If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. ^[1]

46 relations: Artificial Intelligence: A Modern Approach, Backward chaining, Database, Definition, Domain of discourse, Equivalence relation, Euler diagram, First-order logic, Formal system, Forward chaining, Gemination, Glossary of mathematical jargon, Jan Łukasiewicz, John L. Kelley, Logic, Logic programming, Logical biconditional, Logical connective, Logical disjunction, Logical equality, Logical equivalence, Material conditional, Mathematical logic, Mathematics, Metalogic, Necessity and sufficiency, Paul Halmos, Peter Norvig, Philosophy, Phonaesthetics, Polish notation, Polysyllogism, Prentice Hall, Proof theory, Propositional calculus, Statutory interpretation, Stuart J. Russell, Subset, TeX, Truth function, Truth table, Undergraduate Texts in Mathematics, Well-formed formula, WolframAlpha, XNOR gate, XOR gate.
Logical connectives
Necessity and sufficiency

Artificial Intelligence: A Modern Approach

Artificial Intelligence: A Modern Approach (AIMA) is a university textbook on artificial intelligence, written by Stuart J. Russell and Peter Norvig.

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Backward chaining

Backward chaining (or backward reasoning) is an inference method described colloquially as working backward from the goal.

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In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data.

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Definition

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). If and only if and definition are mathematical terminology.

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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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Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

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Euler diagram

An Euler diagram is a diagrammatic means of representing sets and their relationships.

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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 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.

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Forward chaining

Forward chaining (or forward reasoning) is one of the two main methods of reasoning when using an inference engine and can be described logically as repeated application of modus ponens.

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Gemination

In phonetics and phonology, gemination (from Latin 'doubling', itself from gemini 'twins'), or consonant lengthening, is an articulation of a consonant for a longer period of time than that of a singleton consonant.

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Glossary of mathematical jargon

The language of mathematics has a vast vocabulary of specialist and technical terms. If and only if and Glossary of mathematical jargon are mathematical terminology.

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Jan Łukasiewicz

Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic.

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John L. Kelley

John L. Kelley (December 6, 1916, Kansas – November 26, 1999, Berkeley, California) was an American mathematician at the University of California, Berkeley, who worked in general topology and functional analysis.

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Logic

Logic is the study of correct reasoning.

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Logic programming

Logic programming is a programming, database and knowledge representation paradigm based on formal logic.

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Logical biconditional

In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements P and Q to form the statement "P if and only if Q" (often abbreviated as "P iff Q"), where P is known as the antecedent, and Q the consequent. If and only if and logical biconditional are logical connectives.

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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. If and only if and logical connective are logical connectives.

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Logical disjunction

In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as \lor and read aloud as "or". If and only if and logical disjunction are logical connectives.

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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. If and only if and logical equality are logical connectives.

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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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Material conditional

The material conditional (also known as material implication) is an operation commonly used in logic. If and only if and material conditional are logical connectives.

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Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Metalogic

Metalogic is the metatheory of logic.

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Necessity and sufficiency

In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. If and only if and necessity and sufficiency are mathematical terminology.

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Paul Halmos

Paul Richard Halmos (Halmos Pál; 3 March 3 1916 – 2 October 2006) was a Hungarian-born American mathematician and statistician who made fundamental advances in the areas of mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces).

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Peter Norvig

Peter Norvig (born December 14, 1956) is an American computer scientist and Distinguished Education Fellow at the Stanford Institute for Human-Centered AI.

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Philosophy

Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language.

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Phonaesthetics

Phonaesthetics (also spelled phonesthetics in North America) is the study of beauty and pleasantness associated with the sounds of certain words or parts of words.

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Polish notation

Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators precede their operands, in contrast to the more common infix notation, in which operators are placed between operands, as well as reverse Polish notation (RPN), in which operators follow their operands.

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Polysyllogism

A polysyllogism is a complex argument (also known as chain arguments of which there are four kinds: polysyllogisms, sorites, epicheirema, and dilemmas) that strings together any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on.

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Prentice Hall

Prentice Hall was a major American educational publisher.

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Proof theory

Proof theory is a major branchAccording to Wang (1981), pp.

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Propositional calculus

The propositional calculus is a branch of logic.

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Statutory interpretation

Statutory interpretation is the process by which courts interpret and apply legislation.

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Stuart J. Russell

Stuart Jonathan Russell (born 1962) is a British computer scientist known for his contributions to artificial intelligence (AI).

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Subset

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment).

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TeX

TeX (see below), stylized within the system as, is a typesetting program which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978.

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Truth function

In logic, a truth function is a function that accepts truth values as input and produces a unique truth value as output.

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Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.

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Undergraduate Texts in Mathematics

Undergraduate Texts in Mathematics (UTM) is a series of undergraduate-level textbooks in mathematics published by Springer-Verlag.

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Well-formed formula

In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.

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WolframAlpha

WolframAlpha is an answer engine developed by Wolfram Research.

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XNOR gate

The XNOR gate (sometimes ENOR, EXNOR, NXOR, XAND and pronounced as Exclusive NOR) is a digital logic gate whose function is the logical complement of the Exclusive OR (XOR) gate.

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XOR gate

XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd.

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References

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

Also known as All and only, Bi-implication, If & only if, If, and only if, Iff, Just in case (catachresis), Material equivalence, Materially equivalent, Only if, Precisely when, .

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If and only if

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See also

Logical connectives

Necessity and sufficiency

References