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:
“A few ideas seem to be agreed upon. Help none but those who help themselves. Educate only at schools which provide in some form for industrial education. These two points should be insisted upon. Let the normal instruction be that men must earn their own living, and that by the labor of their hands as far as may be. This is the gospel of salvation for the colored man. Let the labor not be servile, but in manly occupations like that of the carpenter, the farmer, and the blacksmith.”
—Rutherford Birchard Hayes (1822–1893)
““... We need the interruption of the night
To ease attention off when overtight,
To break our logic in too long a flight,
And ask us if our premises are right.””
—Robert Frost (1874–1963)