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Existential Quantification in Knowledge

Proposition: For proving with knowledge K union {exists x: F} the goal G, it suffices to prove G with additional knowledge F[x <- a] for some object constant a that does not appear in K, G, or F:

K union {exists x: F}
K union {exists x: F, F[x <- a]}
(a not in K, G, F)

"We prove G. Since we know (exists x: F), we have have some a with F[x <- a]. Thus ...(proof of G with new knowledge F[x <- a])."

A formula (exists x: F) in the knowledge base is an "engine" which returns a new constant a about which we know (only) F[x <- a].

Author: Wolfgang Schreiner
Last Modification: November 30, 1999

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