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

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.

• Fuzzy logics (where claims can be 'sorta true'. E.g. 'I am tall'), probabilistic logics (claims are not known to be true or false, but we do attach some kind of probability .. not to be confused with fuzzy logics; the fuzziness of 'I am tall' is not a matter of a lack of information, but rather with the vagueness of predicates/slipperyness of concepts), quantum logics (where claims can be both true and false at the same time), infinitary logics (not just number of statements, but also length of statements, and length of derivations) Nov 11, 2020 at 14:24
• There are also 3-valued logics (true, false, and unknown). For a systematic taxonomy, maybe put three-valued logic into a class together with fuzzy logic. But again, I am not too sure how to classify probabilistic logics ... they strike me as more pof a modal logic... closer to a kind of epistemic logic. Nov 11, 2020 at 14:32

• 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.