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):(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Collecting different rules for Natural Deduction

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