George Boole: Selected Manuscripts on Logic and Its Philosophy
نویسندگان
چکیده
منابع مشابه
Eigenlogic in the spirit of George Boole
This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of boolean functions in the original form introduced by George Boole. It is then shown that this algebraic polynomial formulation can be naturally extended to operators in finite vector spaces. Logical operators will appear as commuting projectors and the truth values, which ...
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The Berger-Felzenbaum-Fraenkel approach to Covering Systems is exposited. In particular their gorgeous proof of the famous an = an−1 theorem for exact covering systems (found independently by Jamie Simpson), is reviewed, and the analogy of their approach to Boolean tautologies in Disjunctive Normal Form is pointed out.
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This paper reports a computational model of Boole's discovery of Logic as a part of Mathematics. George Boole (1815-1864) found that the symbols of Logic behaved as algebraic symbols, and he then rebuilt the whole contemporary theory of Logic by the use of methods such as the solution of algebraic equations. Study of the diierent historical factors that innuenced this achievement has served as ...
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Boole is a hash function designed by Gregory Rose and was submitted to the NIST Hash competition. It is a stream cipher based hash function which produces digests up to 512 bits. Different variants exist, namely Boole16, Boole32 and Boole64 where the number refers to word size in bits. Boole64 is considered as the official submission. In this paper we demonstrate a collision attack with complex...
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As shown by Pitowsky, the Bell inequalities are related to certain classes of probabilistic inequalities dealt with by George Boole, back in the 1850s. Here a short presentation of this relationship is given. Consequently, the Bell inequalities can be obtained without any assumptions of physical nature, and merely through mathematical argument. The importance of the typically quantum phenomenon...
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ژورنال
عنوان ژورنال: Historia Mathematica
سال: 2002
ISSN: 0315-0860
DOI: 10.1006/hmat.2002.2372