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Indirect Method for Universal Formulas

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

K

forall x: G

~~>

K union {exists x: ~G}

F(alse)

( ~~>

K union {~G[x <- a]}

F(alse)

)

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

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