T6: 12 of 12
Part IV: Rules of Replacement
More powerful than rules of inference are "rules of replacement". These rules involve pairs of logically equivalent sentence forms.
For example, 'P&Q' and 'Q&P' form such a pair. We will write this as...
(This rule is called "CM" for "commutation".)
Our rules of replacement allow us to replace one member of the pair with the other as one step in any derivation. For example...
... if line 1 (say) of a derivation is '(A>B)&(C&~D)' then line 2 can switch first and second disjunct: '(C&~D)&(A>B)'.
We cite the line number of the sentence from which the replacement is made. (For rules of replacement, it is always one line number to be cited.)
Now, rules of replacement are even more powerful than the example above suggests...
Here are the rest of the standard "rules of replacement. Notice that the sentences flanking the arrow are logically equivalent.
|SD+ Rules of Replacement|