The supportingargument's transitivity premise holds for decision problems under standard Turing reductions, but Ladner's theorem demonstrates that if P≠NP there exist problems in NP neither in P nor NP-complete, complicating the universality of the entailment.
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Turing reduction(as used in computer science and computational theory)
A way of comparing how hard two problems are by asking: if you could instantly solve one problem, could you use that to solve another? It's named after Alan Turing, a pioneering computer scientist.
Universality of entailment(as used in logic)
The idea that a logical rule works everywhere and always produces reliable conclusions without exceptions.
transitivity(Applied to the temporal relation 'earlier than' on a set of worlds W)
A property of a relation R such that if wRv and vRu, then wRu