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).
Textbook accounts:
See also:
Wikipedia, Possible world
Stanford Encyclopedia of Philosophy, Possible Worlds
Stanford Encyclopedia of Philosophy, Modal Logic – Possible worlds semantics
Neil Toronto, Jay McCarthy, From Bayesian Notation to Pure Racket, 2010 (pdf)
Last revised on October 21, 2022 at 09:54:29. See the history of this page for a list of all contributions to it.