Editing Classical logic (section)

==Characteristics==

Each logical system in this class shares characteristic properties:<ref>[[Dov Gabbay|Gabbay, Dov]], (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), ''Handbook of Logic in Artificial Intelligence and Logic Programming'', volume 2, chapter 2.6. Oxford University Press.</ref>
# [[Law of excluded middle]] and [[double negation elimination]]
# [[Law of noncontradiction]], and the [[principle of explosion]]
# [[Monotonicity of entailment]] and [[idempotency of entailment]]
# [[Commutativity of conjunction]]
# [[De Morgan duality]]: every [[logical operator]] is dual to another

While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include [[propositional calculus|propositional]] and [[first-order logic|first-order]] logics.<ref name=":0">[[Stewart Shapiro|Shapiro, Stewart]] (2000). Classical Logic. In Stanford Encyclopedia of Philosophy [Web]. Stanford: The Metaphysics Research Lab. Retrieved October 28, 2006, from http://plato.stanford.edu/entries/logic-classical/</ref><ref name="haack">[[Susan Haack|Haack, Susan]], (1996). ''Deviant Logic, Fuzzy Logic: Beyond the Formalism''. Chicago: The University of Chicago Press.</ref> In other words, the overwhelming majority of time spent studying classical logic has been spent studying specifically propositional and first-order logic, as opposed to the other forms of classical logic.

Most semantics of classical logic are [[Principle of bivalence|bivalent]], meaning all of the possible denotations of propositions can be categorized as either true or false.