There's no -logical- basis for logicality in the strict sense of inferential sequence, since logicality itself must be merely preferred at the outset of thought as an operative value. Otherwise, a fallacy of logic is committed in an attempt to provide such a basis. The necessity of logic, even in these statements of mine themselves, is an -existential- necessity based on a situated grasp of a -system- as a whole, with logic as an integral aspect (along with a set of definitions, an instruction set, language rules, contextual simples, and other primitives). But this cannot be said to be merely -arbitrary- since that claim to arbitrariness would -itself- rely on the same uninferable necessity of logic to have any import.
But again---reasoning at that epistemic level is an existentially or heuristically or if you like, an intuitively grasped inference system. It is, and functions as, the ultimate operating system of thought, some grasp of which occurs in not-so-ultimate finite minds with the various tendencies toward willed self-contradiction and the need for constant tune-ups, both caused by defecting from the envisioned ideality of the structure of God's mind. And even though that structure is operatively a set of predications, operative is the key term. God's mind is an irreducible design integrity, as Buckminster Fuller might have said (at least if he had talked to me at length), and IS a set of simultaneous predications, the rational necessity of which determines the structure of the world, God, and all reality. Aside from also being an aspect of God's being, namely God's mind.
So the necessity of logic at that basic level would be intuitive, although not in a vacuum. Logic's necessity in this sense is a situated grasp of a comprehensive and universal system whose aim at truth is existentially necessary (an intuitive sine qua non or epistemic cul-de-sac) as a heuristic package deal. It -would- be arbitrary and relative, except that any claim to that effect would -itself- be dependent on this same -existential-, and not inferential, necessity. Nice try. Too bad. You're still singing my song in spite of yourself.
But just what is it, this necessity? Un-inferred, it's still---itself---an inference system. But in the case of this particular system (or engine, make the synonym circle---still doesn't change anything) the aspects of its nature can only be a mind object, precisely because a universal ultimate inference system and a universal ultimate mind are indistinguishable.