In logic, the scope of a quantifier or connective is the shortest formula in which it occurs,[1] determining the range in the formula to which the quantifier or connective is applied.[2][3][4] The notions of a free variable and bound variable are defined in terms of whether that formula is within the scope of a quantifier,[2][5] and the notions of a dominant connective and subordinate connective are defined in terms of whether a connective includes another within its scope.[6][7]
- ^ Bostock, David (1997). Intermediate logic. Oxford : New York: Clarendon Press; Oxford University Press. pp. 8, 79. ISBN 978-0-19-875141-0.
- ^ a b Cook, Roy T. (March 20, 2009). Dictionary of Philosophical Logic. Edinburgh University Press. pp. 99, 180, 254. ISBN 978-0-7486-3197-1.
- ^ Rich, Elaine; Cline, Alan Kaylor. Quantifier Scope.
- ^ Makridis, Odysseus (February 21, 2022). Symbolic Logic. Springer Nature. pp. 93–95. ISBN 978-3-030-67396-3.
- ^ "3.3.2: Quantifier Scope, Bound Variables, and Free Variables". Humanities LibreTexts. January 21, 2017. Retrieved June 10, 2024.
- ^ Cite error: The named reference
LemmonLogicwas invoked but never defined (see the help page). - ^ Gillon, Brendan S. (March 12, 2019). Natural Language Semantics: Formation and Valuation. MIT Press. pp. 250–253. ISBN 978-0-262-03920-8.