Tautological_consequence
Tautological consequence
Concept in propositional logic
In propositional logic, tautological consequence is a strict form of logical consequence[1] in which the tautologousness of a proposition is preserved from one line of a proof to the next. Not all logical consequences are tautological consequences. A proposition is said to be a tautological consequence of one or more other propositions (, , ..., ) in a proof with respect to some logical system if one is validly able to introduce the proposition onto a line of the proof within the rules of the system; and in all cases when each of (, , ..., ) are true, the proposition also is true.
Another way to express this preservation of tautologousness is by using truth tables. A proposition is said to be a tautological consequence of one or more other propositions (, , ..., ) if and only if in every row of a joint truth table that assigns "T" to all propositions (, , ..., ) the truth table also assigns "T" to .