Proof Strategies

PHIL 122. Spring 2012Karin Howe

My Bag of Tricks: Proof Strategies1. HAMMER!!2. Backwards

Strategy3. Abracadabra!4. "Proof Bits"

Strategy

HAMMER!! Strategy

Use inference rules from the top down to break thepremises into little bloody pieces.

Backwards Strategy Specify a goal which you want

to work towards using theBackwards Strategy. This isusually your conclusion, butmight not be if using theBackwards Strategy fromsomewhere in the middle ofyour proof.

Place your goal at the bottomand then try to specify a line orlines from which you can getyour goal in a single step.

Then do the same for the linesyou specified and repeat untilyou work your way up to thepremises.

Abracadabra! Strategy• Don't like a formula in your

premises? Use the rules ofreplacement to transform itinto something "friendlier"(i.e., easier to take apart)

• This strategy can also beused in conjunction with theBackwards Strategy -- don'tlike that conclusion? Thenuse rules of replacementbackwards to transform theconclusion into somethingeasier to prove!

Some useful Abracadabra! moves

"Proof Bits" Strategy• There are a number of

relatively easy proofs thatrepresent frequently re-occurring patterns ofinference (what Klenk calls"proof bits").

• These "proof bits" can beused as modules within alonger proof, allowing youto break down complicatedproofs into smaller, moremanageable pieces.

Some useful "proof bits"