The Barcan formula is a schema in quantified modal logic concerning the interaction between quantifiers and modal operators. It was introduced as an axiom by Ruth Barcan Marcus in the first extensions of modal propositional logic to include quantification, in papers published in the Journal of Symbolic Logic in 1946 and 1947 under the name Ruth C. Barcan. The formula addresses how necessity and possibility interact with universal and existential quantification across possible worlds, with significant consequences for how a logical system treats the existence of objects in different modal contexts.
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In quantified modal logic, the Barcan formula and the converse Barcan formula (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.
In Branch: Logic and Foundations, Lead sentence
In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i)
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