Proof Strategy for Sentential Logic
- Assume the given premises
- Try to apply rules to generate desired conclusion resting only on given premises (Be methodical!)
- If you need to make an additional assumption, LOOK AT WHAT YOU WANT TO PROVE not at what you have already established and make the assumption according to the hints below, and return to step 2
- ATOMIC SENTENCE, NEGATION, or DISJUNCTION
Assume the denial of what you are trying to prove (aim for RAA)
(If you are trying to prove a disjunction using primitive rules only,
also assume one of the disjuncts and use vI and RAA to conclude a
denial of that disjunct.)
- CONDITIONAL
Assume the antecedent and try to prove the consequent (for ->I)
- CONJUNCTION
Try to prove each conjunct separately (make appropriate assumptions for proving each conjunct)
- BICONDITIONAL
Try to prove each of the corresponding conditionals separately (make the appropriate assumption for each conditional
Proof Strategy for Predicate Logic
The general strategy for doing proofs in predicate logic incorporates the strategy for proofs in sentential logic.
- If you have a Universal sentence, use Universal Elimination to derive one or more instances as needed.
- If you have an existential formula, assume an instance (for Existential Elimination).
- Apply rules until you get to the desired conclusion or need to
make an assumption.
- If you need to make an assumption, look at what you are trying
to prove and use the hints above in conjunction with these below:
- UNIVERSAL
Try to prove an instance of it (and then do Universal Instantiation -- beware of conditions!)
- EXISTENTIAL
Either assume its negation (for RAA) or try to prove an instance of it (and then do Existential Introduction)