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Logical Or
In logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language, English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula S \lor W , assuming that S abbreviates "it is sunny" and W abbreviates "it is warm". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theory, proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous nonclassical logic, non- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Venn 0111 1111
Venn is a surname and a given name. It may refer to: Given name * Venn Eyre (died 1777), Archdeacon of Carlisle, Cumbria, England * Venn Pilcher (1879–1961), Anglican bishop, writer, and translator of hymns * Venn Young (1929–1993), New Zealand politician Surname * Albert Venn (1867–1908), American lacrosse player * Anne Venn (1620s–1654), English religious radical and diarist * Blair Venn, Australian actor * Charles Venn (born 1973), British actor * Harry Venn (1844–1908), Australian politician * Henry Venn (Church Missionary Society) (1796-1873), secretary of the Church Missionary Society, grandson of Henry Venn * Henry Venn (Clapham Sect) (1725–1797), English evangelical minister * Horace Venn (1892–1953), English cricketer * John Venn (1834–1923), British logician and the inventor of Venn diagrams, son of Henry Venn the younger * John Venn (academic) (died 1687), English academic administrator * John Venn (politician) (1586–1650), English politician * John V ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield of physics and electrical engineering which uses Passivity (engineering), active devices such as transistors, diodes, and integrated circuits to control and amplify the flow of electric current and to convert it from one form to another, such as from alternating current (AC) to direct current (DC) or from analog signal, analog signals to digital signal, digital signals. Electronic devices have significantly influenced the development of many aspects of modern society, such as telecommunications, entertainment, education, health care, industry, and security. The main driving force behind the advancement of electronics is the semiconductor industry, which continually produces ever-more sophisticated electronic devices and circuits in respo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Negation
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P, \mathord P, P^\prime or \overline. It is interpreted intuitively as being true when P is false, and false when P is true. For example, if P is "Spot runs", then "not P" is "Spot does not run". An operand of a negation is called a ''negand'' or ''negatum''. Negation is a unary logical connective. It may furthermore be applied not only to propositions, but also to notions, truth values, or semantic values more generally. In classical logic, negation is normally identified with the truth function that takes ''truth'' to ''falsity'' (and vice versa). In intuitionistic logic, according to the Brouwer–Heyting–Kolmogorov interpretation, the negation of a proposition P is the proposition whose proofs are the refutations of P. Definition ''Classical negation'' is an operation on one logical value, typically th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Conjunction
In logic, mathematics and linguistics, ''and'' (\wedge) is the Truth function, truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as \wedge or \& or K (prefix) or \times or \cdot in which \wedge is the most modern and widely used. The ''and'' of a set of operands is true if and only if ''all'' of its operands are true, i.e., A \land B is true if and only if A is true and B is true. An operand of a conjunction is a conjunct. Beyond logic, the term "conjunction" also refers to similar concepts in other fields: * In natural language, the denotation of expressions such as English language, English "Conjunction (grammar), and"; * In programming languages, the Short-circuit evaluation, short-circuit and Control flow, control structure; * In set theory, Intersection (set theory), intersection. * In Lattice (order), lattice theory, logical conjunction (Infimum and supremum, greatest lower bound). Notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Logic Symbols
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, and the LaTeX symbol. Basic logic symbols Advanced or rarely used logical symbols The following symbols are either advanced and context-sensitive or very rarely used: See also * Glossary of logic * Józef Maria Bocheński * List of notation used in Principia Mathematica * List of mathematical symbols * Logic alphabet, a suggested set of logical symbols * * Logical connective * Mathematical operators and symbols in Unicode * Non-logical symbol * Polish notation * Truth function * Truth table * Wikipedia:WikiProject Logic/Standards for notation References Further reading * Józef Maria Bocheński ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double Turnstile
In logic, the symbol ⊨, ⊧ or \models is called the double turnstile. It is often read as " entails", " models", "is a semantic consequence of" or "is stronger than". It is closely related to the turnstile symbol \vdash, which has a single bar across the middle, and which denotes '' syntactic'' consequence (in contrast to ''semantic''). Meaning The double turnstile is a binary relation. It has several different meanings in different contexts: * To show semantic consequence, with a set of sentences on the left and a single sentence on the right, to denote that if every sentence on the left is true, the sentence on the right must be true, e.g. \Gamma \vDash \varphi. This usage is closely related to the single-barred turnstile symbol which denotes syntactic consequence. * To show satisfaction, with a model (or truth-structure) on the left and a set of sentences on the right, to denote that the structure is a model for (or satisfies) the set of sentences, e.g. \mathcal \model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in computing as well as various types of logic. Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null are treated as false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called falsy and truthy. For example, in Lisp, nil, the empty list, is treated as false, and all other values are treated as true. In C, the number 0 or 0.0 is false, and all other values are treated as true. In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Operation
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a cla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics Of Logic
In logic, the semantics of logic or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations of) natural languages. This field seeks to provide precise mathematical models that capture the pre-theoretic notions of truth, validity, and logical consequence. While logical syntax concerns the formal rules for constructing well-formed expressions, logical semantics establishes frameworks for determining when these expressions are true and what follows from them. The development of formal semantics has led to several influential approaches, including model-theoretic semantics (pioneered by Alfred Tarski), proof-theoretic semantics (associated with Gerhard Gentzen and Michael Dummett), possible worlds semantics (developed by Saul Kripke and others for modal logic and related systems), algebraic semantics (connecting logic to abstract algebra), and game semantics (interpreting logical validity through game ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iterated Binary Operation
In mathematics, an iterated binary operation is an extension of a binary operation on a set ''S'' to a function on finite sequences of elements of ''S'' through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. Other operations, e.g., the set-theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names. In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted :\sum,\ \prod,\ \bigcup, and \bigcap, respectively. More generally, iteration of a binary function is generally denoted by a slash: iteration of f over the sequence (a_, a_ \ldots, a_) is denoted by f / (a_, a_ \ldots, a_), following t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Józef Maria Bocheński
Józef Maria Bocheński or Innocentius Bochenski (30 August 1902 – 8 February 1995) was a Polish Dominican, logician and philosopher. Biography Bocheński was born on 30 August 1902 in Czuszów, then part of the Russian Empire, to a family with patriotic and pro-independence traditions. His predecessors had fought in the Napoleonic wars and various national uprisings. His father, Adolf Józef Bocheński (1870–1936), who greatly developed the family estate, was a landowning activist, volunteer in the 1919-21 war with the Soviet Union and a doctor of agricultural sciences; his interest in economic history influenced Józef's own reflections on economic doctrine and his personal aversion to Marxism. Józef's mother, Maria Małgorzata née Dunin-Borkowska (1882–1931), was interested in theology, the author of the biographies of St John of the Cross and St Teresa of Jesus and the founder of a parish in Ponikwa. In charge of raising the children, she was known for her r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
