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).
The original articles:
Saul A. Kripke, A Completeness Theorem in Modal Logic, The Journal of Symbolic Logic 24 1 (1959) 1-14 [doi:10.2307/2964568, jstor:2964568, pdf]
Saul A. Kripke, Semantical Considerations on Modal Logic, Acta Philosophical Fennica 16 (1963) 83-94 [pdf]
Saul A. Kripke, Semantical Analysis of Modal Logic I. Normal Modal Propositional Calculi, Mathematical Logic Quaterly 9 5-6 (1963) 67-96 [doi:10.1002/malq.19630090502]
Saul A. Kripke, Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi, in The Theory of Models (Proceedings of the 1963 International Symposium at Berkeley) Studies in Logic and the Foundations of Mathematics (1965) 206-220 [doi:10.1016/B978-0-7204-2233-7.50026-5]
Modern exposition:
In general see the reference at modal logic, such as:
Raymond D. Bradley, Norman Swartz, Possible Worlds – An Introduction to Logic and its Philosophy, Hackett Publishing (1979) [webpage, pdf]
Rod Girle, Possible Worlds, McGill-Queen’s University Press (2003) [jstor:j.cttq48cx]
Johan van Benthem, §2.2 of: Modal Logic for Open Minds (2010) [ISBN:9781575865980,pdf, webpage]
Daniel Nolan, Topics in the Philosophy of Possible Worlds, Routledge (2002) [ISBN:9780415516303]
Valentin Goranko, Martin Otto, Model Theory of Modal Logic, Section 5 in: Handbook of Modal Logic, Studies in Logic and Practical Reasoning 3 (2007) 249-329 [pdf, book webpage, publisher page]
and more philosophically (“modal realism”):
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)
References which consider, in one way or another, the notions of
in relation to each other:
Mario Bunge, Possibility and Probability, in: Foundations of Probability Theory, Statistical Interference, and Statistical Theories of Science, Reidel (1976) 17-34 doi:10.1007/978-94-010-1438-0_2
Brian Skyrms, Part III of: Possible Worlds, Physics and Metaphysics, Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition 30 5 (1976) 323-332 jstor:4319099
Paul Tappenden, p. 101 (4 of 17) in: Identity and Probability in Everett’s Multiverse, The British Journal for the Philosophy of Science, 51 1 (2000) 99-114 jstor:3541750
Daniel Nolan, p. 22 of: Topics in the Philosophy of Possible Worlds, Routledge (2002) ISBN:9780415516303
Rod Girle, Ch. 8 of: Possible Worlds, McGill-Queen’s University Press (2003) jstor:j.cttq48cx
Simon Saunders, p. 196 in: Chance in the Everett Interpretation, in: Many Worlds?, Oxford University Press (2010) 181–205 doi:10.1093/acprof:oso/9780199560561.003.0008
Nuriya Nurgalieva, Lídia del Rio, Inadequacy of Modal Logic in Quantum Settings, EPTCS 287 (2019) 267-297 arXiv:1804.01106, doi:10.4204/EPTCS.287.16
Alastair Wilson, p. 20 of: Modal Metaphysics and the Everett Interpretation (2006) philsci:2635, pdf
Vladislav Terekhovich, Modal Approaches in Metaphysics and Quantum Mechanics arXiv:1909.10046
Alastair Wilson, The Nature of Contingency: Quantum Physics as Modal Realism, Oxford University Press (2020) ISBN:9780198846215
Raoni W. Arroyo, Jonnas R. B. Arenhart, Whence deep realism for Everettian quantum mechanics?, Foundations of Physics 52 121 (2022) [arXiv:2210.16713, doi:10.1007/s10701-022-00643-0]
Beware that there is also
which, even if some vocabulary is superficially alike, does not refer either to modal logic nor to the many-worlds interpretation.
Last revised on August 1, 2023 at 14:21:02. See the history of this page for a list of all contributions to it.