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Modus ponens

In propositional logic, modus ponens (/ˈmoʊdəs ˈpoʊnɛnz/; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q. P is true. Therefore, Q must also be true."

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Field
Classical logic · Propositional calculus
First stated by
Theophrastus
Statement
P {\displaystyle P} implies Q {\displaystyle Q} . P {\displaystyle P} is true. Therefore, Q {\displaystyle Q} must also be true.
Symbolic statement
P → Q , P ⊢ Q {\displaystyle P\to Q,\;P\;\vdash \ Q}
Type
Deductive argument form · Rule of inference

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Modus ponens

Nodes59
Edges58
Triples43
Avg. degree1.97
Density0.033898
Components1

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Modus ponens

Top relations

related to Alleged cases of failure · 9
Modus ponens → Either Shakespeare, Hamlet, Hobbes, If, Philosophers, Shakespeare, The, Therefore, Vann McGee
related to Status · 7
Modus ponens → Enderton, If, In, Its, Modus, Russell, While
related to Algebraic semantics · 6
Modus ponens → Boolean, Confirming, In, Logical, Typically, With
related to External links · 6
Modus ponens → EMS Press, Encyclopedia, Mathematics, Modus, PhilPapersModus, Wolfram MathWorld
related to Explanation · 3
Modus ponens → If, The, Therefore
Field · 2
Modus ponens → Classical logic, Propositional calculus
Type · 2
Modus ponens → Deductive argument form, Rule of inference
is a · 2
Modus ponens → Cut rule, mixed hypothetical syllogism and is closely related to another valid form of argument
First stated by · 1
Modus ponens → Theophrastus
Statement · 1
Modus ponens → P {\displaystyle P} implies Q {\displaystyle Q} . P {\displaystyle P} is true. Therefore, Q {\displaystyle Q} must also be true.

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Important terminology

modus ponens true argument displaystyle logic also conditional inference form implication rule must implies antecedent statement one deductive shakespeare therefore

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Modus ponensFieldClassical logic1.00infobox
Modus ponensFieldPropositional calculus1.00infobox
Modus ponensFirst stated byTheophrastus1.00infobox
Modus ponensStatementP {\displaystyle P} implies Q {\displaystyle Q} . P {\displaystyle P} is true. Therefore, Q {\displaystyle Q} must also be true.1.00infobox
Modus ponensSymbolic statementP → Q , P ⊢ Q {\displaystyle P\to Q,\;P\;\vdash \ Q}1.00infobox
Modus ponensTypeDeductive argument form1.00infobox
Modus ponensTypeRule of inference1.00infobox
Modus ponensis amixed hypothetical syllogism and is closely related to another valid form of argument0.90text
Modus ponensis aCut rule0.90text
Modus ponensrelated to Algebraic semanticsIn0.60section
Modus ponensrelated to Algebraic semanticsTypically0.60section
Modus ponensrelated to Algebraic semanticsLogical0.60section

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