Is it possible to get a synoptic view of the ways in which a logic can, so to say, deviate from classical logic?
I think one can find rather easily a list ( though maybe incomplete) of non-classical logics.
But it seems more difficult to find a presentation of the field that exhibits in a systematic fashion under which respects a logic can be non classical.
The respects I can think of are the following :
(1) type of objects over which quantifiers range --> first order/ second order logic
(2) validity of "ex falso" or not --> paraconsistent logics
(3) use of modal operators, or not --> modal logics
(4) finite or infinite number of premises --> compactness ( not sure of this)
There is an attempt at such a presentation in Theodore Sider's book Logic For Philosophy, but I'd be much interested in other references.
Note : I'm not asking for an absolutely complete list of points of departure from clasical logic; I suppose it would be too long. Rather, what interests me is the systematicity of the presentation.