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The principle of distributivity is valid in classical logic, but both valid and invalid in quantum logic. The article "Is Logic Empirical?" discusses the case that quantum logic is the correct, empirical logic, on the grounds that the principle of distributivity is inconsistent with a reasonable interpretation of quantum phenomena. [1]
Especially in order theory one finds numerous important variants of distributivity, some of which include infinitary operations, such as the infinite distributive law; others being defined in the presence of only one binary operation, such as the according definitions and their relations are given in the article distributivity (order theory).
Modern philosophers reject quantum logic as a basis for reasoning, because it lacks a material conditional; a common alternative is the system of linear logic, of which quantum logic is a fragment. Mathematically, quantum logic is formulated by weakening the distributive law for a Boolean algebra, resulting in an orthocomplemented lattice .
"Is Logic Empirical?" is the title of two articles (one by Hilary Putnam and another by Michael Dummett) [1] [2] that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of ...
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.
Distributivity is a basic concept that is treated in any textbook on lattice and order theory. See the literature given for the articles on order theory and lattice theory. More specific literature includes: G. N. Raney, Completely distributive complete lattices, Proceedings of the American Mathematical Society, 3: 677 - 680, 1952.
A science fair or engineering fair is an event hosted by a school that offers students the opportunity to experience the practices of science and engineering for themselves. In the United States, the Next Generation Science Standards makes experiencing the practices of science and engineering one of the three pillars of science education.
where is a metalogical symbol meaning that is a syntactic consequence of , in the one case, in the other, in some logical system; or as a rule of inference : P ∨ P ∴ P {\displaystyle {\frac {P\lor P}{\therefore P}}}