A Routley-Meyer semantics for Ackermann’s logics of “strenge implication”

José M. Méndez

DOI: http://dx.doi.org/10.12775/LLP.2009.010

Abstract


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.

Keywords


Ackermann’s logics; Routley-Meyer semantics; relevant logics; paraconsistent logics

Full Text:

PDF

References


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].








logo
 
 
 
Financed by MNiSW on the basis of agreement no. 706/P-DUN/2018 (dated 10/05/18). Project 1: “Preparation of articles in English for eight editions of the journal Logic and Logical Philosophy over the period 2018–19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 64800 zł. Project 4: “Digitalisation of eight editions of the journal Logic and Logical Philosophy over the period 2018-19; Vol. 27, No. 1–4 (2018), Vol. 28, No. 1–4 (2019)”; amount from the DUN grant: 18600 zł.


ISSN: 1425-3305 (print version)
ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism