Scope Glossary
Definition
The scope of an occurrence of a connective or quantifier in a formula is the smallest subformula in which that occurrence lies.
Comments
Clearly, any connective or quantifier in a formula is the main operator of its scope.
The importance of the concept is that it gives us a convenient way to say that one operator is "below" another in the formula—it lies within its scope.
Examples
- In the formula NOT(p AND q) IMP ((p OR r) IMP NOTs) the scope of the first 'NOT' is NOT(p AND q).
- In the same formula, The scope of the 'AND' is p AND q.
- In the same formula, the second 'NOT' occurs within the scope of the second 'IMP'.