It seems to me that “logical judgment” comes in a wide range of forms, from the preconscious syntheses of our evolved common sense that appear to us ready-made, to the most elaborately explicit works of interpretation. I see judgment as referring principally to a process, and only secondarily to the outcome of the process — to the deliberation more than to the verdict, as it were.
There is a traditional use of “judgment” as a synonym for “logical proposition”. I find this a bit odd; it would make more sense to think of a judgment as at the very least an assertion or denial of a proposition, even in contexts where the connotation of interpretive, deliberative process is suppressed, and the focus is only on an outcome.
In combination with traditional ideas about predication, this identification of judgments with propositions led to a notion of acts of logical judgment in which acts of grammatical predication such as construction of the sentence “Socrates is a human” were viewed as prototypical.
Even Kant’s discussion of the application of concepts in the first Critique bears noticeable traces of this predicative analysis of logical judgment. I think Kant across the larger body of his work played a major role in developing alternatives to the predicative approach that narrowly construed “judgment” as the application of a predicate to a subject. Indeed Brandom argues that Kantian concepts are only intelligible in terms of their contribution to the activity of judging. Nonetheless, when Kant talks about subsuming particulars under universals, the discussion still recalls the predicative approach. Certainly the application of universals to particulars is important, but it is only one of several dimensions that come into play in the constitution of meaning, and it is not the most fundamental.
In referring to the constitution of meaning, I have already implicitly moved beyond the predicative analysis. The problem with the predicative analysis is that it takes meanings for granted, and really only addresses their syntactic combination as pre-existing units. We need to address the broader territory of judgments about meaning and value that go below the level of pre-existing units and preconceived identities. Meanings of terms in context turn out to depend on judgments, which in turn depend on others, and it is the ties of mutual dependency that bind together this open-endedly expanding network that give relative definiteness to our determinations.