If the warrantWarrant of an argument is conclusive a priori, are the premisesPremise adequately connected to the conclusionConclusion if and only if they entail it? The classical analysis of entailmentParadoxof entailment leads to well-known paradoxes. A contradiction entails any statement whatsoever, while any statement entails a tautology. Further, contingent statements can be said to entail entailments, where assertions of entailmentParadoxof entailment are necessary statements. One can avoid paradoxes ofEntailmentparadoxes of necessity by confining one’s attention just to first-degree entailments which contain no assertions of entailmentParadoxof entailment as subformulas. HitchcockHitchcock, David has proposed a revised concept of entailmentParadoxof entailment as a way to avoid paradoxes ofEntailmentparadoxes of relevance. For Γ to entail P, Γ ∪ {P} instances an argument form which has no instances with all true premisesPremise and a false conclusionConclusion though the form has some instance with all true premisesPremise and some instance with a false conclusionConclusion. While this explication of entailment is semantic, AndersonAnderson, Alan Ross and BelnapBelnap, Nuel have proposed a syntactic analysis. Their language allows just first-degree entailments. Further restricting their study just to entailments holding between propositional compounds, AndersonAnderson, Alan Ross and BelnapBelnap, Nuel define a concept of explicitly tautologicalEntailmenttautological entailment which avoids both the paradoxes ofEntailmentparadoxes of necessity and relevance.