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Logical biconditional

Index 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. [1]

28 relations: Antecedent (logic), Associative property, Biconditional elimination, Biconditional introduction, Categorical proposition, Commutative property, Consequent, Distributive property, Exclusive or, Hadamard transform, Harper (publisher), Idempotence, If and only if, Józef Maria Bocheński, Logic, Logical connective, Logical disjunction, Logical equality, Logical equivalence, Material conditional, Mathematics, Monotonic function, Necessity and sufficiency, Negation, Pons asinorum, Proposition, Truth value, XNOR gate.

Antecedent (logic)

An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Biconditional elimination

Biconditional elimination is the name of two valid rules of inference of propositional logic.

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Biconditional introduction

In propositional logic, biconditional introduction is a valid rule of inference.

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Categorical proposition

In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term).

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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Consequent

A consequent is the second half of a hypothetical proposition.

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Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

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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).

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Hadamard transform

The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms.

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Harper (publisher)

Harper is an American publishing house, currently the flagship imprint of global publisher HarperCollins.

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Idempotence

Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.

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If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

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Józef Maria Bocheński

Józef Maria Bocheński (Czuszów, Congress Poland, Russian Empire, 30 August 1902 – 8 February 1995, Fribourg, Switzerland) was a Polish Dominican, logician and philosopher.

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Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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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.

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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.

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Logical equality

Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus.

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Logical equivalence

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

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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 "→".

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

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Negation

In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.

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Pons asinorum

In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum, typically translated as "bridge of asses".

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Proposition

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

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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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XNOR gate

The XNOR gate (often written Exclusive-NOR, sometimes: EXNOR, ENOR, NXOR, XAND) is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate.

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Redirects here:

Biconditional, Biconditionality, Biconditionals, Logical XNOR, Material biconditional.

References

[1] https://en.wikipedia.org/wiki/Logical_biconditional

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