Contents

# Contents

## Idea

In the context of modal logic, by possible world semantics one means the interpretation of the possibility and necessity modalities as existential quantification and universal quantification over a context of “possible worlds”. Such a model is sometimes referred to as a Kripke frame.

For formalization of this in terms of hyperdoctrines/dependent type theory see at necessity and possibility – In first-order logic and dependent type theory.

Under categorical semantics such a context interprets as an object of some category whose interpretation is similar to that of a probability space in measure theory – which is one sensible formalization of possible worlds (e.g. Toronto-McCarthy 10, slide 23).

## References

Last revised on November 11, 2017 at 05:52:10. See the history of this page for a list of all contributions to it.