The logical calculus preserves justification, rather than truth, across transformations yielding derived propositions.
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The logical calculus we heard all night was this:
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This led to their seminal neural networks paper " A Logical Calculus of Ideas Immanent in Nervous Activity ".
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Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter century.
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The resulting " characteristic " included a logical calculus, some combinatorics, algebra, his " analysis situs " ( geometry of situation ), a universal concept language, and more.
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The same Wikipedia article unlikely perhaps may be qualified both as an axiom / theorem of some logical calculus and a rule of inference ( or metatheorem ).
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He is best remembered for having written along with Warren McCulloch, a seminal paper entitled " A Logical Calculus of Ideas Immanent in Nervous Activity " ( 1943 ).
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The first logical calculus capable of dealing with such inferences was Gottlob Frege's " Begriffsschrift " ( 1879 ), the ancestor of modern predicate logic, which dealt with quantifiers by means of variable bindings.
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A " formal system " ( also called a " logical calculus ", or a " logical system " ) consists of a formal language together with a derive one expression from one or more other expressions.
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Yet an article entitled " The Logical Calculus " ( Johnson 1892 ) reveals that he had nontrivial technical capabilities in his youth, and that he was significantly influenced by the formal logical work of Charles Sanders Peirce.
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