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Metavariable (logic)
In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence :''Let A and B be two sentences of a language ℒ'' the symbols A and B are part of the metalanguage in which the statement about the object language ℒ is formulated. John Corcoran considered this terminology unfortunate because it obscures the use of schemata and because such "variables" do not actually range over a domain. The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with nonterminal symbols in formal grammars where the nonterminals on the right of a production can be substituted by different instances.. Attempts to formalize the notion of metavariable result in some kind of type theory.Masahiko Sato, Takafumi Sakurai, Yukiyoshi Kameyama, and Atsushi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symbol (formal)
A logical symbol is a fundamental concept in logic, type–token distinction, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term ''symbol'' in common use sometimes refers to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in the formal languages studied in mathematics and logic, the term ''symbol'' refers to the idea, and the marks are considered to be a type-token distinction, token instance of the symbol. In logic, symbols build literal utility to illustrate ideas. Overview Symbols of a formal language need not be symbols ''of'' anything. For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses). Symbols of a formal language must be capable of being specified without any reference to any interpretation (logic), interpretation of them. A symbol o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metalanguage
In logic and linguistics, a metalanguage is a language used to describe another language, often called the ''object language''. Expressions in a metalanguage are often distinguished from those in the object language by the use of italics, quotation marks, or writing on a separate line. The structure of sentences and phrases in a metalanguage can be described by a metasyntax. For example, to say that the word "noun" can be used as a noun in a sentence, one could write ''"noun" is a ''. Types of metalanguage There are a variety of recognized types of metalanguage, including ''embedded'', ''ordered'', and ''nested'' (or ''hierarchical'') metalanguages. Embedded An ''embedded metalanguage'' is a language formally, naturally and firmly fixed in an object language. This idea is found in Douglas Hofstadter's book, ''Gödel, Escher, Bach'', in a discussion of the relationship between formal languages and number theory: "... it is in the nature of any formalization of number theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Corcoran (logician)
John Corcoran ( ; March 20, 1937 – January 8, 2021) was an American logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work on concepts such as the nature of inference, relations between conditions, argument-deduction-proof distinctions, the relationship between logic and epistemology, and the place of proof theory and model theory in logic. Nine of Corcoran's papers have been translated into Spanish, Portuguese, Persian, and Arabic; his 1989 "signature" essay was translated into three languages. Fourteen of his papers have been reprinted; one was reprinted twice. His work on Aristotle's logic of the '' Prior Analytics'' is regarded as being highly faithful both to the Greek text and to the historical context. It is the basis for many subsequent investigations. His mathematical results on definitional equivalence of formal character-string theories, sciences of strings of characters over finite alphabets, are foundationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schema (logic)
In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language. The logical form of an argument is called the argument form of the argument. History The importance of the concept of form to logic was already recognized in ancient times. Aristotle, in the '' Prior Analytics'', was one of the first people to employ variable letters to represent valid inferences. Therefore, Jan Łukasiewicz claims that the introduction of variables was "one of Aristotle's greatest inventions." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonterminal
In formal languages, terminal and nonterminal symbols are parts of the ''vocabulary'' under a formal grammar. ''Vocabulary'' is a finite, nonempty set of symbols. ''Terminal symbols'' are symbols that cannot be replaced by other symbols of the vocabulary. ''Nonterminal symbols'' are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar. A formal grammar defines a formal language over the vocabulary of the grammar. In the context of formal language, the term ''vocabulary'' is more commonly known as ''alphabet''. Nonterminal symbols are also called ''syntactic variables''. Terminal symbols Terminal symbols are those symbols that can appear in the formal language defined by a formal grammar. The process of applying the production rules successively to a start symbol might not terminate, but if it terminates when there is no more production rule can be applied, the output string will consist only of terminal symb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Grammars
A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings — only their form. In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas. A formal grammar is a set of rules for rewriting strings, along with a "start symbol" from which rewriting starts. Therefore, a grammar is usually thought of as a language generator. However, it can also sometimes be used as the basis for a " recognizer"—a function in computing that determines whether a given string belongs to the language or is grammatically incorrect. To describe such recognizers, formal language theory uses separate formalisms, known as automata theory. One of the interesting res ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Theory
In mathematics and theoretical computer science, a type theory is the formal presentation of a specific type system. Type theory is the academic study of type systems. Some type theories serve as alternatives to set theory as a foundation of mathematics. Two influential type theories that have been proposed as foundations are: * Typed λ-calculus of Alonzo Church * Intuitionistic type theory of Per Martin-Löf Most computerized proof-writing systems use a type theory for their foundation. A common one is Thierry Coquand's Calculus of Inductive Constructions. History Type theory was created to avoid paradoxes in naive set theory and formal logic, such as Russell's paradox which demonstrates that, without proper axioms, it is possible to define the set of all sets that are not members of themselves; this set both contains itself and does not contain itself. Between 1902 and 1908, Bertrand Russell proposed various solutions to this problem. By 1908, Russell arrive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EACSL
The European Association for Computer Science Logic (EACSL), founded 14 July 1992, . Description of goals from EACSL official website. is an international professional non-profit organization representing the interests of its members and promoting logic in the areas of and education. It supports both basic and application oriented research to advance the connections between basic research and industrial applications. The current president is Prof. Thomas Schwentick ( [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture Notes In Computer Science
''Lecture Notes in Computer Science'' is a series of computer science books published by Springer Science+Business Media since 1973. Overview The series contains proceedings, post-proceedings, monographs, and Festschrifts. In addition, tutorials, state-of-the-art surveys, and "hot topics" are increasingly being included. The series is indexed by DBLP. See also *'' Monographiae Biologicae'', another monograph series published by Springer Science+Business Media *'' Lecture Notes in Physics'' *'' Lecture Notes in Mathematics'' *'' Electronic Workshops in Computing'', published by the British Computer Society image:Maurice Vincent Wilkes 1980 (3).jpg, Sir Maurice Wilkes served as the first President of BCS in 1957. The British Computer Society (BCS), branded BCS, The Chartered Institute for IT, since 2009, is a professional body and a learned ... References External links * Academic journals established in 1973 Computer science books Series of non-fiction books ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Explicit Substitution
In computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus; the "freshness" conditions in such implicit calculi are a notorious source of errors. The concept has appeared in a large number of published papers in quite different fields, such as in abstract machines, predicate logic, and symbolic computation. Overview A simple example of a lambda calculus with explicit substitution is "λx", which adds one new form of term to the lambda calculus, namely the form M⟨x:=N⟩, which reads "M where x will be substituted by N". (The meaning of the new term is the same as the common idiom let x:=N in M from many programming languages.) λx can be written with the following rewriting rules: # (λx.M) N → M&la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A K Peters
A K Peters, Ltd. was a publisher of scientific and technical books, specializing in mathematics and in computer graphics, robotics, and other fields of computer science. They published the journals '' Experimental Mathematics'' and the '' Journal of Graphics Tools'', as well as mathematics books geared to children. Background Klaus Peters wrote a doctoral dissertation on complex manifolds at the University of Erlangen in 1962, supervised by Reinhold Remmert. He then joined Springer Verlag, becoming their first specialist mathematics editor. As a Springer director from 1971, he hired Alice Merker for Springer New York: they were married that year, and moved to Heidelberg. Leaving Springer, they founded Birkhäuser Boston in 1979; Birkhäuser ran into financial difficulties, and was taken over by Springer. Klaus and Alice then spent a period running a Boston office for Harcourt Brace Jovanovich and their imprint Academic Press. With the takeover of Harcourt Brace Jovanovich by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
