Causal form

• Apr 17th 2013, 02:26 PM
doctorpi
Causal form
What is the causal form of ((p ⇒ q) ⇒ (p ⇒ r))
And the negation of the result?
• Apr 17th 2013, 02:57 PM
emakarov
Re: Causal form
Do you mean clausal form, i.e., a conjunctive normal form?

What have you tried to find it, and what exactly is your difficulty?
• Apr 17th 2013, 03:03 PM
doctorpi
Re: Causal form
(p=>q)=>(p=>r)
(¬pvq)=>(¬pvr)
¬(¬pvq)v(¬pvr)
(p^¬q)v(¬pvr)
.
And here is where I'm not sure.

With the result I have to negate it because is a conclusion to include in a Resolution, and I'm not sure again of the result.
• Apr 17th 2013, 03:30 PM
emakarov
Re: Causal form
Quote:

Originally Posted by doctorpi
(p=>q)=>(p=>r)
(¬pvq)=>(¬pvr)
¬(¬pvq)v(¬pvr)
(p^¬q)v(¬pvr)
.
And here is where I'm not sure.

At this point, use distributivity laws.

[(p ∧ ¬q) ∨ ¬p] ∨ r
[(p ∨ ¬p) ∧ (¬q ∨ ¬p)] ∨ r
¬q ∨ ¬p ∨ r

Quote:

Originally Posted by doctorpi
With the result I have to negate it because is a conclusion to include in a Resolution, and I'm not sure again of the result.

The negation is q ∧ p ∧ ¬r.