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Predicate (mathematical logic)

Index Predicate (mathematical logic)

In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory. [1]

29 relations: Arity, Atomic formula, Autoepistemic logic, Binary relation, Boolean expression, Boolean-valued function, Characteristic function (probability theory), Classifying topos, First-order logic, Free variables and bound variables, Function (mathematics), Fuzzy logic, Indicator function, Law of excluded middle, Mathematical logic, Opaque predicate, Plural quantification, Predicate functor logic, Probability distribution, Property (philosophy), Proposition, Propositional calculus, Propositional function, Propositional variable, Set theory, Set-builder notation, Template processor, Truth value, Truth-bearer.

Arity

In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.

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Atomic formula

In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.

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Autoepistemic logic

The autoepistemic logic is a formal logic for the representation and reasoning of knowledge about knowledge.

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Binary relation

In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.

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Boolean expression

In computer science, a Boolean expression is an expression in a programming language that produces a Boolean value when evaluated, i.e. one of true or false.

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Boolean-valued function

A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f: X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B.

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Characteristic function (probability theory)

In probability theory and statistics, the characteristic function of any real-valued random variable completely defines its probability distribution.

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Classifying topos

In mathematics, a classifying topos for some sort of structure is a topos T such that there is a natural equivalence between geometric morphisms from a cocomplete topos E to T and the category of models for the structure in E.

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First-order logic

First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

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Free variables and bound variables

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.

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Indicator function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset.

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Law of excluded middle

In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.

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Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

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Opaque predicate

In computer programming, an opaque predicate is a predicate—an expression that evaluates to either "true" or "false"—for which the outcome is known by the programmer a priori, but which, for a variety of reasons, still needs to be evaluated at run time.

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Plural quantification

In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular, values.

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Predicate functor logic

In mathematical logic, predicate functor logic (PFL) is one of several ways to express first-order logic (also known as predicate logic) by purely algebraic means, i.e., without quantified variables.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Property (philosophy)

In philosophy, mathematics, and logic, a property is a characteristic of an object; a red object is said to have the property of redness.

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Proposition

The term proposition has a broad use in contemporary analytic philosophy.

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Propositional calculus

Propositional calculus is a branch of logic.

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Propositional function

A propositional function in logic, is a sentence expressed in a way that would assume the value of true or false, except that within the sentence is a variable (x) that is not defined or specified, which leaves the statement undetermined.

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Propositional variable

In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false.

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Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

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Set-builder notation

In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements or stating the properties that its members must satisfy.

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Template processor

A template processor (also known as a template engine or template parser) is software designed to combine templates with a data model to produce result documents.

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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.

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Truth-bearer

A truth-bearer is an entity that is said to be either true or false and nothing else.

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Boolean predicates, Logical predicate, Predicate (computer programming), Predicate (logic), Predicate (mathematics), Predication (computer programming).

References

[1] https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)

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