Set theory as modal logic
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A logical systemBM+ is proposed, which, is a prepositional calculus enlarged with prepositional quantifiers and with two modal signs, □ and Δ These modalities are submitted to a finite number of axioms. □ is the usual sign of necessity, Δ corresponds to transmutation of a property (to be white) into the abstract property (to be the whiteness). An imbeddingσ of the usual theory of classesM intoBM+ is constructed, such that a formulaA is provable inM if and only ifσ(A) is provable inBM+. There is also an inverse imbeddingπ with an analogous property.
KeywordsFinite Number Mathematical Logic Modal Logic Modal Sign Computational Linguistic
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