| Simplification (SIMP) | P ^ Q (therefore) P, Q |
| Conjunctive Arguement (CA) | P, Q (therefore) P ^ Q |
| Disjunctive Arguement (DA) | P v Q, ~P (therefore) Q |
| Strong Disjunctive Arguement (SDA) | P w Q, P (therefore) ~Q |
| Addition (ADD) | P (therefore) P v X |
| Modus Ponens (MP) | P --> Q, P (therefore) Q |
| Application of MP (AMP) | Q --> R, P --> R (therefore) (P v Q) --> R |
| Modus Tollens (MT) | P --> Q, ~Q (therefore) ~P |
| Material Implication (MI) | P --> Q Q v ~P ~P v Q something else I couldn't see on the paper D= |
| Contraposition (MI^2) | P --> Q ~Q --> ~P |
| Tautology (TAU) | S v S (therefore) S |
| Distributive Property (DIS) | P ^ (Q v R) (therefore) (P ^ Q) v (P ^ R) |
| Conditional Sylogism (CS) | P --> Q, Q --> R (therefore) P --> R |
| De Morgan (DeM) | ~(P ^ Q) (therefore) ~P v ~Q |