SYMBOLIC LOGIC
SYMBOLIC LOGIC
RULES OF INFERENCE VS. RULES OF DEDUCTION
RULES OF DEDUCTION
RULES OF INFERENCE RULES OF REPLACEMENT
allow you to infer one formula allow you to replace one
(expression of a fact) from formula with an equivalent
another. formula, or vice-versa
are not reversible. are reversible
p & q ~~p
p p
but not and
p p
p & q ~~p
can only be used in a formula if they can be used to replace
correspond to the main connective of any part of a formula, no
that formula matt
If you have
p & q p ( (q & ~~r)
you can use “Simplification” p ( (q & r)
to derive p
cannot be used in one part of a line can be used to replace either
or formula, (1) a formula that takes up an
entire line of a deduction or
(2) a part of a formula.
If you have If you have
(p & q) ( r (~~p & q) ( r
you cannot derive you can derive
p ( r (p & q) ( r
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