Propositional logic extended with a pedagogically useful relevant implication

• Authors: Batens Diderik
• Languages of publication: EN

Abstracts

EN

First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that has all classical theorems as theorems.

Keywords

EN

relevant implication; classical logic

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2014
• Volume: 23
• Issue: 3
• Pages: 245–276

Dates

published

2014-09-01

online

2013-09-02

Contributors

author

Batens Diderik

• Centre for Logic and Philosophy of Science, Ghent University, Belgium

References

• Alan Ross Anderson and Nuel D. Belnap, Jr., Entailment. The Logic of Relevance and Necessity, volume 1, Princeton University Press, 1975.
• Alan Ross Anderson, Nuel D. Belnap, Jr., and J. Michael Dunn, Entailment. The Logic of Relevance and Necessity, volume 2, Princeton University Press, 1992.
• Diderik Batens, Logicaboek. Praktijk en theorie van het redeneren, Garant, Antwerpen/Apeldoorn, 1992. 7: 2008.
• Diderik Batens, “It might have been Classical Logic”, Logique et Analyse 218 (2012): 241–279.
• Graham Priest, In Contradiction. A Study of the Transconsistent, Oxford University Press, Oxford, 2006. Second expanded edition (first edition 1987).
• Richard Routley, Relevant Logics and their Rivals, volume 1, Ridgeview, Atascadero, Ca., 1982.
• Richard Routley and Robert K. Meyer, “The semantics of entailment”, pages 199–243 in Truth, Syntax and Modality, Hughues Leblanc (ed.), North-Holland, Amsterdam, 1973.

Identifiers

DOI

10.12775/LLP.2013.024