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): ;
- 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 extensions of K. However a number of deontic and epistemic logics, for example, are non-normal, often because they give up the Kripke schema.
Famous quotes containing the words normal and/or logic:
“The normal present connects the past and the future through limitation. Contiguity results, crystallization by means of solidification. There also exists, however, a spiritual present that identifies past and future through dissolution, and this mixture is the element, the atmosphere of the poet.”
—Novalis [Friedrich Von Hardenberg] (1772–1801)
““... We need the interruption of the night
To ease attention off when overtight,
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—Robert Frost (1874–1963)