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Minimal negation in the ternary relational semantics

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EN
Abstrakty
EN
Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.
Słowa kluczowe
Rocznik
Tom
Strony
47--65
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Departamento de Filosofia, Lógika y Filosofia de la Ciencia, Campus Unamuno, Edificio F. E. S., Universidad de Salamanca, E-37007 Salamanca, Spain
  • Departamento de Filosofia, Lógika y Filosofia de la Ciencia, Campus Unamuno, Edificio F. E. S., Universidad de Salamanca, E-37007 Salamanca, Spain
autor
  • Departamento de Filosofia, Lógika y Filosofia de la Ciencia, Campus Unamuno, Edificio F. E. S., Universidad de Salamanca, E-37007 Salamanca, Spain
Bibliografia
  • [1] Anderson, A.R., N.D. Belnap et al, Entailment: The Logic of Relevance and Necessity, vol. I, Princeton University Press, Princeton, 1975.
  • [2] Anderson, A.R., N.D. Belnap, J.M. Dunn et al, Entailment: The Logic of Relevance and Necessity, vol. II, Princeton University Press, Princeton, 1992.
  • [3] Dunn, J.M. “Generalized ortho-Negation” in Negation: a Notion in Focus, edited by H. Wansing, De Gruyter, Berlin, 1996.
  • [4] Dunn, J.M. and R.K. Meyer, “Combinators and Structurally Free Logic”, Logic Journal of the IGPL, vol. 5 (1997), pp.505-537.
  • [5] Dunn, J.M. “A Comparative Study of various Model-theoretic Treatments of Negation: A history of Formal Negation”, pp. 23-51 in: What is negation?, edited by D. Gabbay and H. Wansing, Kluwer, Dordrecht, 1999.
  • [6] Johansson, I., “Der Minimalkalküll, ein reduzierter intuitionistischer Formalismus” Compositio Mathematica 4 (1936), pp.119-36.
  • [7] Kolmogorov, A. N., “On the principle of tertium non datur”, in van Heijenoort, From Frege to Gödel, C.U.P., 1967, pp. 414-437.
  • [8] Mares, E. (1995) “A star-free semantics for R”, Journal of Symbolic Logic, vol. 60, pp. 579-590.
  • [9] Méndez, J.M., “Constructive R” Bulletin of the Section of Logic, Vol. 16 (1987), pp.167-175.
  • [10] Méndez, J.M. and F. Salto, “Intuitionistic Propositional Logic without‘contraction’ but with ‘reductio’”, Studia Logica Vol.66 (2000), pp.409-418.
  • [11] Méndez, J.M., Salto, F. and G. Robles, “Anderson and Belnap´s minimal positive logic with minimal negation”. Reports on Mathematical Logic Vol. 36 (2002) pp. 117-130
  • [12] Meyer, R.K. “Conserving Positive Logics”, Notre Dame Journal of Formal Logic .Vol. 14 (1973), pp.224-236.
  • [13] Meyer, R.K. and R. Routley, “Algebraic Analysis of Entailment”, Logique et Analyse Vol.15 (1972), pp.407-428.
  • [14] Priest, G. and R. Sylvan “Simplified Semantics for Basic Relevant Logics”, Journal of Philosophical Logic Vol.21 (1992) pp.217-232.
  • [15] Restall, G. “Four Valued Semantics for Relevant Logics (and some of their rivals)”, Journal of Philosophical Logic Vol.24 (1995) pp.139-160.
  • [16] Restall, G. An Introduction to Substructural Logics, Routledge, London, 1999.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ1-0019-0094
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