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羅賓斯代數


基於 Huntington (1933ab) 的工作,羅賓斯猜想羅賓斯代數的方程,即交換律、結合律和羅賓斯公理

 !(!(x v y) v !(x v !y))=x,

其中 !x 表示 x v y 表示 ,蘊含了布林代數的那些方程。該猜想最終透過計算機證明 (McCune 1997)。


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布林代數, 亨廷頓公理, 羅賓斯猜想, 羅賓斯公理, 溫克勒條件

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參考文獻

Fitelson, B. "Using Mathematica to Understand the Computer Proof of the Robbins Conjecture." Mathematica in Educ. Res. 7, 17-26, 1998. http://library.wolfram.com/infocenter/Articles/1475/. Fitelson, B. "Proof of the Robbins Conjecture." http://library.wolfram.com/infocenter/MathSource/291/.Huntington, E. V. "New Sets of Independent Postulates for the Algebra of Logic, with Special Reference to Whitehead and Russell's Principia Mathematica." Trans. Amer. Math. Soc. 35, 274-304, 1933a.Huntington, E. V. "Boolean Algebra. A Correction." Trans. Amer. Math. Soc. 35, 557-558, 1933b.Kolata, G. "Computer Math Proof Shows Reasoning Power." New York Times, Dec. 10, 1996.McCune, W. "Solution of the Robbins Problem." J. Automat. Reason. 19, 263-276, 1997.McCune, W. "Robbins Algebras are Boolean." http://www.cs.unm.edu/~mccune/papers/robbins/.Nelson, E. "Automated Reasoning." http://www.math.princeton.edu/~nelson/ar.html.

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羅賓斯代數

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Weisstein, Eric W. "羅賓斯代數。" 來自 —— 資源。 https://mathworld.tw/RobbinsAlgebra.html

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