I'm only interested in the inference rules. I've read that people use different sets of rules, and I'm trying to find all of those different sets. Here's the ones I have so far (read "/" as a line break): 1. Modus Ponens (M.P.) 2. Modus Tollens (M.T.) 3. Hypothetical Syllogism (H.S.): p -> q / q -> r / ∴ p -> r. 4. Disjunctive Syllogism (D.S.): p V q / ~p / ∴ q. 5. Constructive Dilemma (C.D.): (p -> q) & (r -> s) / p V r / ∴ q V s. 6. Absorption (Abs.): p -> q / ∴ p -> (p & q). 7. Simplification (Simp.): p & q / ∴ p. 8. Conjunction (Conj.): p / q / ∴ p & q. 9. Addition (Add.): p / ∴ p V q. (1-9) is a complete set. I've found a set differing from (1-9) only by replacing (6) with 6b. Destructive Dilemma (D.D.): (p -> q) & (r -> s) / ~q V ~s / ∴ ~p V ~r. Does anyone know of any more?