Ashley P.

asked • 10/12/19

Axioms --> Clausal Form

Question :

Consider the following sentences and prove that "Diana will win the game"


1.All Players are clever.

2.Anyone who is clever and dedicated can play the game well.

3.Anyone who is playing the game well will win his/her game.

4.Diana is a dedicated player.


So my first attempt was representing the using axioms as follows(Please note that I'll be using the following notations as follows:

VX - For all X(Universal quantifier)

EX - For some X(Existential quantifier)



Let P(X) be X is a player

C(X) be X is clever

D(X) be X is dedicated

G(X) be X can play the game well

W(X) be X will win his/her game


Axiom Form :


1. VX [P(X) --> C(X) ]

2. [ ( C(X) ^ D(X) ) --> G(X) ]

3. VX [ G(X) --> W(X) ]

4. P(Diana) --> D(X)


Clausal Form :


1. ~P(X) v C(X)

2. ~C(X) v ~D(X) v G(X)

3. ~G(X) v W(X)

4. ~P(Diana) v D(X)


Can anyone please explain how to prove that "Diana will win the game" , using above clausal forms.


Thanks!


1 Expert Answer

By:

Patrick B. answered • 10/12/19

Math and computer tutor/teacher

Ashley P.

Thanks a lot for the response! But this is to be solved using the resolution principle . Plus could you tell me whether I've converted the sentences to axioms form, in a correct manner? Thanks!
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10/13/19

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