Propositons

A proposition is a declarative sentence or the content of such a sentence that expresses a claim that can be true or false.

In propositional logic, propositions are the basic units. Atomic propositions cannot be further decomposed into simpler truth-bearing parts; compound propositions are formed by logical connectives: and, or, not, implies, if and only if. Their truth values are determined by the truth values of their components, and the rules of logic are captured in truth tables.

In philosophy, propositions are often treated as abstract entities that bear truth conditions. They are the meanings or contents of sentences, possibly sharing the same content across different linguistic forms. Philosophers distinguish proposition from the sentence, and discuss issues such as reference, belief, and possible worlds.

In linguistics, propositions are the content of declarative clauses that can be embedded under propositional attitude verbs like believe, hope, or doubt; the same proposition can be presented in different ways in different languages.

In mathematics and formal reasoning, a proposition is a statement that can be proved true or false. Theorem is a proposition that has been demonstrated within a formal system; a conjecture is a proposition yet to be proved or disproved.