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Indirect Method for Existential Formulas

Instead of proving (exists x: G), we assume (~exists x: G), i.e., (forall x: ~G) and deriving a contradiction:

K

exists x: G

~~>

K union {forall x: ~G}

F(alse)

.

"We prove (exists x: G). Assume (forall x: ~G). Then ... (derivation of a contradiction with additional knowledge (forall x: ~G))."

We will see later how to work with universal formulas in knowledge.