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Poretsky's Law Of Forms
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 Platon Sergeevich Poretsky (russian: Платон Серге́евич Порецкий; October 3, 1846 in Elisavetgrad, Russian Empire – August 9, 1907 in Gorodnyansky Uyezd, Chernigov Governorate, Russian Empire) was a noted Russian Imperial .... See also * Archie Blake (mathematician) * 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= ... [...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 variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is 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 Huntington, the term "Boolean algebra" wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exclusive Or
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , , , , , and . The negation of XOR is the logical biconditional, which yields true if and only if the two inputs are the same. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator ''excludes'' that case. This is sometimes thought of as "one or the other but not both". This could be written as "A or B, but not, A and B". Since it is associative, it may be considered to be an ''n''-ary operator which is true if and only if an odd number of arguments are true. That is, ''a'' XOR ''b'' XOR ... may be treated as XOR(''a'',''b'',...). Truth table The truth table of A XOR B shows that it outputs true whenever the inputs differ: Equivalences, elimination, and introduc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platon Poretsky
Platon Sergeevich Poretsky (russian: Платон Серге́евич Порецкий; October 3, 1846 in Elisavetgrad, Russian Empire – August 9, 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. He discovered Poretsky's law of forms and gave the first general treatment of antecedent and consequent Boolean reasoning,Platon Poretsky, "Sept lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Archie Blake (mathematician)
Archie Blake (born 1906) is 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 (or earlier), 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 U.S. Coast and Geodetic Survey in Washington, D.C., since 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 Army Surgeon General, Washington, D.C. He also worked for the Cornell Aeronautica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blake–Poretsky Law
In Boolean logic, a formula for a Boolean function ''f'' is in Blake canonical form (BCF), also called the complete sum of prime implicants, the complete sum, or the disjunctive prime form, when it is a disjunction of all the prime implicants of ''f''. Relation to other forms The Blake canonical form is a special case of disjunctive normal form. The Blake canonical form is not necessarily minimal (upper diagram), however all the terms of a minimal sum are contained in the Blake canonical form. On the other hand, the Blake canonical form is a canonical form, that is, it is unique up to reordering, whereas there can be multiple minimal forms (lower diagram). Selecting a minimal sum from a Blake canonical form amounts in general to solving the set cover problem, so is NP-hard. History Archie Blake presented his canonical form at a meeting of the American Mathematical Society in 1932, and in his 1937 dissertation. He called it the "simplified canonical form"; it was named ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dover Publications, Inc
Dover () is a town and major ferry port in Kent, South East 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 south-east 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 during the English channel migrant crisis. The Port of Dover provides ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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