Proposition

A proposition is the content expressed by a declarative sentence and is capable of being true or false. Different sentences can express the same proposition.

Truth value: A value, usually true or false, assigned to a proposition or logical formula. A proposition’s capacity to be true or false is expressed by its truth value.
Sentence: A grammatically complete expression in a language, typically composed of words and governed by syntactic rules. A sentence is a linguistic expression; a proposition is the content it can express.
Propositional logic: A formal system that represents propositions and studies how their truth values combine. It treats propositions as units connected by operators such as negation and conjunction.
Inference: A reasoning step in which one or more claims support a conclusion. Logical relations among propositions determine which conclusions follow from premises.
Declarative sentence: A sentence that makes a statement rather than asking a question or issuing a command. Declarative sentences are the standard linguistic vehicles for expressing propositions.
Statement: An act or product of asserting that something is the case. A statement is an assertion, while a proposition is the content that may be asserted.
Possible-world semantics: An approach to meaning that evaluates expressions by the worlds in which they are true. It models propositions as sets of possible worlds where they hold.
Entailment: A relation in which the truth of one or more propositions guarantees the truth of another. Entailment captures when one proposition’s truth requires another’s truth.
Sentence meaning: The semantic content conventionally associated with a sentence in a language. The proposition is the truth-evaluable content associated with a declarative sentence.
Belief: A mental attitude in which a person accepts a proposition as true. Belief is an attitude toward a proposition, not the truth-evaluable content itself.

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