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# Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". [1]

57 relations: A, A K Peters, Adjoint functors, Binary relation, Category theory, Charles Sanders Peirce, Composite number, Converse implication, Converse nonimplication, Counterexample, Domain of discourse, Element (mathematics), Exclusive or, Existential quantification, False (logic), First-order logic, Free variables and bound variables, Functor, Image (mathematics), Interpretation (logic), James Franklin (philosopher), Judgment (mathematical logic), List of logic symbols, Logical biconditional, Logical conjunction, Logical connective, Logical constant, Logical disjunction, Logical equivalence, Logical NOR, Logical truth, Material conditional, Material nonimplication, Mathematical logic, Natural number, Power set, Predicate (mathematical logic), Predicate variable, Presheaf (category theory), Property (philosophy), Propositional function, Quantifier (logic), Rule of inference, Sans-serif, Satisfiability, Saunders Mac Lane, Set (mathematics), Sheffer stroke, Symbol (formal), Tilde, ... Expand index (7 more) »

## A

A (named, plural As, A's, as, a's or aes) is the first letter and the first vowel of the ISO basic Latin alphabet.

## 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.

In mathematics, specifically category theory, adjunction is a possible relationship between two functors.

## 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.

## Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms).

## Charles Sanders Peirce

Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".

## Composite number

A composite number is a positive integer that can be formed by multiplying together two smaller positive integers.

## Converse implication

Converse implication is the converse of implication, written ←. That is to say; that for any two propositions P and Q, if Q implies P, then P is the converse implication of Q. It is written P \leftarrow Q, but may also be notated P \subset Q, or "Bpq" (in Bocheński notation).

## Converse nonimplication

In logic, converse nonimplication is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication).

## Counterexample

In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule or law.

## 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.

## Element (mathematics)

In mathematics, an element, or member, of a set is any one of the distinct objects that make up that set.

## Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

## Existential quantification

In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".

## False (logic)

In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective.

## 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.

## 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.

## Functor

In mathematics, a functor is a map between categories.

## Image (mathematics)

In mathematics, an image is the subset of a function's codomain which is the output of the function from a subset of its domain.

## Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language.

## James Franklin (philosopher)

James Franklin (born 1953 in Sydney) is an Australian philosopher, mathematician and historian of ideas.

## Judgment (mathematical logic)

In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in the metalanguage.

## List of logic symbols

In logic, a set of symbols is commonly used to express logical representation.

## Logical biconditional

In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "P if and only if Q", where P is an antecedent and Q is a consequent.

## Logical conjunction

In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.

## 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.

## Logical constant

In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal.

## Logical disjunction

In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.

## Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

## Logical NOR

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or.

## Logical truth

Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.

## Material conditional

The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".

## Material nonimplication

Material nonimplication or abjunction (Latin ab.

## Mathematical logic

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

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

## 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.

## Predicate variable

In first-order logic, a predicate variable is a predicate letter which can stand for a relation (between terms) but which has not been specifically assigned any particular relation (or meaning).

## Presheaf (category theory)

In category theory, a branch of mathematics, a presheaf on a category C is a functor F\colon C^\mathrm\to\mathbf.

## 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.

## 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.

## Quantifier (logic)

In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.

## Rule of inference

In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).

## Sans-serif

In typography and lettering, a sans-serif, sans serif, gothic, or simply sans letterform is one that does not have extending features called "serifs" at the end of strokes.

## Satisfiability

In mathematical logic, satisfiability and validity are elementary concepts of semantics.

## Saunders Mac Lane

Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.

## Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

## Sheffer stroke

In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written ↑, also written | (not to be confused with "||", which is often used to represent disjunction), or Dpq (in Bocheński notation), denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".

## 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.

## Tilde

The tilde (in the American Heritage dictionary or; ˜ or ~) is a grapheme with several uses.

## Topos

In mathematics, a topos (plural topoi or, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).

## Turned A

Turned A (capital: Ɐ, lowercase: ɐ, math symbol ∀) is a symbol based upon the letter A. Lowercase ɐ (in two story form) is used in the International Phonetic Alphabet to identify the near-open central vowel.

## Type theory

In mathematics, logic, and computer science, a type theory is any of a class of formal systems, some of which can serve as alternatives to set theory as a foundation for all mathematics.

## Universal generalization

In predicate logic, generalization (also universal generalization or universal introduction, GEN) is a valid inference rule.

## Universal instantiation

In predicate logic universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.

## Vacuous truth

In mathematics and logic, a vacuous truth is a statement that asserts that all members of the empty set have a certain property.

## Valuation (logic)

In logic and model theory, a valuation can be.

## References

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