Regular modal logic

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In modal logic, a regular modal logic is a modal logic containing (as axiom or theorem) the duality of the modal operators:

and closed under the rule

Every normal modal logic is regular, and every regular modal logic is classical.

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<span class="mw-page-title-main">Saul Kripke</span> American philosopher and logician (1940–2022)

Saul Aaron Kripke was an American analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Princeton University. Kripke is considered one of the most important philosophers of the latter half of the 20th century. Since the 1960s, he has been a central figure in a number of fields related to mathematical and modal logic, philosophy of language and mathematics, metaphysics, epistemology, and recursion theory.

<span class="mw-page-title-main">De Morgan's laws</span> Pair of logical equivalences

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<span class="mw-page-title-main">Method of analytic tableaux</span>

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In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic Logic. It is a normal modal logic, and one of the oldest systems of modal logic of any kind. It is formed with propositional calculus formulas and tautologies, and inference apparatus with substitution and modus ponens, but extending the syntax with the modal operator necessarily and its dual possibly.

In modal logic, a classical modal logicL is any modal logic containing the duality of the modal operators

In algebra and logic, a modal algebra is a structure such that

The formal fallacy or the modal fallacy is a special type of fallacy that occurs in modal logic. It is the fallacy of placing a proposition in the wrong modal scope, most commonly confusing the scope of what is necessarily true. A statement is considered necessarily true if and only if it is impossible for the statement to be untrue and that there is no situation that would cause the statement to be false. Some philosophers further argue that a necessarily true statement must be true in all possible worlds.

A non-normal modal logic is a variant of modal logic that deviates from the basic principles of normal modal logics.

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