The text I'm reading distinguishes logical necessity, logical consequence, logical truth, and tautology from one another; however it doesn't make their distinctions especially perspicuous.
As far as I interpreted it,
- Logical consequence: truth of the antecedent or premises guarantees the truth of the consequent or conclusions.
- Logical truth: Any statement that must be valuated true, even if the set of premises is the empty set. (3=3, p v ~p, etc)
- Tautology: Any statement that must be valuated true, but only when the statement is stated. (as opposed to logical truths)
- Logical necessity: for any set of statements containing the logically necessary statement in question, the logically necessary statement can be evaluated as true under at least one valuation.