Disjunction

A logical connective that combines propositions and is true when at least one component proposition is true. In classical logic, inclusive disjunction is also true when both are true.

Truth table: A table that lists a logical expression’s truth value for every assignment of truth values to its variables. Its rows specify exactly when a disjunction is true or false.
Proposition: A declarative statement that can be assigned a truth value. Each component of a disjunction is a proposition.
Resolution (logic): An inference rule that derives a clause by eliminating complementary literals from two clauses. Resolution combines clauses containing disjunctions to support automated proof.
Intuitionistic logic: A logic that interprets proof and truth constructively, rejecting some classical principles. Its disjunction property requires a proof of a disjunction to establish one side.
Inclusive disjunction: A disjunction that is true when either or both of its component propositions are true. This is the standard classical interpretation of disjunction.
Logical connective: An expression that combines or modifies propositions to form more complex logical expressions. Disjunction belongs to the family of operations that build compound propositions.
Disjunctive normal form: A Boolean expression written as a disjunction of conjunctions of literals. It organizes logical formulas around disjunctions of simpler terms.
Relevant logic: A family of nonclassical logics that restricts inference to preserve relevance between premises and conclusions. Its accounts of disjunction challenge some classical inferences involving unrelated alternatives.
Exclusive disjunction: A connective that is true when exactly one of its component propositions is true. It differs from inclusive disjunction when both propositions are true.
Conjunction: A logical connective that is true only when all its component propositions are true. It requires both components to hold, unlike inclusive disjunction.

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