uses a similar classification but calls the two main classes anti-classical and extra-classical. Although some systems of classification for non-classical logic have been proposed, such as those of Haack and Burgess as described above for example, many people who study non-classical logic ignore these classification systems. As such, none of the classification systems in this section should be treated as standard. In an extension, new and different logical constants are added, for instance the "" in modal logic, which stands for "necessarily." In extensions of a logic, the set of well-formed formulas generated is a proper superset of the set of well-formed formulas generated by classical logic. the set of theorems generated is a proper superset of the set of theorems generated by classical logic, but only in that the novel theorems generated by the extended logic are only a result of novel well-formed formulas. (See also Conservative extension.) In a deviation, the usual logical constants are used, but are given a different meaning than usual. Only a subset of the theorems from the classical logic hold. A typical example is intuitionistic logic, where the law of excluded middle does not hold. Additionally, one can identify a variations (or variants), where the content of the system remains the same, while the notation may change substantially. For instance many-sorted predicate logic is considered a just variation of predicate logic. This classification ignores however semantic equivalences. For instance, Gödel showed that all theorems from intuitionistic logic have an equivalent theorem in the classical modal logic S4. The result has been generalized to superintuitionistic logics and extensions of S4. The theory of abstract algebraic logic has also provided means to classify logics, with most results having been obtained for propositional logics. The current algebraic hierarchy of propositional logics has five levels, defined in terms of properties of their Leibniz operator: protoalgebraic, (finitely) equivalential, and (finitely) algebraizable. See also Logic in Eastern philosophy Logic in China Logic in India References Further reading A revised version was published as Brief introduction to non-classical logics, with a primer on the classical one. Chapters 7-16 cover the main non-classical logics of broad interest today. Probably covers more logics than any of the other titles in this section; a large part of this 1500-page monograph is cross-sectional, comparing—as its title implies—the logical connectives in various logics; decidability and complexity aspects are generally omitted though. External links Video of