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Drinker paradox, the Glossary

The drinker paradox (also known as the drinker's theorem, the drinker's principle, or the drinking principle) is a theorem of classical predicate logic that can be stated as "There is someone in the pub such that, if he or she is drinking, then everyone in the pub is drinking." It was popularised by the mathematical logician Raymond Smullyan, who called it the "drinking principle" in his 1978 book What Is the Name of this Book? The apparently paradoxical nature of the statement comes from the way it is usually stated in natural language.^[1]

Antecedent (logic)

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

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Automated reasoning

In computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning.

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Classical logic

Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic.

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Correlation does not imply causation

The phrase "correlation does not imply causation" refers to the inability to legitimately deduce a cause-and-effect relationship between two events or variables solely on the basis of an observed association or correlation between them.

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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. Drinker paradox and First-order logic are predicate logic.

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Henk Barendregt

Hendrik Pieter (Henk) Barendregt (born 18 December 1947, Amsterdam) is a Dutch logician, known for his work in lambda calculus and type theory.

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Intuitionistic logic

Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.

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List of paradoxes

This list includes well known paradoxes, grouped thematically.

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Material conditional

The material conditional (also known as material implication) is an operation commonly used in logic.

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Mathematical logic

Mathematical logic is the study of formal logic within mathematics.

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Natural language

In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation.

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Paradox

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation.

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Predicate (mathematical logic)

In logic, a predicate is a symbol that represents a property or a relation. Drinker paradox and predicate (mathematical logic) are predicate logic.

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Prentice Hall

Prentice Hall was a major American educational publisher.

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Principle of explosion

In classical logic, intuitionistic logic, and similar logical systems, the principle of explosion is the law according to which any statement can be proven from a contradiction.

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Proof assistant

In computer science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration.

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Raymond Smullyan

Raymond Merrill Smullyan (May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher.

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Reification (information retrieval)

In information retrieval and natural language processing reification is the process by which an abstract idea about a person, place or thing, is turned into an explicit data model or other object created in a programming language, such as a feature set of demographichttp://cs.iit.edu/~culotta/pubs/culotta15predicting.pdf or psychographichttps://arxiv.org/abs/2403.14380 attributes or both.

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Relevance logic

Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related.

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Temporal logic

In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am always hungry", "I will eventually be hungry", or "I will be hungry until I eat something").

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References

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

Also known as Drinker's paradox, Drinker's principle, Drinkers' principle, Drinking principle, Smullyan's paradox, The Drinking Principle.