Natural Implication and Modus Ponens Principle
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21.04.2015
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In [6] the definition of natural implication was introduced. One of the criteria for naturalimplication is the normality of logical matrix [2, p. 134], a condition sufficient for verification of modus ponens. In this paper two definitions of modus ponens are regarded: in the designation-preserving sense and in the tautologousness-preserving sense. These formulations are considered as applied to two-valued and three-valued cases. In two- valued case these formulations are equivalent. But in case of three-valued logic we have another situation: they are not equivalent, but the first formulation entails the second, the reverse is not the case. According to that fact, the definition of natural implication is transformed and truth tables for extended class of natural implications are presented.
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Томова Н. Е. Natural Implication and Modus Ponens Principle // Логические исследования / Logical Investigations. 2015. Т. 21. № 1. C. 138-143.
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Литература
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Tomova, N.E. Estestvennye trekhznachnye logiki: Funktsional’nye svoistva i otnosheniya [Natural three-valued logics: functional properties and relations], Moscow: IFRAN Publ., 2012. 89 pp. (In Russian)
Lukasiewicz, J., Tarski, A. “Investigations into the sentential calculus”, in: J. Lukasiewicz, Selected Works, ed. by L. Borkowski. Amsterdam & Warszawa: North-Holland & PWN, 1970, pp. 131–152.
Malinowski, G. “On Many-Valuedness, Sentential Identity, Inference and Lukasiewicz Modalities”, Logica Trianguli, 1997, vol. 1, pp. 59–72.
Priest, G. (1979). “The Logic of Paradox”, Journal of Philosophical Logic, 1979, vol. 8, no 1, pp. 219–241.
Rescher, N. Many-Valued Logic. New York: McGraw Hill, 1969. 359 pp.
Tomova, N. “A lattice of implicative extensions of regular Kleene’s logics”, Reports on mathematical logic, 2012, vol. 47, pp. 173—182.
Tomova, N.E. Estestvennye trekhznachnye logiki: Funktsional’nye svoistva i otnosheniya [Natural three-valued logics: functional properties and relations], Moscow: IFRAN Publ., 2012. 89 pp. (In Russian)