Strict conditional: Difference between revisions

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Revision as of 21:42, 19 October 2020

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Some logicians, such as [[Paul Grice]], have used [[conversational implicature]] to argue that, despite apparent difficulties, the material conditional is just fine as a translation for the natural language 'if...then...'. Others still have turned to [[relevance logic]] to supply a connection between the antecedent and consequent of provable conditionals.

==Constructive logic==

In a constructive setting, the symmetry between ⥽ and <math>\Box</math> is broken, and the two connectives can be studied independently. Constructive strict implication can be used to investigate [[interpretability]] of [[Heyting arithmetic]] and to model [[arrow (computer science)|arrows]] and guarded [[recursion (computer science)|recursion]] in computer science<ref>{{cite journal

| doi = 10.1016/j.indag.2017.10.003

| author1 = Tadeusz Litak

| author2 = Albert Visser

| title = Lewis meets Brouwer: Constructive strict implication

| journal = Indagationes Mathematicae

| volume = 29

| issue = 1

| pages = 36-90

| year = 2018

| url = https://arxiv.org/abs/1708.02143 }}</ref>.

==See also==