Modus ponendo tollens

An inference form that affirms one of two mutually exclusive alternatives to conclude that the other is false. It is valid when the alternatives cannot both be true.

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Disjunction: A compound proposition asserting that at least one of two or more propositions is true. The inference begins with a disjunction whose alternatives cannot both hold.
Modus ponens: An inference form that derives a consequent from a conditional and its antecedent. It uses a conditional rather than mutually exclusive alternatives.
Latin logical terminology: The Latin vocabulary used to name and describe traditional forms of logical inference. The form's name encodes its characteristic move: affirming to deny.
Exclusive disjunction in programming: The use of exclusive-or operations in programming languages and digital circuits. A Boolean exclusive-or supplies alternatives that cannot both be true.
Exclusive or: A connective that is true exactly when one of its two inputs is true and the other is false. This connective states the mutual exclusivity required for the inference.
Modus tollens: An inference form that denies a conditional's consequent to infer that its antecedent is false. Despite the similar name, it reasons from a conditional, not an exclusive disjunction.
Stoic logic: The ancient Greek logical tradition developed by Stoic philosophers, especially Chrysippus. Ancient analysis of disjunctions provides historical context for this inference pattern.
Boolean algebra: An algebraic system for manipulating variables with truth values and logical operations. Boolean algebra provides a precise setting for checking this inference computationally.
Negation: A logical operation that reverses the truth value of a proposition. The conclusion negates the alternative excluded by the affirmed one.
Disjunctive syllogism: An inference form that denies one disjunct to infer the other. It starts from an inclusive disjunction and eliminates an option by denying it.