This paper is a response to a presented paper. Original author's comments on this response. To this I offer a hearty Amen. As a mathematician I've had plenty of experience in the logic of entailment-every theorem is entailed by some relevant set of mathematical axioms As a philosopher who works in the logic of conditionals, I'm aware how entailment works outside mathematical contexts.
Entailment is the strongest logical connection by far.
To say that X entails Y is to say that it's impossible for X to be true and Y false. Thus, to say that X does not entail Y is to say that it is possible for X to be true and Y false. But since Shapiro leaves Y completely open-ended on the questions of origins, to say that biological evolution does not entail any account of origins, be it theistic, materialistic, or whatever, is simply to say that biological evolution is logically compatible with any number of positions on the origin of life and the universe. Let Y denote the claim that Bob shot Al. Al may have been suicidal and shot himself.