The following statement, for example, is not correctly formalized by material implication: This condition should clearly be false: the degree of Bill Gates has nothing to do with whether Elvis is still alive.
An encoding using the strict conditional is: In modal logic, this formula means (roughly) that, in every possible world in which Bill Gates graduated in medicine, Elvis never died.
Since one can easily imagine a world where Bill Gates is a medicine graduate and Elvis is dead, this formula is false.
[8] 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 strict implication can be used to investigate interpretability of Heyting arithmetic and to model arrows and guarded recursion in computer science.