THE LOGIC NOTES

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

  1. In the formula  NOT(p AND q) IMP ((p OR r) IMP NOTs the scope of the first 'NOT' is NOT(p AND q).
  2. In the same formula, The scope of the 'AND' is p AND q.
  3. In the same formula, the second 'NOT' occurs within the scope of the second 'IMP'.

Links