Modus ponens:

P > Q
P
------
Q

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Modus tolens:

P > Q
~Q
------
~P
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Hypothetical syllogism:

P > Q
Q > R
------
P > R
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Disjunctive syllogism:

P v Q
~P
------
Q

AND

P v Q
~Q
------
P

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MORE RULE OF INFERENCE TO COME