Strict conditional

In logic, a strict conditional (symbol: $\Box$ , or ⥽) is a conditional governed by a modal operator, that is, a logical connective of modal logic. It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic. For any two propositions p and q, the formula p → q says that p materially implies q while $\Box (p\rightarrow q)$ says that p strictly implies q.^[1] Strict conditionals are the result of Clarence Irving Lewis's attempt to find a conditional for logic that can adequately express indicative conditionals in natural language.^[2]^[3] They have also been used in studying Molinist theology.^[4]

^ Graham Priest, An Introduction to Non-Classical Logic: From if to is, 2nd ed, Cambridge University Press, 2008, ISBN 0-521-85433-4, p. 72.
^ Lewis, C.I.; Langford, C.H. (1959) [1932]. Symbolic Logic (2 ed.). Dover Publications. p. 124. ISBN 0-486-60170-6.
^ Nicholas Bunnin and Jiyuan Yu (eds), The Blackwell Dictionary of Western Philosophy, Wiley, 2004, ISBN 1-4051-0679-4, "strict implication," p. 660.
^ Jonathan L. Kvanvig, "Creation, Deliberation, and Molinism," in Destiny and Deliberation: Essays in Philosophical Theology, Oxford University Press, 2011, ISBN 0-19-969657-8, p. 127–136.