Absorption / modus tollens / modus ponendo tollens
Negation introduction
Rules of replacement
Associativity
Commutativity
Distributivity
Double negation
De Morgan's laws
Transposition
Material implication
Exportation
Tautology
Predicate logic
Rules of inference
Universal generalization / instantiation
Existential generalization / instantiation
In propositional logic, modus ponens (/ˈmoʊdəsˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'),[1]implication elimination, or affirming the antecedent,[2] is a deductive argument form and rule of inference.[3] It can be summarized as "P implies Q.P is true. Therefore, Q must also be true."
Modus ponens is a mixed hypothetical syllogism and is closely related to another valid form of argument, modus tollens. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of modus ponens.
The history of modus ponens goes back to antiquity.[4] The first to explicitly describe the argument form modus ponens was Theophrastus.[5] It, along with modus tollens, is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal.
^Stone, Jon R. (1996). Latin for the Illiterati: Exorcizing the Ghosts of a Dead Language. London: Routledge. p. 60. ISBN 0-415-91775-1.
^"Oxford reference: affirming the antecedent". Oxford Reference.
^Enderton 2001:110
^Susanne Bobzien (2002). "The Development of Modus Ponens in Antiquity", Phronesis 47, No. 4, 2002.
^"Ancient Logic: Forerunners of Modus Ponens and Modus Tollens". Stanford Encyclopedia of Philosophy.
In propositional logic, modusponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), implication...
(derived by modusponens) Likewise, every use of modusponens can be converted to a use of modus tollens and transposition. The modus tollens rule can...
In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument...
modusponens, not to be mistaken with modus tollens, which is another valid argument form that has a like-sounding name and structure. Modusponens (sometimes...
inference for propositional logic. It is closely related to modusponens and modus tollendo ponens. MPT is usually described as having the form: Not both A...
hypothetical syllogism either affirms the antecedent (modusponens) or denies the consequent (modus tollens). An invalid hypothetical syllogism either affirms...
contrast to modusponens, reasoning with modus tollens goes in the opposite direction to that of the conditional. The general expression for modus tollens...
criminal profiler Latin phrases Modusponens – Rule of logical inference Modus tollens – Rule of logical inference Modus vivendi – Arrangement that allows...
premise; instead, he reverses the argument from being in the form of modusponens to modus tollens. This logical maneuver is often called a G. E. Moore shift...
conclusion (or conclusions). For example, the rule of inference called modusponens takes two premises, one in the form "If p then q" and another in the...
the Quebec Agreement. Latin phrases Modus operandi – Habits of working Modusponens – Rule of logical inference Modus tollens – Rule of logical inference...
commonly studied Hilbert systems have either just one rule of inference – modusponens, for propositional logics – or two – with generalisation, to handle predicate...
conclusion follows a pattern called a rule of inference. For example, modusponens is a rule of inference according to which all arguments of the form "(1)...
to the problem of infinite regress: modusponens is placed as a rule within the system, the validity of modusponens is eschewed without the system. In...
Material implication can also be characterized inferentially by modusponens, modus tollens, conditional proof, and classical reductio ad absurdum.[citation...
of the symbols and symbol sequences. Rule of inference, detachment, modusponens : The rule that allows the theory to "detach" a "conclusion" from the...
output based on input variables. Modusponens and modus tollens are the most important rules of inference. A modusponens rule is in the form Premise: x...
not be false. Valid arguments follow a rule of inference, such as modusponens or modus tollens. Deductive reasoning plays a central role in formal logic...
valid and two are invalid. Affirming the antecedent (modusponens) and denying the consequent (modus tollens) are valid. Affirming the consequent and denying...
inference rule of sequent calculus. It is a generalisation of the classical modusponens inference rule. Its meaning is that, if a formula A appears as a conclusion...
argument from definition. The most reliable forms of logic are modusponens, modus tollens, and chain arguments because if the premises of the argument...
these laws, and none of these laws provides inference rules, such as modusponens or De Morgan's laws. The law is also known as the law / principle of...
the use of the procedure of modusponens to "detach" Q: "No Xs are Zs" and dispense with the terms on the left. Modusponens (or "the fundamental rule of...
modusponens, which states that arguments of the form "(1) p; (2) if p then q; (3) therefore q" are valid. An example of an argument following modus ponens...
these laws, and none of these laws provide inference rules, such as modusponens or De Morgan's laws. The law of non-contradiction and the law of excluded...
Destructive dilemma is the disjunctive version of modus tollens. The disjunctive version of modusponens is the constructive dilemma. The destructive dilemma...
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