Here, because of the simple syntax of pure Prolog programs, " implied by " can be understood very simply as derivability using modus ponens and universal instantiation alone.
2.
"Universal instantiation " concludes that, if the propositional function is known to be universally true, then it must be true for any arbitrary element of the Universe of Discourse.
3.
Irving Copi noted that universal instantiation " . . . follows from variants of rules for'natural deduction', which were devised independently by Gerhard Gentzen and StanisBaw Ja [ kowski in 1934 ."
4.
The idea that some of our rules of inference should depend on empirical information, which may not be forthcoming, is so foreign to the character of logical inquiry that a thorough re-examination of the two inferences [ existential generalization and universal instantiation ] may prove worth our while.
5.
In predicate logic "'universal instantiation "'( "'UI "', also called "'universal specification "'or "'universal elimination "', and sometimes confused with 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.
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