Admissibility of Ackermann’s rule δ in relevant logics

Gemma Robles

DOI: http://dx.doi.org/10.12775/LLP.2013.018

Abstract


It is proved that Ackermann’s rule δ is admissible in a wide spectrum of relevant logics satisfying certain syntactical properties.


Keywords


admissible rules; rule δ; rule assertion; substructural logics; relevant logics

Full Text:

PDF

References


Ackermann, W., “Begründung einer strengen Implikation”, Journal of Symbolic Logic, 21 (1956), 2: 113–128. DOI: 10.2307/2268750

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, NJ, Princeton University Press, 1992.

Brady, R.T., “A Routley-Meyer Affixing style semantics for logics containing Aristotle’s thesis”, Studia Logica, 48 (1989), 2: 235–241. DOI: 10.1007/BF02770514

Brady, R.T. (ed.), Relevant logics and their rivals, vol. II, Ashgate, 2003.

Hacking, I., “What is strict implication?”, Journal of Symbolic Logic, 28 (1963): 51–71. DOI: 10.2307/2271336

Robles, G., “A semantical proof of the admissibility of the rule assertion in some relevant and modal logics”, Bulletin of the Section of Logic, 41 (2012), 1/2: 51–60.

Robles, G., and J.M. Méndez, “A class of simpler logical matrices for the variable-sharing property”, Logic and Logical Philosophy, 20 (2011), 3: 241–249. DOI: 10.12775/LLP.2011.014

Robles, G., and J.M. Méndez, “A general characterization of the variable-sharing property by means of logical matrices”, Notre Dame Journal of Formal Logic, 53 (2012), 2: 223–244. DOI: 10.1215/00294527-1715707

Routley, R., R.K. Meyer, V. Plumwood and R.T. Brady, Relevant Logics and their Rivals, vol. 1, Atascadero, CA, Ridgeview Publishing Co., 1982.

Sylvan, R., and V. Plumwood, “Non-normal relevant logics”, in [5], pp. 10–16.




Bookmark and Share




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