The formula A (it is noncontingent whether A) is true at a point in a Kripke model just in case all points accessible to that point agree on the truth-value of A. We can think of -based modal logic as a special case of what we call the general modal logic of agreement, interpreted with the aid of models supporting a ternary relation, S, say, with OA (which we write instead of A to emphasize the generalization involved) true at a (...) point w just in case for all points x, y, with Swxy, x and y agree on the truth-value of A. The noncontingency interpretation is the special case in which Swxy if and only if Rwx and Rwy, where R is a traditional binary accessibility relation. Another application, related to work of Lewis and von Kutschera, allows us to think of OA as saying that A is entirely about a certain subject matter. (shrink)

Hilbert-style axiomatic systems are presented for versions of the modal logics K, where {D, 4, 5}, with noncontingency as the sole modal primitive. The classes of frames characterized by the axioms of these systems are shown to be first-order definable, though not equal to the classes of serial, transitive, or euclidean frames. The canonical frame of the noncontingency logic of any logic containing the seriality axiom is proved to be nonserial. It is also shown that any class of frames definable (...) in the noncontingency language contains the class of functional frames, and dually, there exists a greatest consistent normal noncontingency logic. (shrink)

Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency , by comparison with the usual language based on necessity.

Normal propositional modal systems This first chapter has two main aims. One is to give a general account of the propositional modal systems that we shall ...

The paper considers the question of when the operator L of necessity in modal logic can be expressed in terms of the operator meaning it is non-contingent that.