Post by Fringe Pioneer on Feb 24, 2011 19:17:08 GMT
A proof consists of justified steps that use any or all of the rules of inference and substitution, and premises or assumptions, to reach a given conclusion. A premise is an assertion that some truth functional statement is true, an assumption is a statement that is used in a subproof as something that could be true unless a contradiction arises (in which case the assumption is proven as false), and a justified step is any other step with an accompanying explanation of how the step was derived.
Below is a sample proof with a single premise and the desired conclusion.
Prove: A ≡ C
StepJustification (A · B) ∨ (~A · ~B) Premise ((A · B) ∨ ~A) · ((A · B) ∨ ~C) 1, Dist ((A ∨ ~A) · (C ∨ ~A)) · ((A ∨ C) · (C ∨ ~C)) 2, Dist (A ∨ ~A) · (C ∨ ~A) 3, Simp. (A ∨ ~C) · (C ∨ ~C) 3, Simp. C ∨ ~A 4, Simp. ~A ∨ C 6, Comm. A ⊃ C 7, C.E. A ∨ ~C 5, Simp. ~C ∨ A 9, Comm. C ⊃ A 10, C.E. (A ⊃ C) · (C ⊃ A) 8, 11, Conj. A ≡ C 12, B.E.
Post by Fringe Pioneer on Feb 24, 2011 22:29:58 GMT
It's not quite, although predicate logic (this is sentential logic, not predicate logic) has some similarities to it. According to my philosophy professor, set theory is in between predicate logic and arithmetical logic, or something of the like...
Here are the various symbols and for what they stand.