As an interested outsider who is prone to reading about different formulations of logic, I've become interested in better understanding the big picture of what people are trying to accomplish as they are researching logic, or merely talking about logic as a proper subject of philosophy.
For instance: in the course of the extended commentary in my earlier question on the motivations of Dialetheism, it occurred to me that I might be misinterpreting some of the answers. While I think I correctly understand what people are saying about models of logic in themselves, I may be badly misinterpreting the relationship which they are drawing between logical statements, and states of affairs — there are claims that this logic, or that logic, are useful for certain situations; and as someone raised in a very solidly formal classical tradition, I would end up responding something along the lines of "things don't really work that way", or "I can see why you might call this a logic but I would describe it some other way". But perhaps these reactions miss the point?
Fact — There exist several logics. When philosophers investigate them, what is their intent? Obviously this will depend on the philosopher. But I can envision two different sorts of research programme concerning logic, whose names I will invent ad hoc without reference to anything in particular:
Empirical logic: explore logic with the intent of determining what manner of logic best describes the world at large. Without making too many assumptions about the world, but responding to it in a more-or-less empirical fashion (taking data from the world around you, but not necessarily in a strictly scientific manner: all personal experiences are grist for the mill), what sort of logic provides the best modus operandum?
Abstract logic: explore logic without any particular concern for whether one's subject of study has direct application, and certainly without insisting that it be particularly useful in all practical circumstances. Observe when the reasoning in other philosophers' work (on the subjects of ontology, epistemology, ethics, etc.) can be described by some particular logical system, when these do not seem to be simple "classical" logic. Also: devise models of logic merely to explore what curious or desirable properties or achievements might be possible in a logical system.
The distinction that I imagine between the two is parallel to that of physics versus pure mathematics: one is concerned with devising the right model to capture the whole world (or at least provide a united framework for a sizeable and more-or-less well-defined chunk of it), while the other is more concerned with devising models for the sake of exploring what models one can devise, and exploring the properties of the models they devise. A distinction between inventing tools and finding the right tools; a modal distinction in their goals, between determining what logics you could imagine and determining what logics you should use.
Of course, the above are only two concievable (and very broad!) research programmes; they might not be exhaustive, or mutually exclusive. They also may not be particularly useful for drawing distinctions between the different objectives of people working in logic: maybe there are better (or less trivial) distinctions than what I've guessed at above.
Bearing this in mind: what are the major research programmes in modern logic? In each branch, what are the most prominent schools of thought, and who are the most prominent thinkers/authors?