Non-logical symbol, the Glossary
In logic, the formal languages used to create expressions consist of symbols, which can be broadly divided into constants and variables.[1]
Table of Contents
25 relations: A K Peters, Arity, Cartesian product, Domain of discourse, Equality (mathematics), Equivalence relation, First-order logic, Formal language, Formal system, Function (mathematics), Integer, Interpretation (logic), Logic, Logical connective, Logical constant, Logical equivalence, Predicate (mathematical logic), Quantifier (logic), Rudolf Carnap, Semantics of logic, Sentence (mathematical logic), Statement (logic), Structure (mathematical logic), Symbol (formal), Variable (mathematics).
- Logic symbols
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.
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Arity
In logic, mathematics, and computer science, arity is the number of arguments or operands taken by a function, operation or relation.
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Cartesian product
In mathematics, specifically set theory, the Cartesian product of two sets and, denoted, is the set of all ordered pairs where is in and is in.
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Domain of discourse
In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.
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Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally, two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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First-order logic
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Formal language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules called a formal grammar. Non-logical symbol and formal language are formal languages.
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Formal system
A formal system is an abstract structure and formalization of an axiomatic system used for inferring theorems from axioms by a set of inference rules. Non-logical symbol and formal system are formal languages.
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Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of.
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Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
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Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language. Non-logical symbol and interpretation (logic) are formal languages.
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Logic
Logic is the study of correct reasoning.
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Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Non-logical symbol and logical connective are logic symbols.
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Logical constant
In logic, a logical constant or constant symbol of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Non-logical symbol and logical constant are logic symbols.
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Logical equivalence
In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model.
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Predicate (mathematical logic)
In logic, a predicate is a symbol that represents a property or a relation.
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Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula.
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Rudolf Carnap
Rudolf Carnap (18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter.
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Semantics of logic
In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal languages and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of logical consequence.
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Sentence (mathematical logic)
In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables.
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Statement (logic)
In logic and semantics, the term statement is variously understood to mean either.
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Structure (mathematical logic)
In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.
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Symbol (formal)
A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Non-logical symbol and symbol (formal) are formal languages and logic symbols.
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Variable (mathematics)
In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object.
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See also
Logic symbols
- Ampersand
- Arrow (symbol)
- Conjunction/disjunction duality
- Descending wedge
- Double turnstile
- Existential quantification
- Free variables and bound variables
- Glossary of Principia Mathematica
- Horseshoe (symbol)
- List of logic symbols
- Literal (mathematical logic)
- Logical connective
- Logical connectives
- Logical constant
- Lozenge (shape)
- Metavariable
- Modal operator
- Non-logical symbol
- Predicate variable
- Propositional variable
- Sheffer stroke
- Symbol (formal)
- Tee (symbol)
- Therefore sign
- Tilde
- Triple bar
- Turned A
- Turnstile (symbol)
- Universal quantification
- Up tack
- Vertical bar
- Wedge (symbol)
References
[1] https://en.wikipedia.org/wiki/Non-logical_symbol
Also known as Descriptive sign, Individual constant, Non-logical constant, Non-logical symbols.