In [[logic]], a '''strict conditional''' is a [[modal operator]], that is, a [[logical connective]] of [[modal logic]]. It is [[logical equivalence|logicallogically equivalent]] to the [[material conditional]] of classical logic, combined with the [[Logical truth|necessity]] operator from [[modal logic]]. For any two [[proposition]]s <math>p</math> and <math>q</math>, the [[well-formed formula|formula]] <math>p \rightarrow q</math> says that <math>p</math> [[material conditional|materially implies]] <math>q</math> while <math>\Box (p \rightarrow q)</math> says that <math>p</math> [[logical consequence|strictly implies]] <math>q</math>.<ref>Graham Priest, ''An Introduction to Non-Classical Logic: From if to is'', 2<sup>nd</sup> ed, Cambridge University Press, 2008, ISBN 0-521-85433-4, [http://books.google.com/books?id=rMXVbmAw3YwC&pg=PA72 p. 72.]</ref> Strict conditionals are the result of [[Clarence Irving Lewis]]'s attempt to find a conditional for logic that can adequately express [[indicative conditional]]s in natural language.<ref>Nicholas Bunnin and Jiyuan Yu (eds), ''The Blackwell Dictionary of Western Philosophy'', Wiley, 2004, ISBN 1-4051-0679-4, "strict implication," [http://books.google.com/books?id=OskKWI1YA7AC&pg=PA660 p. 660.]</ref> They have also been used in studying [[Molinism|Molinist]] theology.<ref>Jonathan L. Kvanvig, "Creation, Deliberation, and Molinism," in ''Destiny and Deliberation: Essays in Philosophical Theology'', Oxford University Press, 2011, ISBN 0-19-969657-8, [http://books.google.com/books?id=nQliRGPVpTwC&pg=PA127 p. 127–136.]</ref>
