2.5.2: Propositional Rules
Rules for \(\land\)
Rules for \(\lor\)
Rules for \(\lif\)
Rules for \(\lnot\)
Rules for \(\lfalse\)
Note that \(\Intro{\lnot}\) and \(\FalseCl\) are very similar: The difference is that \(\Intro{\lnot}\) derives a negated sentence \(\lnot A\) but \(\FalseCl\) a positive sentence \(A\) .
Whenever a rule indicates that some assumption may be discharged, we take this to be a permission, but not a requirement. E.g., in the \(\Intro{\lif}\) rule, we may discharge any number of assumptions of the form \(A\) in the derivation of the premise \(B\) , including zero.