Logics that explore the properties of relations of implication stronger than strict implication. It was shown by C. I. Lewis that with the classical notion of entailment anything whatever follows from a contradiction, and a tautology follows from any arbitrary proposition. Logicians regarding these consequences as unacceptable have sought to define relations of entailment stronger (more restrictive) than strict implication, to preserve the distinction between good and bad ways of arguing even in the presence of contradictions and tautologies.