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Poretsky Law
In Boolean algebra, Poretsky's law of forms shows that the single Boolean equation f(X)=0 is equivalent to g(X)=h(X) if and only if g=f\oplus h, where \oplus represents exclusive or. The law of forms was discovered by Platon Poretsky. See also * Archie Blake (mathematician) Charles Archibald Blake (November 24, 1906 - January 7, 1971), name officially changed to Archie Blake was an American mathematician. He is well known for the Blake canonical form, a normal form for expressions in propositional logic. In order ... * Blake–Poretsky law References * (NB. This publication is also referred to as "On methods of solution of logical equalities and on inverse method of mathematical logic".) *https://web.archive.org/web/20170416231752/http://www2.fiit.stuba.sk/~kvasnicka/Free%20books/Brown_Boolean%20Reasoning.pdf -->* * {{cite book , title=A Survey of Symbolic Logic , author-first=Clarence Irving , author-last=Lewis , author-link=Clarence Irving Lewis , date=1918 , page=14 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exclusive Or
Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR ''excludes'' that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J Translated as and by the infix operators XOR (, , or ), EOR, EXOR, \dot, \overline, \underline, , \oplus, \nleftrightarrow, and \not\equiv. Definition The truth table of A\nleftrightarrow B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduction Exclusive disjunction essentially ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platon Poretsky
Platon Sergeevich Poretsky (; 3 October 1846 in Elisavetgrad, Russian Empire – 9 August 1907 in Gorodnyansky Uyezd, Chernigov Governorate, Russian Empire) was a noted Russian Imperial astronomer, mathematician, and logician. Graduated from Kharkov University, he worked in Astrakhan and Pulkovo in St. Petersburg. Later, as an astronomer at Kazan University, following the advice of his older colleague Professor of Mathematics A. V. Vasiliev at Kazan University (father of Nicolai A. Vasiliev) to learn the works of George Boole, Poretsky developed "logical calculus" and through specific "logical equations" applied it to the theory of probability. Thus, he extended and augmented the works of logicians and mathematicians George Boole, William Stanley Jevons and Ernst Schröder (known as Boole–Jevons–Schröder–Poretsky method). He discovered Poretsky's law of forms and gave the first general treatment of antecedent and consequent Boolean reasoning, laying the groundwork for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archie Blake (mathematician)
Charles Archibald Blake (November 24, 1906 - January 7, 1971), name officially changed to Archie Blake was an American mathematician. He is well known for the Blake canonical form, a normal form for expressions in propositional logic. In order to compute the canonical form, he moreover introduced the concept of consensus, which was a precursor of the resolution principle, today a common technique in automated theorem proving. Career In 1930, he became a member of the American Mathematical Society (AMS). He presented his canonical form at the AMS meeting at Columbia University on 29 Oct 1932. In 1937, this work lead to a Ph.D. from the University of Chicago, supervised by Raymond Walter Barnard. He worked for the United States Coast and Geodetic Survey in Washington, D.C., from 1936 (or earlier) as a mathematician, since 1938 as an Assistant Mathematician, and since 1939 as an Associated Mathematician. In 1946, he was appointed a Senior Statistician in the Office of the Arm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover Publications, Inc
Dover ( ) is a town and major ferry port in Kent, southeast England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies southeast of Canterbury and east of Maidstone. The town is the administrative centre of the Dover District and home of the Port of Dover. Archaeological finds have revealed that the area has always been a focus for peoples entering and leaving Britain. The name derives from the River Dour that flows through it. In recent times the town has undergone transformations with a high-speed rail link to London, new retail in town with St James' area opened in 2018, and a revamped promenade and beachfront. This followed in 2019, with a new 500m Pier to the west of the Harbour, and new Marina unveiled as part of a £330m investment in the area. It has also been a point of destination for many illegal migrant crossings. The Port of Dover provides much of the town's employment, as does touri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
