Modal logic

Normal modal logic

In logic, a normal modal logic is a set L of modal formulas such that L contains: * All propositional tautologies; * All instances of the Kripke schema: and it is closed under: * Detachment rule (modus ponens): implies ; * Necessitation rule: implies . The smallest logic satisfying the above conditions is called K. Most modal logics commonly used nowadays (in terms of having philosophical motivations), e.g. C. I. Lewis's S4 and S5, are normal (and hence are extensions of K). However a number of deontic and epistemic logics, for example, are non-normal, often because they give up the Kripke schema. Every normal modal logic is regular and hence classical. (Wikipedia).

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From playlist Programming

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From playlist Logic for Programmers

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From playlist Complex Analysis

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From playlist Symbolic Logic and Proofs (Discrete Math)

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From playlist Logic

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From playlist Logic and Foundations

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From playlist Mathematics

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From playlist GCSE Maths Videos

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From playlist Workshop: "Proofs and Computation"

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From playlist Logic Tutorial

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From playlist Logic & Philosophy of Mathematics

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Related pages

Tautology (logic) | Deontic logic | Equivalence relation | Modal logic | Preorder | Kripke semantics | Serial relation | Classical modal logic | Directed set | C. I. Lewis | Regular modal logic | Saul Kripke | Modus ponens | Provability logic | S5 (modal logic)