Formal logic is a relatively young discipline, with classical first-order logic considered as the
`standard logic' (taking the place of other possible alternative systems); this is the logic of introductory (and even advanced) logic textbooks.

Classical logic had as main purpose the analysis of mathematical arguments and comes with a high level of idealization: every sentence is impersonal,
either true or false and refers just to facts, truth is permanent,
implication is non-causal. Temporal, modal, doxastic aspects are not important,
and *should not be* important in mathematical proofs. However, classical logic is not adequate in the analysis of scientific and everyday reasoning.

Even in mathematics, classical logic has been considered inadequate:
* intuitionistic logic* was born from the inadequacy of classical logic in representing the * computational*content of deductive arguments.

Assumptions can be used * ad libitum* in a mathematical proof, but if assumptions represent entities with a price (that can be a concrete or a computational one) we need to take their multiplicity into account.
* Linear logic* and more generally * substructural* logics have been proposed as a more suitable tool for the investigation of problems in which
* resources* have a role. In a similar guise, * conditional logics* have been developed for the study of causation,
for which the standard material implication is not adequate.

Non-classical logics have applications in various fields, not just the traditional ones (philosophy, mathematics, computer science)
but also new ones in the social sciences, such as collective epistemology and formal ethics.

Even if non-classical logics are developed as alternatives to classical logic, they are often extensions of the latter, so the formal apparatus * builds* on the one of classical logic.
However, both the theory (models and deductive systems) and the metatheory (general results about them) have to be carefully re-built.

Non-classical logics provide a challenging field for the application and development of both semantical and proof-theoretical logical methods.