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8.1: Implicational Rules of Inference
Comment: The focus of the rest of the course will be on systems of natural
deduction, in which one uses a set of inference rules to demonstrate, step by
step, that the conclusion of an argument follows from the premises.
Advantages of Natural Deduction
? Generally less cumbersome than truth tables.
? Reflects more closely the way we actually reason.
Definition (sorta): A proof is a series of "steps" that
leads, by way of valid inference rules, from the premises
of a symbolic argument to its conclusion.
An inference rule is valid if and only if, any statement that follows
from a set of statements by means of the rule must be true if all of
the statements in the set are true.
Implication Rules
Rule 1: Modus ponens (MP) p ? q
p
? q
1. If it's either raining or snowing, the ground is wet. (R?S) ? W
2. It's either raining or snowing. R?S
So, 3. The ground is wet. W
Rule 2: Modus tollens (MT) p ? q
?q
? ?p
1. If it's either raining or snowing, the ground ...

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