Lewis meets Brouwer: Constructive strict implication
Litak T, Visser A (2018)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2018
Journal
Book Volume: 29
Pages Range: 36-90
Journal Issue: 1
DOI: 10.1016/j.indag.2017.10.003
Open Access Link: https://arxiv.org/abs/1708.02143
Abstract
C. I. Lewis invented modern modal logic as a theory of "strict implication". Over the classical propositional calculus one can as well work with the unary box connective. Intuitionistically, however, the strict implication has greater expressive power than the box and allows to make distinctions invisible in the ordinary syntax. In particular, the logic determined by the most popular semantics of intuitionistic K becomes a proper extension of the minimal normal logic of the binary connective. Even an extension of this minimal logic with the "strength" axiom, classically near-trivial, preserves the distinction between the binary and the unary setting. In fact, this distinction and the strong constructive strict implication itself has been also discovered by the functional programming community in their study of "arrows" as contrasted with "idioms". Our particular focus is on arithmetical interpretations of the intuitionistic strict implication in terms of preservativity in extensions of Heyting's Arithmetic.
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APA:
Litak, T., & Visser, A. (2018). Lewis meets Brouwer: Constructive strict implication. Indagationes Mathematicae, 29(1), 36-90. https://doi.org/10.1016/j.indag.2017.10.003
MLA:
Litak, Tadeusz, and Albert Visser. "Lewis meets Brouwer: Constructive strict implication." Indagationes Mathematicae 29.1 (2018): 36-90.
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