Connexive logics. An overview and current trends

Hitoshi Omori, Heinrich Wansing



In this introduction, we offer an overview of main systems developed in the growing literature on connexive logic, and also point to a few topics that seem to be collecting attention of many of those interested in connexive logic. We will also make clear the context to which the papers in this special issue belong and contribute.


connexive logic; principle of conjunctive contrariety; consequential implication; cancellation account of negation; contra-classical logics

Full Text:



Richard B. Angell, “A propositional logic with subjunctive conditionals”, Journal of Symbolic Logic 27, 3 (1962): 327–343. DOI:

Ross Brady, “A Routley-Meyer affixing style semantics for logics containing Aristotle’s thesis”, Studia Logica 48, 2 (1989): 235–241. DOI:

John Cantwell, “The logic of conditional negation”, Notre Dame Journal of Formal Logic 49, 3 (2008): 245–260. DOI:

Michael De and Hitoshi Omori, “Classical negation and expansions of Belnap-Dunn logic”, Studia Logica 103, 4 (2015): 825–851. DOI:

Paul Egré and Guy Politzer, “On the negation of indicative conditionals”, pages 10–18 in M. Franke M. Aloni and F. Roelofsen (eds.), Proceedings of the Amsterdam Colloquium, 2013.

Luis Estrada-González and Elisángela Ramírez-Cámara, “A comparison of connexive logics”, IfCoLog Journal of Logics and their Applications 3, 3 (2016): 341–355.

Lloyd Humberstone, “Contra-classical logics”, Australasian Journal of Philosophy 78, 4 (2000): 438–474. DOI:

Norihiro Kamide and Heinrich Wansing, Proof Theory of N4-related Paraconsistent Logics, vol. 54 of Studies in Logic, College Publications, London, 2015.

Andreas Kapsner, “Strong connexivity”, Thought 1, 2 (2012): 141–145. DOI:

Storrs McCall, “Connexive implication”, Journal of Symbolic Logic 31, 3 (1966): 415–433. DOI:

Storrs McCall, “Connexive implication and the syllogism”, Mind 76, 303 (1967): 346–356. DOI:

Storrs McCall, “Connexive Gentzen”, Logic Journal of the IGPL 22, 6 (2014): 964–981. DOI:

Chris Mortensen, “Aristotle’s thesis in consistent and inconsistent logics”, Studia Logica 43, 1/2 (1984): 107–116. DOI:

Everett Nelson, “Intensional relations”, Mind 39 (1930): 440–453.

Sergei Odintsov, Constructive Negations and Paraconsistency, vol. 26 of Trends in Logic, Springer, 2008. DOI:

Grigory Olkhovikov, “On a new three-valued paraconsistent logic” (in Russian), pages 96–113 in Logic of Law and Tolerance, Ural State University Press, Yekaterinburg, 2001.

Hitoshi Omori, “A simple connexive extension of the basic relevant logic BD”, IfCoLog Journal of Logics and their Applications 3, 3 (2016): 467–478.

Hitoshi Omori, “From paraconsistent logic to dialetheic logic”, pages 111–134 in Holger Andreas and Peter Verdée (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics, Springer, 2016. DOI:

Hitoshi Omori and Katsuhiko Sano, “Generalizing functional completeness in Belnap-Dunn logic”, Studia Logica 103, 5 (2015): 883–917. DOI:

Hitoshi Omori and Heinrich Wansing, “40 years of FDE: An introductory overview”, Studia Logica 105, 6 (2017): 1021–1049. DOI:

Hitoshi Omori and Heinrich Wansing, “On contra-classical variants of Nelson logic N4 and its classical extension”, Review of Symbolic Logic 11, 4 (2018): 805–820. DOI:

Niki Pfeifer, “Experiments on Aristotle’s thesis: Towards an experimental philosophy of conditionals”, The Monist 95, 2 (2012): 223–240. DOI:

Claudio Pizzi, “Boethius’ thesis and conditional logic”, Journal of Philosophical Logic 6, 1 (1977): 283–302. DOI:

Claudio Pizzi, “Aristotle’s thesis between paraconsistency and modalization”, Journal of Applied Logic 3, 1 (2005): 119–131. DOI:

Claudio Pizzi and Timothy Williamson, “Strong Boethius’ thesis and consequential implication”, Journal of Philosophical Logic 26, 5 (1997): 569–588. DOI:

Graham Priest, “Negation as cancellation and connexive logic”, Topoi 18, 2 (1999): 141–148.

Shahid Rahman and Helge Rückert, “Dialogical connexive logic”, Synthese 127 (2001): 105–139.

Richard Routley, “Semantics for connexive logics I”, Studia Logica 37, 4 (1978): 393–412. DOI:

Richard Routley and Hugh Montgomery, “On systems containing Aristotle’s thesis”, Journal of Symbolic Logic 33, 1 (1968): 82–96. DOI:

Richard Routley and Valerie Routley, “Negation and contradiction”, Revista Colombiana de Matemáticas 19, 4 (1985): 201–230.

Heinrich Wansing, “Connexive modal logic”, pages 367–383 in Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds, and Heinrich Wansing (eds.), Advances in Modal Logic. Volume 5, King’s College Publications, 2005.

Heinrich Wansing, “A note on negation in categorial grammar” Logic Journal of the IGPL 15 (2007): 271–286. DOI:

Heinrich Wansing, “Connexive logic”, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2014 edition, 2014.

Heinrich Wansing and Daniel Skurt, “Negation as cancellation, connexive logic, and qLPm”, Australasian Journal of Logic 15 (2018): 476–488. DOI:

Heinrich Wansing, Hitoshi Omori, and Thomas Ferguson (eds.), Connexive Logics, special issue of IfCoLog Journal of Logics and their Applications, 2016.

John Woods, “Two objections to system CC1 of connexive implication”, Dialogue 7, 3 (1968): 473–475. DOI:

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism