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Basic Intuitionistic Conditional Logic

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Abstract

Conditional logics have traditionally been intended to formalize various intuitively correct modes of reasoning involving (counterfactual) conditional expressions in natural language. Although conditional logics have by now been thoroughly studied in a classical context, they have yet to be systematically examined in an intuitionistic context, despite compelling philosophical and technical reasons to do so. This paper addresses this gap by thoroughly examining the basic intuitionistic conditional logic ICK, the intuitionistic counterpart of Chellas’ important classical system CK. I give ICK both worlds semantics and algebraic semantics, and prove that these are equivalent. I give a Gödel-type embedding of ICK into CK (augmented with an S4 box connective) and a Glivenko-type embedding of CK into ICK. I axiomatize ICK and prove soundness, completeness, and decidability results. Finally, I discuss extending ICK.

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Acknowledgements

The author would like to thank an anonymous referee, Melvin Fitting, and Graham Priest for comments and suggestions.

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  1. Philosophy Program, The Graduate Center, CUNY, 365 5th Ave., Rm. 7113, New York, NY, 10016, USA

    Yale Weiss

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  1. Yale Weiss
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Weiss, Y. Basic Intuitionistic Conditional Logic. J Philos Logic 48, 447–469 (2019). https://doi.org/10.1007/s10992-018-9471-4

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  • DOI: https://doi.org/10.1007/s10992-018-9471-4

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