. In this paper, a new logic, paraconsistent linear-time temporal logic (PLTL), is obtained semantically from the linear-time temporal logic LTL by adding a paraconsistent negation. Some theorems for embedding PLTL into LTL are proved, and PLTL is shown to be decidable. A Gentzentype sequent calculus PLT! for PLTL is introduced, and the completeness and cut-elimination theorems for this calculus are proved. In addition, a display calculus äPLT! for PLTL is defined.
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Tom
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1--23
Opis fizyczny
Bibliogr. 21 poz.
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autor
autor
- Waseda Institute for Advanced Study, 1-6-1 NishiWaseda, Shinjuku-ku, Tokyo 169-8050, Japan, drnkamide08@kpd.biglobe.ne.jp
Bibliografia
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- [2] A.R. Anderson and N.D. Belnap, Entailment: The Logic of Relevance and Necessity, Vol. I, Princeton University Press, Princeton, NJ, 1975.
- [3] N.D. Belnap, Display Logic, Journal of Philosophical Logic 11, pp. 375-417, 1982. Reprinted with minor changes as §62 of A.R. Anderson, N.D. Belnap, and J.M. Dunn, Entailment: the logic of relevance and necessity. Vol. 2, Princeton University Press, Princeton, 1992.
- [4] Y. Gurevich, Intuitionistic logic with strong negation, Studia Logica 36, pp. 49-59, 1977.
- [5] G.J. Holzmann, The SPIN model checker: Primer and reference manual, Addison-Wesley, 2006.
- [6] C. Kalicki, Infinitary propositional intuitionistic logic, Notre Dame Journal of Formal Logic 21, pp. 216-228, 1980.
- [7] N. Kamide, An equivalence between sequent calculi for linear-time temporal logic, Bulletin of the Section of Logic 35, pp. 187-194, 2006.
- [8] N. Kamide and H.Wansing, Combining linear-time temporal logic with constructiveness and paraconsistency, Journal of Applied Logic 6, pp. 33-61, 2010.
- [9] H. Kawai, Sequential calculus for a first order infinitary temporal logic, Zeitschrift f¨ur Mathematische Logik und Grundlagen der Mathematik 33, pp. 423-432, 1987.
- [10] D. Nelson, Constructible falsity, Journal of Symbolic Logic 14, pp. 16-26, 1949.
- [11] S.P. Odintsov, Constructive Negations and Paraconsistency, Trends in Logic Vol. 26, Spinger-Verlag, Berlin, 2008.
- [12] S.P. Odintsov and H. Wansing, Inconsistency-tolerant description logic: Motivation and basic systems, in: V.F. Hendricks and J. Malinowski, Editors, Trends in Logic: 50 Years of Studia Logica, Kluwer Academic Publishers, Dordrecht, pp. 301-335, 2003.
- [13] S.P. Odintsov and H.Wansing, Inconsistency-tolerantDescription Logic. Part II: Tableau Algorithms, Journal of Applied Logic 6, pp. 343-360, 2008.
- [14] A. Pnueli, The temporal logic of programs, Proceedings of the 18th IEEE Symposium on Foundations of Computer Science, pp. 46-57, 1977.
- [15] G. Priest, Paraconsistent Logic, Handbook of Philosophical Logic (Second Edition), Vol. 6, D. Gabbay and F. Guenthner (eds.), Kluwer Academic Publishers, Dordrecht, pp. 287-393, 2002.
- [16] G. Priest and K. Tanaka, Paraconsistent Logic, in: The Stanford Encyclopedia of Philosophy (Summer 2009 Edition), Edward N. Zalta (ed.), URL = hhttp://plato.stanford.edu/archives/sum2009/entries/logicparaconsistent/i.
- [17] W. Rautenberg, Klassische und nicht-klassische Aussagenlogik, Vieweg, Braunschweig, 1979.
- [18] G. Restall, Displaying and deciding substructural logics 1: Logics with contraposition, Journal of Philosophical Logic 27, pp. 179-216, 1998.
- [19] N. Vorob'ev, A constructive propositional logic with strong negation, Doklady Akademii Nauk SSSR 85, pp. 465-468, 1952 (in Russian).
- [20] H. Wansing, The logic of information structures, Lecture Notes in Artificial Intelligence 681, 163 pages, 1993.
- [21] H.Wansing, Displaying modal logic, Trends in Logic Vol. 3, Kluwer Academic Publishers, Dordrecht, 1998.
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Bibliografia
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