I think of logic in general as mainly concerned with the perspicuous rendering of distinctions for use in reasoning, rather than with the arbitration of truth based on some other presumed truth as a starting point.
An emphasis on this expressive or semantic role was, I think, what led Aristotle to insist that what modern people call logic should be viewed as a tool (organon) and not a “science”.
The great scholar of Latin medieval logic L. M. De Rijk, in his major study Aristotle: Semantics and Ontology (2002), recommended replacing references to Aristotle’s own “logic” with references to semantics, or investigation of meaning.
Hegel contended that traditional metaphysics should be replaced by a kind of “logic” that addresses meaningful content.
Brandom has given us an unprecedentedly thorough and clear account of the conditions that make meaningful content possible in the first place.
On the formal side, type theory and category theory provide a new, unified view of logic, mathematics, and formal languages that fits very well with this “meaning before truth” perspective.