| 释义 |
prenex, a. Logic.|ˈpriːnɛks|
[ad. late L. prae-nex(us tied or bound up in front: see pre- A. 1 and nexus.]
Of or relating to a quantifier placed initially in a formula whose scope affects the whole formula; spec. in phr. prenex normal form (see quot. 1944).
1944A. Church in Ann. Math. Stud. xiii. 60 Thus we have that a w.f.f. is in prenex normal form if and only if all its quantifiers are initially placed, no two quantifiers are upon the same variable, and every variable occurring in a quantifier occurs at least once within the scope of that quantifier. Ibid. 61 Use of the prenex normal form was introduced by C. S. Peirce, although in a different terminology and notation. 1950W. V. Quine Methods of Logic (1952) iv. 226 Let us speak of a quantifier as prenex in a sentence when..it is initial..and its scope reaches to the end of the sentence. Ibid. 243 The prenex universal quantifiers..are dropped for ease in reading. 1951Jrnl. Symbolic Logic XVI. 32 For any formula F of our m-valued formalization there is a formula G in prenex normal form which is weakly equivalent to F. 1965Hughes & Londey Elem. Formal Logic xli. 297 A wff in which all the quantifiers occur at the beginning, all are affirmative, and in which their scope extends to the end of the whole wff, is said to be in Prenex Normal Form. 1974Boolos & Jeffrey Computability & Logic ix. 112 Thus..F2 is in prenex form but F1 is not; since F2 is a prenex formula logically equivalent to F1, F2 is a prenex form of F1. |