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:
“Separation anxiety is normal part of development, but individual reactions are partly explained by experience, that is, by how frequently children have been left in the care of others.... A mother who is never apart from her young child may be saying to him or her subliminally: “You are only safe when I’m with you.””
—Cathy Rindner Tempelsman (20th century)
“Our argument ... will result, not upon logic by itself—though without logic we should never have got to this point—but upon the fortunate contingent fact that people who would take this logically possible view, after they had really imagined themselves in the other man’s position, are extremely rare.”
—Richard M. Hare (b. 1919)