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