A Routley-Meyer semantics for Ackermann’s logics of “strenge implication”
DOI:
https://doi.org/10.12775/LLP.2009.010Słowa kluczowe
Ackermann’s logics, Routley-Meyer semantics, relevant logics, paraconsistent logicsAbstrakt
The aim of this paper is to provide a Routley-Meyer semantics for Ackermann’s logics of “strenge Implikation” Π ′ and Π ′′ . Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π ′ and Π ′′ are proved. A brief discussion on Π ′ , Π ′′ and paraconsistency is included.Bibliografia
Ackermann, W., “Begründung einer strengen Implikation”, Journal of Symbolic Logic 21, 2 (1956): 113–128.
Anderson, A.R., and N.D. Belnap, Jr., Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press, 1975.
Anderson, A.R., N.D. Belnap, Jr., and J.M. Dunn, Entailment. The Logic of Relevance and Necessity, vol. II, Princeton University Press, 1992.
Lewis, C.I., and H. Langford, Symbolic Logic, Dover, New York, 1959 (1932).
Meyer, R.K., and R. Routley, “Algebraic analysis of entailment I”, Logique et Analyse 15 (1972): 407–428.
Priest, G., and K. Tanaka, “Paraconsistent Logic”, in: E.N. Zalta (ed.), The Standford Encyclopedia of Philosophy, Winter Edition 2004. http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/
Robles. G., and J.M. Méndez, “The basic constructive logic for a weak sense of consistency, Journal of Logic Language and Information, 17, 1 (2008): 89–107.
Routley, R., and R.K. Meyer, “Semantics of Entailment III”, Journal of Philosophical Logic, 1 (1972): 192–208.
Routley, R., R.K. Meyer, V. Plumwood, and R.T. Brady Relevant Logics and their Rivals, vol. 1, Atascadero, CA: Ridgeview Publishing Co., 1982.
Routley, R., R.K. Meyer, V. Plumwood, and R.T. Brady, “Semantics of Entailment IV”, Appendix I in [9].
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