Logical Implication or Entailment

Consider

where represents some set of premises and y represents the conclusion. This simply means that the conjuction of all the premises entails the conclusion. We say that if and only if all the models of are models of .

To show , show that is a tautology. We call a tautology of the form a Logical Implication.

In predicate calculus, we use to denote deduction

where represents the set of assumptions and represents the conclusion. This expression reads " is deduced from ." If , often denoted , then it is call a proof. That is is deduced soley from the axioms.

(FirstOrderMathematicalLogicAngeloMargaris)

See LogicNotes

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LogicalImplication (last edited 2020-02-02 17:44:06 by scot)