What are the various respects under which a logic can deviate from classical logic, thus being " non-classical"?

Question

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.

Answer 1

One attempt at classifying ways to alternate logic could be:

• extending or restricting the language: This covers the transition to logics of higher order (introducing new types of variables and predicates) or, in the other direction, monadic logic (restricting the language to 1-place predicates), as well as e.g. modal logic (introducing additional modal operators). Of course, an extension of the language always comes with an extension of the semantics.
• altering the range of semantic values: e.g. many-valued logics, fuzzy logics.
• altering the semantics of the logical constants: e.g. intuitionistic logic and minimal logic, where $\neg$ does not adhere to the classical truth table semantics, as well as paraconsistent logic, where $\bot$ does not "mean" a proposition from which anything may be inferred.