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Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective. The most common logical connectives are binary connectives (also called dyadic connectives) which join two sentences which can be thought of as the function's operands. Also commonly, negation is considered to be a unary connective. Logical connectives along with quantifiers are the two main types of logical constants used in formal systems such as propositional logic and predicate logic
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Discourse Connective
A discourse marker is a word or a phrase that plays a role in managing the flow and structure of discourse. Since their main function is at the level of discourse (sequences of utterances) rather than at the level of utterances or sentences, discourse markers are relatively syntax-independent and usually do not change the truth conditional meaning of the sentence.[1] Examples of discourse markers include the particles oh, well, now, then, you know, and I mean, and the discourse connectives so, because, and, but, and or.[2] The term discourse marker was coined by Deborah Schiffrin in her 1988 book Discourse Markers.[3][4]Contents1 Definition 2 Usage 3 See also 4 NotesDefinition[edit] In Practical English Usage, Michael Swan defines a discourse marker as "a word or expression which shows the connection between what is being said and the wider context"
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Unary Function
A unary function is a function that takes one argument. A unary operator belongs to a subset of unary functions, in that its range coincides with its domain. Examples[edit] The successor function, denoted succ displaystyle operatorname succ , is a unary operator. Its domain and codomain are the natural numbers, its definition is as follows: succ : N → N n ↦ ( n + 1 ) displaystyle begin aligned operatorname succ :quad &mathbb N rightarrow mathbb N \&nmapsto (n+1)end aligned In many programming languages such as C, executing this operation is denoted by postfixing + + displaystyle mathrel + + to the operand, i.e
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Intersection (set Theory)
In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.[1] For explanation of the symbols used in this article, refer to the table of mathematical symbols.Contents1 Basic definition1.1 Intersecting and disjoint sets2 Arbitrary intersections 3 Nullary intersection 4 See also 5 References 6 Further reading 7 External linksBasic definition[edit]Intersection of three sets:   A ∩ B ∩ C displaystyle ~Acap Bcap C Intersections of the Greek, English and Russian alphabet, considering only the shapes of the letters and ignoring their pronunciationExample of an intersection with setsThe intersection of two sets A and B, denoted by A ∩ B, is the set of all objects that are members of both the sets A and B
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Giuseppe Peano
Giuseppe Peano
Giuseppe Peano
(Italian: [dʒuˈzɛppe peˈaːno]; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much notation. The standard axiomatization of the natural numbers is named the Peano axioms in his honor. As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction. He spent most of his career teaching mathematics at the University of Turin
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Prime (symbol)
؋ ​₳ ​ ฿ ​₿ ​ ₵ ​¢ ​₡ ​₢ ​ $ ​₫ ​₯ ​֏ ​ ₠ ​€ ​ ƒ ​₣ ​ ₲ ​ ₴ ​ ₭ ​ ₺ ​₾ ​ ₼ ​ℳ ​₥ ​ ₦ ​ ₧ ​₱ ​₰ ​£ ​ 元 圆 圓 ​﷼ ​៛ ​₽ ​₹ ₨ ​ ₪ ​ ৳ ​₸ ​₮ ​ ₩ ​ ¥ 円Uncommon typographyasterism ⁂fleuron, hedera ❧index, fist ☞interrobang ‽irony punctuation ⸮lozenge ◊tie ⁀RelatedDiacritics Logic symbolsWhitespace charactersIn other scriptsChinese Hebrew Japanese Korean Category Portal Bookv t eThis article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.The prime symbol ( ′ ), double prime symbol ( ″ ), triple prime symbol ( ‴ ), quadruple prime symbol ( ⁗ ) etc., are used to designate units and for other purposes in mathematics, the sciences, linguistics and music
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Begriffsschrift
Begriffsschrift
Begriffsschrift
(German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. Begriffsschrift
Begriffsschrift
is usually translated as concept writing or concept notation; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, of pure thought." Frege's motivation for developing his formal approach to logic resembled Leibniz's motivation for his calculus ratiocinator (despite that, in the foreword Frege clearly denies that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declares to be a quite hard and idealistic, however not impossible, task)
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Arend Heyting
Arend Heyting
Arend Heyting
(Dutch: [ˈɦɛi̯tɪŋ]; 9 May 1898 – 9 July 1980) was a Dutch mathematician and logician. Biography[edit] Heyting was a student of Luitzen Egbertus Jan Brouwer
Luitzen Egbertus Jan Brouwer
at the University of Amsterdam, and did much to put intuitionistic logic on a footing where it could become part of mathematical logic. Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics
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Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "One cannot say of something that it is and that it is not in the same respect and at the same time."Contents1 History 2 In formal logic2.1 Proof by contradiction 2.2 Symbolic representation 2.3 The notion of contradiction in an axiomatic system and a proof of its consistency3 Philosophy3.1 Pragmatic contradictions 3.2 Dialectical materialism4 Outside formal logic 5 See also 6 Footnotes 7 References 8 External linksHistory[edit] By creation of a paradox, Plato's Euthydemus dialogue demonstrates the need for the notion of contradiction
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Truth
Related concepts and fundamentals:Agnosticism Epistemology Presupposition Probabilityv t e Time
Time
Saving Truth
Truth
from Falsehood and Envy, François Lemoyne, 1737Truth, holding a mirror and a serpent (1896). Olin Levi Warner, Library of Congress Thomas Jefferson Building, Washington, D.C. Truth
Truth
is most often used to mean being in accord with fact or reality, or fidelity to an original or standard.[1] Truth
Truth
may also often be used in modern contexts to refer to an idea of "truth to self," or authenticity. Truth
Truth
is usually held to be opposite to falsehood, which, correspondingly, can also take on a logical, factual, or ethical meaning. The concept of truth is discussed and debated in several contexts, including philosophy, art, and religion
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Arity
In logic, mathematics, and computer science, the arity /ˈærɪti/ ( listen) of a function or operation is the number of arguments or operands that the function takes. The arity of a relation (or predicate) is the dimension of the domain in the corresponding Cartesian product. (A function of arity n thus has arity n+1 considered as a relation.) The term springs from words like unary, binary, ternary, etc. Unary functions or predicates may be also called "monadic"; similarly, binary functions may be called "dyadic". In mathematics arity may also be named rank,[1][2] but this word can have many other meanings in mathematics. In logic and philosophy, arity is also called adicity and degree.[3][4] In linguistics, arity is usually named valency.[5] In computer programming, there is often a syntactical distinction between operators and functions; syntactical operators usually have arity 0, 1, or 2 (the ternary operator ?: is also common)
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Compound Sentence (linguistics)
In grammar, sentence clause structure is the classification of sentences based on the number and kind of clauses in their syntactic structure. Such division is an element of traditional grammar.Contents1 Types 2 Simple sentences 3 Compound sentences 4 Complex and compound-complex sentences 5 Incomplete sentence 6 Run-on (fused) sentences 7 See also 8 References 9 External linksTypes[edit] A simple sentence consists of only one clause. A compound sentence consists of two or more independent clauses. A complex sentence has at least one independent clause plus at least one dependent clause.[1] A set of words with no independent clause may be an incomplete sentence, also called a sentence fragment. A sentence consisting of at least one dependent clauses and at least two independent clauses may be called a complex-compound sentence or compound-complex sentence. Sentence 1 is an example of a simple sentence
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Grammatical Conjunction
In grammar, a conjunction (abbreviated CONJ or CNJ) is a part of speech that connects words, phrases, or clauses that are called the conjuncts of the conjoining construction. The term discourse marker is mostly used for conjunctions joining sentences. This definition may overlap with that of other parts of speech, so what constitutes a "conjunction" must be defined for each language. In general, a conjunction is an invariable grammatical particle and it may or may not stand between the items in a conjunction. The definition may also be extended to idiomatic phrases that behave as a unit with the same function, e.g. "as well as", "provided that". A simple literary example of a conjunction: "the truth of nature, and the power of giving interest"
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Moses Schönfinkel
Moses Ilyich Schönfinkel, also known as Moisei Isai'evich Sheinfinkel' (Russian: Моисей Исаевич Шейнфинкель; 4 September 1889–1942), was a Russian logician and mathematician, known for the invention of combinatory logic.Contents1 Life 2 Work 3 Publications 4 See also 5 ReferencesLife[edit] Schönfinkel attended the Novorossiysk University
Novorossiysk University
of Odessa, studying mathematics under Samuil Osipovich Shatunovskii
Samuil Osipovich Shatunovskii
(1859–1929), who worked in geometry and the foundations of mathematics. From 1914 to 1924, Schönfinkel was a member of David Hilbert's group at the University of Göttingen.[1] On 7 December 1920 he delivered a talk to the group where he outlined the concept of combinatory logic
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Sentence (linguistics)
In non-functional linguistics, a sentence is a textual unit consisting of one or more words that are grammatically linked. In functional linguistics, a sentence is a unit of written texts delimited by graphological features such as upper case letters and markers such as periods, question marks, and exclamation marks
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Word
In linguistics, a word is the smallest element that can be uttered in isolation with objective or practical meaning. This contrasts deeply with a morpheme, which is the smallest unit of meaning but will not necessarily stand on its own. A word may consist of a single morpheme (for example: oh!, rock, red, quick, run, expect), or several (rocks, redness, quickly, running, unexpected), whereas a morpheme may not be able to stand on its own as a word (in the words just mentioned, these are -s, -ness, -ly, -ing, un-, -ed). A complex word will typically include a root and one or more affixes (rock-s, red-ness, quick-ly, run-ning, un-expect-ed), or more than one root in a compound (black-board, sand-box)
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