nLab Kripke frame

Frames in Modal Logics

Frames in Modal Logics


This entry is about the notion of frame in modal logic, also called Kripke frames, after the philosopher and logician Saul Kripke. It is a device used by Kripke as a component of a form of semantics for modal logic, in particular, via the concept of a geometric model.

The concept of a frame is an example of a concept with an attitude, being merely a non-empty set equipped with a binary relation in the standard case (or some variant in the multimodal case). Its attitude arises from its use as the first two components of triples that are Kripke models.

Beware that this is an entirely different concept than that of the same name used in geometric logic, where the concept of frames (see there) refers to an abstraction of the algebraic structure of lattices of open subsets of a topological space.

For modal logics involving multiple modal operators, frames are given by that number of binary relations defined on a non-empty set.


Generally this entry is based on

Last revised on May 23, 2023 at 09:07:20. See the history of this page for a list of all contributions to it.