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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. Hence, this formula seems a correct translation of the original sentence.
==Problems==
Although the strict conditional is much closer to being able to express natural language conditionals than the material conditional, it has its own problems with antecedents that are necessarily true or false.<ref>Roy A. Sorensen, ''A Brief History of the Paradox: Philosophy and the labyrinths of the mind'', Oxford University Press, 2003, ISBN 0195159039, [http://books.google.com/books?id=PB8I0kHeKy4C&pg=PA105 p. 105.]</ref> The following sentence, for example, is not correctly formalized by a strict conditional:
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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.
==In mathematics==
The rule of [[Modal logic#Axiomatic systems|necessitation]] in modal logic allows us to infer the necessity of any theorem which has been proved without requiring hypotheses, i.e. from <math>\vdash A</math>, infer <math>\vdash \Box A</math>.<ref>James W. Garson, ''Modal Logic for Philosophers'', Cambridge University Press, 2006, ISBN 0521682290, [http://books.google.com/books?id=xFNbDZPZERcC&pg=PA30 p. 30.]</ref> If the theorem has the form of a conditional, i.e. <math>\vdash P \rightarrow Q</math>, it follows that <math>\vdash \Box (P \rightarrow Q)</math>. Thus theorems having the form of a conditional are also strict conditionals.
==See also==
* [[Counterfactual conditional]]
* [[Indicative conditional]]
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