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Logic and Logical Philosophy

Connexive Conditional Logic. Part I
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Connexive Conditional Logic. Part I

Authors

  • Heinrich Wansing Ruhr-Universität, Bochum http://orcid.org/0000-0002-0749-8847
  • Matthias Unterhuber Ruhr-University Bochum

DOI:

https://doi.org/10.12775/LLP.2018.018

Keywords

conditional logic, connexive logic, paraconsistent logic, Chellas frames, Segerberg frames, general frames, first-degree entailment logic, Aristotle’s theses, Boethius’ theses, extension/anti-extension pairs, tableaux

Abstract

In this paper, first some propositional conditional logics based on Belnap and Dunn’s useful four-valued logic of first-degree entailment are introduced semantically, which are then turned into systems of weakly and unrestrictedly connexive conditional logic. The general frame semantics for these logics makes use of a set of allowable (or admissible) extension/antiextension pairs. Next, sound and complete tableau calculi for these logics are presented. Moreover, an expansion of the basic conditional connexive logics by a constructive implication is considered, which gives an opportunity to discuss recent related work, motivated by the combination of indicative and counterfactual conditionals. Tableau calculi for the basic constructive connexive conditional logics are defined and shown to be sound and complete with respect to their semantics. This semantics has to ensure a persistence property with respect to the preorder that is used to interpret the constructive implication.

Author Biographies

Heinrich Wansing, Ruhr-Universität, Bochum

Department of Philosophy I, Logic and Epistemology

Matthias Unterhuber, Ruhr-University Bochum

Faculty of Philosophy and Educational Research, Department of Philosophy II

References

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Published

2018-12-28

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1.
WANSING, Heinrich and UNTERHUBER, Matthias. Connexive Conditional Logic. Part I. Logic and Logical Philosophy. Online. 28 December 2018. Vol. 28, no. 3, pp. 567-610. [Accessed 4 July 2025]. DOI 10.12775/LLP.2018.018.
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