Logical connective

A logical connective is an operator that combines propositions or truth values to form a compound proposition, such as negation, conjunction, or implication.

Proposition: A proposition is a declarative statement that can be true or false. Connectives take propositions as inputs and form compound propositions.
Truth table: A truth table lists an expression's truth value for every possible assignment of truth values to its variables. It gives a complete account of a truth-functional connective's behavior.
Propositional calculus: Propositional calculus is a formal system for reasoning with propositions and truth-functional operators. It studies arguments built from logical connectives.
Intuitionistic logic: Intuitionistic logic is a nonclassical logic that rejects unrestricted use of the law of excluded middle. Its connective meanings are tied to constructive proof rather than classical truth tables.
Truth value: A truth value is the value true or false assigned to a proposition in classical logic. Truth-functional connectives determine compound truth values from their inputs.
Negation: Negation is a unary connective that reverses a proposition's truth value in classical logic. It is the simplest connective, operating on one proposition.
Logical equivalence: Logical equivalence holds between formulas that have the same truth value under every interpretation. Equivalent connective expressions can replace one another without changing truth conditions.
Modal logic: Modal logic extends classical logic with operators such as necessity and possibility. Modal operators add structure beyond ordinary truth-functional connectives.
Logical form: Logical form is the abstract structure of an expression, separated from its particular content. Connectives reveal how a compound proposition is structured.
Conjunction: Conjunction is a binary connective that is true exactly when both of its component propositions are true. It combines propositions with the truth condition underlying logical 'and'.

Linked from 23 pages