| 释义 |
De Morgan's laws Logic and Math.|dəˈmɔːgən|
[Named after the English mathematician Augustus De Morgan (1806–71), but known to logicians in the Middle Ages.]
Two laws of the propositional calculus, viz. that the negation of a conjunction is logically equivalent to the alternation of the negations of the conjoined expressions, and that the negation of an alternation is logically equivalent to the conjunction of the negations of the alternated expressions; also, the analogous truths in the algebra of classes. Symbolically, ∼(p.q) ≡∼p{logicor}∼q and ∼(p{logicor}q) ≡∼p.∼q. Also, De Morgan's theorem(s); De Morgan absol.
1918C. I. Lewis Survey Symbolic Logic ii. 125, 3.4 and 3.41 together state De Morgan's Theorem. 1932― & C. H. Langford Symb. Logic ii. 33 These always follow from their correlates by some use of De Morgan's Theorem. 1950W. V. Quine Methods of Logic (1952) §10. 53 De Morgan's laws are useful in enabling us to avoid negating conjunctions and alternations. 1957P. Suppes Introd. Logic ix. 205 Equations (23) and (24) are De Morgan's laws. 1965P. Caws Philos. Sci. xlii. 325 Which by De Morgan is seen to be equivalent. |