In logic universal instantiation (UI, sometimes confused with Dictum de omni) is an inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. Logic is the study of the principles of valid demonstration and Inference. In Aristotelean logic, dictum de omni et nullo ( the maxim of all and none) is the principle that whatever is affirmed or denied of a whole kind K may be affirmed or Inference is the act or process of deriving a Conclusion based solely on what one already knows It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom. In Predicate logic, universal quantification is an attempt to formalize the notion that something (a Logical predicate) is true for everything, or every It is one of the basic principles used in quantification theory. First-order logic (FOL is a formal Deductive system used in mathematics philosophy linguistics and computer science
Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal. "
In symbols the rule as an axiom schema is
for some term a and where A(a / x) is the result of substituting a for all free occurrences of x in A. In Mathematical logic, an axiom schema generalizes the notion of Axiom.
And as a rule of inference it is
from ⊢ ∀x A infer ⊢ A(a/x),
with A(a/x) the same as above. In Logic, a rule of inference (also called a transformation rule) is a function from sets of formulae to formulae
Irving Copi noted that universal instantiation ". Irving Marmer Copi (born Copilovich, July 28 1917, Duluth, Minnesota &ndash August 19 2002, Honolulu . . follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanislaw Jaskowski in 1934. In Philosophical logic, natural deduction is an approach to Proof theory that attempts to provide a Deductive system which is a formal model of logical Gerhard Karl Erich Gentzen ( November 24, 1909, Greifswald, Germany &ndash August 4, 1945, Prague, Czechoslovakia Stanisław Jaśkowski ( April 22, 1906 &ndash November 16, 1965) was a Polish Logician who made important contributions " -pg. 71. Symbolic Logic; 5th ed.