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Barcan formula
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In quantified [[modal logic]], the '''Barcan formula''' and the '''converse Barcan formula'''<!--boldface per WP:R#PLA--> (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas were introduced as axioms by [[Ruth Barcan Marcus]], in the first extensions of modal propositional logic to include quantification.<ref>Journal of Symbolic Logic (1946),11 and (1947), 12 under Ruth C. Barcan</ref> Related formulas include the [[Buridan formula]].
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