Predicate logic | Rules of inference

Universal instantiation

In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as for every formula A and every term a, where is the result of substituting a for each free occurrence of x in A. is an instance of And as a rule of inference it is from infer Irving Copi noted that universal instantiation "...follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934." (Wikipedia).

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Related pages

Existential instantiation | Dictum de omni et nullo | Logical consequence | Natural deduction | Rule of inference | Axiom schema | Willard Van Orman Quine | Existential generalization | Validity (logic) | Substitution (logic) | Stanisław Jaśkowski | Existential quantification