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An eight - valued praconsistent logic

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Języki publikacji
EN
Abstrakty
EN
It is known that many-valued paraconsistent logics are useful for expressing uncertain and inconsistency-tolerant reasoning in a wide range of Computer Science. Some four-valued and sixteen-valued logics have especially been well-studied. Some four-valued logics are not so fine-grained, and some sixteen-valued logics are enough fine-grained, but rather complex. In this paper, a natural eight-valued paraconsistent logic rather than four-valued and sixteen-valued logics is introduced as a Gentzen-type sequent calculus. This eight-valued logic is enough fine-grained and sim- pler than sixteen-valued logic. A triplet valuation semantics is introduced for this logic, and the completeness theorem for this semantics is proved. The cut-elimination theorem for this logic is proved, and this logic is shown to be decidable.
Rocznik
Tom
Strony
3--21
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
  • Teikyo University, Faculty of Science and Engineering, Department of Human Information Systems, Toyosatodai 1-1, Utsunomiya-shi, Tochigi 320-8551, Japan.
Bibliografia
  • [1] A. Almukdad and D. Nelson, Constructible falsity and inexact predicates, Journal of Symbolic Logic 49:1 (1984), 231-233.
  • [2] O. Arieli and A. Avron, Logical bilattices and inconsistent data, Proceedings of the 9th IEEE Annual Symposium on Logic in Computer Science, IEEE Press, 1994, pp. 468-476.
  • [3] O. Arieli and A. Avron, Reasoning with logical bilattices, Journal of Logic, Language and Information 5 (1996), 25-63.
  • [4] N. D. Belnap, A useful four-valued logic, in: J.M. Dunn and G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, Reidel, Dordrecht, 1977, pp. 5-37.
  • [5] J. M. Dunn, Intuitive semantics for rst-degree entailment and `coupled trees', Philosophical Studies 29:3 (1976), 149-168.
  • [6] Y. Gurevich, Intuitionistic logic with strong negation, Studia Logica 36 (1977),49-59.
  • [7] N. Kamide, On natural eight-valued reasoning, Proceedings of the 43rd IEEE International Symposium on Multiple-Valued Logic (ISMVL 2013), pp. 231-236.
  • [8] N. Kamide and H. Wansing, Combining linear-time temporal logic with constructiveness and paraconsistency, Journal of Applied Logic 8 (2010), 33-61.
  • [9] N. Kamide and H. Wansing, A paraconsistent linear-time temporal logic, Fundamenta Informaticae 106:1 (2011), 1-23.
  • [10] N. Kamide and H. Wansing, Completeness and cut-elimination theorems for trilattice logics, Annals of Pure and Applied Logic 162:10 (2011), 816-835.
  • [11] N. Kamide and H.Wansing, Proof theory of Nelson's paraconsistent logic: A uniform perspective, Theoretical Computer Science 415 (2012), 1-38.
  • [12] D. Nelson, Constructible falsity, Journal of Symbolic Logic 14 (1949), 16-26.
  • [13] S. P. Odintsov, On axiomatizing Shramko-Wansing's logic, Studia Logica 91:3 (2009), 407-428.
  • [14] W. Rautenberg, Klassische und nicht-klassische Aussagenlogik, Vieweg, Braunschweig, 1979.
  • [15] Y. Shramko and H. Wansing, Some useful 16-valued logics: how a computer network should think, Journal of Philosophical Logic 34:2 (2005), 121-153.
  • [16] Y. Shramko and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values, Trends in Logic. Vol. 36, Spinger-Verlag, Dordrecht, 2011, pp. 1-263.
  • [17] N. N. Vorob'ev, A constructive propositional calculus with strong negation (in Russian), Doklady Akademii Nauk SSR 85 (1952), 465-468.
  • [18] H. Wansing, The logic of information structures, Lecture Notes in Articial Intelligence 681, Springer-Verlag, 1993, pp. 1-163.
  • [19] H. Wansing, The power of Belnap: sequent systems for SIXTEEN3, Journal of Philosophical Logic 39:4 (2010), 369-393.
  • [20] D. Zaitsev, A few more useful 8-valued logics for reasoning with tetralattice EIGHT4, Studia Logica 92:2 (2009), 265-280.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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