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Existential generalization

In predicate logic, existential generalization (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier ( ∃ {\displaystyle…

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Field
Predicate logic
Statement
There exists a member x {\displaystyle x} in a universal set with a property of Q {\displaystyle Q}
Symbolic statement
Q ( a ) → ∃ x Q ( x ) , {\displaystyle Q(a)\to \ \exists {x}\,Q(x),}
Type
Rule of inference

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Existential generalization

Nodes14
Edges13
Triples10
Avg. degree1.86
Density0.142857
Components1

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Existential generalization

Top relations

related to Quine · 6
Existential generalization → According, It, Socrates, The, Willard Van Orman Quine, Yet
Field · 1
Existential generalization → Predicate logic
Statement · 1
Existential generalization → There exists a member x {\displaystyle x} in a universal set with a property of Q {\displaystyle Q}
Symbolic statement · 1
Existential generalization → Q ( a ) → ∃ x Q ( x ) , {\displaystyle Q(a)\to \ \exists {x}\,Q(x),}
Type · 1
Existential generalization → Rule of inference

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Important terminology

displaystyle existential example therefore made cup tea logic rule inference exists generalization loves wag tail alice someone also universal predicate

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Existential generalizationFieldPredicate logic1.00infobox
Existential generalizationStatementThere exists a member x {\displaystyle x} in a universal set with a property of Q {\displaystyle Q}1.00infobox
Existential generalizationSymbolic statementQ ( a ) → ∃ x Q ( x ) , {\displaystyle Q(a)\to \ \exists {x}\,Q(x),}1.00infobox
Existential generalizationTypeRule of inference1.00infobox
Existential generalizationrelated to QuineAccording0.60section
Existential generalizationrelated to QuineWillard Van Orman Quine0.60section
Existential generalizationrelated to QuineSocrates0.60section
Existential generalizationrelated to QuineThe0.60section
Existential generalizationrelated to QuineYet0.60section
Existential generalizationrelated to QuineIt0.60section

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