In Modal logic, a frame is defined as a pair (W,R), where W is a non-empty set (of possible worlds, states, or other terminology), and R is a binary relation on W.

However, what exactly is a 'class of frames'? Is this just any random collection of frames? Or frames of a certain family/characteristic? Is there any official definition of 'a class of frames'? I couldn't find any, neither in the book, nor on the internet.

1 Answer 1


See Semantics of modal logic :

A Kripke frame or modal frame is a pair ⟨W,R⟩, where W is a (possibly empty) set (the set of worlds), and R is a binary relation on W (the accessibility relation).

A class of frames is a collection of frames sharing some "relevant" property of the accessibility relation.

For example, if we "impose" the frame condition on R of reflexivity, we have that all the frames of the corresponding class satisfy the axiom


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