Propositional logic extended with a pedagogically useful relevant implication

Diderik Batens



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.


relevant implication; classical logic

Full Text:



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.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism