"logical principle" is correct and can be used in written English.
You can use it to refer to a general rule of reasoning that is based on logic, such as cause and effect or non-contradiction. For example: "The logical principle of non-contradiction states that a thing cannot both be and not be at the same time."
Aristotle somewhat similarly had argued that the logical principle of noncontradiction, which he took to express a highly general truth about the world, must be accepted as axiomatic on the ground that its correctness is presupposed in any argument directed against it.
This could hardly be regarded as a logical principle.
As a logical principle, the PC is about opposite assertions.
No logical principle stops scientists from choosing different background assumptions against which to interpret their observations.
The logical principle corresponding to weak Königʼs lemma is the universal transfer principle from Nonstandard Analysis.
With Rescher and Brandom's work, worlds at which some logical principle involving some extensional connective fails have entered the scene.
As Jack Meiland (1976) construes Erdmann's philosophy of logic, the psychological interpretation of logical principles is meant to explain why we cannot conceive of radically different logical systems.
Nevertheless, already on this informal level one is forced to reject one of the logical principles ever-present in classical logic: the principle of the excluded middle $(A\vee \neg A)$.
Book III of Richard Whately's Elements of Logic (1826) is devoted to giving an account, based on "logical principles," of fallacies.
As he reasonably points out, logic comprises the rules of correct thinking, and the principles of logic are known to us as conscious representations;[86] thinking and consciousness are objects of psychological inquiry; therefore any account of logic must include a psychological description of the genesis of logical principles (L I: 13).
Although Tonk is Prior's best known example of non-conservative extension, he also noted the non-conservative effect of familiar logical principles concerning conjunction when added to a purely implicational intermediate logic; references, details, and further discussion can be found in Humberstone (2014).
