MarketScope (logic)
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Scope (logic)

In logic, the scope of a quantifier or connective is the shortest formula in which it occurs, determining the range in the formula to which the quantifier or connective is applied. The notions of a free variable and bound variable are defined in terms of whether that formula is within the scope of a quantifier, and the notions of a dominant connective and subordinate connective are defined in terms of whether a connective includes another within its scope.

Connectives
The scope of a logical connective occurring within a formula is the smallest well-formed formula that contains the connective in question.' The connective with the largest scope in a formula is called its dominant connective, main connective,'' main operator, major connective, or principal connective; a connective within the scope of another connective is said to be subordinate to it.'''' For instance, in the formula (\left( \left( P \rightarrow Q \right) \lor \lnot Q \right) \leftrightarrow \left( \lnot \lnot P \land Q \right)), the dominant connective is ↔, and all other connectives are subordinate to it; the → is subordinate to the ∨, but not to the ∧; the first ¬ is also subordinate to the ∨, but not to the →; the second ¬ is subordinate to the ∧, but not to the ∨ or the →; and the third ¬ is subordinate to the second ¬, as well as to the ∧, but not to the ∨ or the →.'''''' If an order of precedence is adopted for the connectives, viz., with ¬ applying first, then ∧ and ∨, then →, and finally ↔, this formula may be written in the less parenthesized form \left ( P \rightarrow Q \right) \lor \lnot Q \leftrightarrow \lnot \lnot P \land Q , which some may find easier to read.'''''' == Quantifiers ==
Quantifiers
The scope of a quantifier is the part of a logical expression over which the quantifier exerts control. is the scope of the quantifier == See also ==
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