It seems that investigations of language and logic have focused on truth as the assumed designated value (the value preserved by valid entailments). It is only in later, non-classical logic that non-truth based designated values were introduced to govern the inferential steps from sentences bearing other semantic values; the value of correctness is one I have in mind.

Why is Truth the default designated value in logic and language?
When, and by who, if by anyone at all determined it as such?
Are there any philosophers who take other semantic values as more fundamental and/or more basic that truth (which?)

From what I've read in non-classical logic, logic can merely be used to maintain the designated value within the system, which is why correctness-functional entailment can produce correct conclusions from correct premises. The preservation of any semantic value can be termed valid inference depending on which semantic value is chosen. It is simply not the case that logic only deals with truth, as can be seen in Ian Rumfitt's "Truth and Meaning", which uses correctness-functional entailment, with correctness as the designated value in the deductive system, to govern the inferential steps of three-valued logic (as an intended solution to problems for truth like the Liar Paraodox).

I have seen no arguments to support the notion that the system is fundamentally truth-functional. Certainly no more than that a decimal mathematics is more fundamental than a duodecimal one. If there were some argument that indicated that truth is not only fundamental in logic, but also necessarily fundamental, I would be very interested in this. I doubt that I have identified a lack of literature, as it seems most philosophical topics have been covered with at least some depth. 

Any comments and recommendations on this topic will be much appreciated.