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:
“Unlike the normal pattern, I know I have grown more liberal as I’ve grown older. I have become more convinced that there is room for improvement in the world.”
—Walter Wellesley (Red)
“You can no more bridle passions with logic than you can justify them in the law courts. Passions are facts and not dogmas.”
—Alexander Herzen (1812–1870)