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Logic and Logical Philosophy

Note on Contradictions in Francez-Weiss Logics
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Note on Contradictions in Francez-Weiss Logics

Authors

  • Satoru Niki Department of Philosophy I, Ruhr University Bochum https://orcid.org/0000-0002-0882-806X

DOI:

https://doi.org/10.12775/LLP.2024.031

Keywords

connexive logic, contradictory logic, relevant logics, sequent calculus, strong negation

Abstract

It is an unusual property for a logic to prove a formula and its negation without ending up in triviality. Some systems have nonetheless been observed to satisfy this property: one group of such non-trivial negation inconsistent logics has its archetype in H. Wansing’s constructive connexive logic, whose negation-implication fragment already proves contradictions. N. Francez and Y. Weiss subsequently investigated relevant subsystems of this fragment, and Weiss in particular showed that they remain negation inconsistent. In this note, we take a closer look at this phenomenon in the systems of Francez and Weiss, and point out two types of necessary conditions, one proof-theoretic and one relevant, which any contradictory formula must satisfy. As a consequence, we propose a nine-fold classification of provable contradictions for the logics.

References

Almukdad, A., and D. Nelson, “Constructible falsity and inexact predicates”, The Journal of Symbolic Logic, 49(1), 1984: 231–233. DOI: https://doi.org/10.2307/2274105

Avron, A., “ Relevant entailment—semantics and formal systems”, The Journal of Symbolic Logic, 49(2), 1984: 334–342. DOI: https://doi.org/10.2307/2274169

Bimbó, K., Proof Theory: Sequent Calculi and Related Formalisms, CRC Press, 2014. DOI: https://doi.org/10.1201/b17294

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

Dunn, J M., “R-Mingle is nice, and so is Arnon Arnon”, pages 141–165 in Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer, 2021. DOI: https://doi.org/10.1007/978-3-030-71258-7_7

Dunn, J M., and G. Restall, “Relevance logic”, pages 1–128 in Handbook of Philosophical Logic, vol. 6, Springer, 2002. DOI: https://doi.org/10.1007/978-94-017-0460-1_1

Francez, N., “Relevant connexive logic”, Logic and Logical Philosophy, 28(3), 2019: 409–425. DOI: https://doi.org/10.12775/LLP.2019.007

Kamide, N., “Substructural logics with mingle”, Journal of Logic, Language and Information, 11, 2002: 227–249. DOI: https://doi.org/10.1023/A:1017586008091

Kamide, N., and H. Wansing, “Proof theory of Nelson’s paraconsistent logic: A uniform perspective”, Theoretical Computer Science, 415, 2012: 1–38. DOI: https://doi.org/10.1016/j.tcs.2011.11.001

Kamide, N. and H. Wansing, Proof Theory of N4-related Paraconsistent Logics, College Publications London, 2015.

Mares, E., “Relevance logic”, in E. N. Zalta and U. Nodelman (eds.), The Stanford Encyclopedia of Philosophy, Stanford University, Fall 2022 edition. https://plato.stanford.edu/entries/logic-relevance/

McCall, S., “A history of connexivity”, pages 415–449 in D. M. Gabbay, F. J. Pelletier and J. Woods (eds.), Logic: A History of its Central Concepts, volume 11 of Handbook of the History of Logic, North-Holland, 2012.

Mints, G., A Short Introduction to Intuitionistic Logic, Kluwer Academic Publishers, 2000.

Mortensen, C., “Aristotle’s thesis in consistent and inconsistent logics”, Studia Logica, 43, 1984: 107–116. DOI: https://doi.org/10.1007/BF00935744

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

Omori, H., and H. Wansing, “Connexive logic, connexivity, and connexivism: Remarks on terminology”, Studia Logica 112, 2024: 1–35. DOI: https://doi.org/10.1007/s11225-023-10082-1

Ono, H., Proof Theory and Algebra in Logic, Springer, Singapore, 2019. DOI: https://doi.org/10.1007/978-981-13-7997-0

Sambin, G., “Some points in formal topology”, Theoretical Computer Science, 305(1), 2003: 347–408. DOI: https://doi.org/10.1016/S0304-3975(02)00704-1

Tamura, S., “The implicational fragment of R-mingle”, Proceedings of the Japan Academy, 47(1), 1971: 71–75. DOI: https://doi.org/10.3792/pja/1195520115

Urquhart, A. I. F., “Completeness of weak implication”, Theoria, 37(3), 1971: 274–282. DOI: https://doi.org/10.1111/j.1755-2567.1971.tb00072.x

Urquhart, A., “Semantics for relevant logics”, The Journal of Symbolic Logic, 37(1), 1972: 159–169. DOI: https://doi.org/10.2307/2272559

Urquhart, A., “The semantics of entailment”, PhD thesis, University of Pittsburgh, 1973.

Wansing, H., “Connexive modal logic”, pages 387–399 in R. Schmidt, I. Pratt-Hartmann, M. Reynolds and H. Wansing (eds.), Advances in Modal Logic, vol. 5, College Publications, 2005.

Wansing, H., “Connexive logic”, in E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Stanford University, Summer 2023 edition. https://plato.stanford.edu/entries/logic-connexive/

Wansing, H., and S. Ayhan, “Logical multilateralism”, Journal of Philosophical Logic, 52, 2023: 1603–1636. DOI: https://doi.org/10.1007/s10992-023-09720-9

Weiss, Y., “Semantics for pure theories of connexive implication”, The Review of Symbolic Logic, 15(3), 2022: 591–606. DOI: https://doi.org/10.1017/S1755020320000374

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Published

2024-12-12

How to Cite

1.
NIKI, Satoru. Note on Contradictions in Francez-Weiss Logics. Logic and Logical Philosophy. Online. 12 December 2024. pp. 1-30. [Accessed 20 May 2025]. DOI 10.12775/LLP.2024.031.
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