Admissibility of Ackermann’s rule δ in relevant logics

• Authors: Gemma Robles

Abstracts

EN

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

Keywords

EN

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

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2013
• Volume: 22
• Issue: 4
• Pages: 411–427

Dates

published

2013-12-01

Contributors

author

Gemma Robles

• Dpto. de Psicología, Sociología y Filosofía, Universidad de León, Campus de Vegazana, s/n, 24071, León, Spain

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.

Identifiers

DOI

10.12775/LLP.2013.018