15-399 Constructive Logic
Lecture 3: Notational Definition
We explain a new means for defining logical connectives: notational
definition. We use this idea to define negation and logical equivalence.
We also discuss derived rules of inference and exercise our understanding
of the meaning for various connectives by considering laws describing
the interactions between them.
We will see that disjunction, with the meaning we assigned to it, does
not satisfy the law of excluded middle in general. Many other
properties which may be familiar from classical logic, continue
to hold, however.