Possibility Semantics

In Melvin Fitting (ed.), Selected Topics from Contemporary Logics. London: College Publications (forthcoming)

Authors
Wesley H. Holliday
University of California, Berkeley
Abstract
In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a set can be viewed as a "possible world," with the key property of a world being primeness—a world makes a disjunction true only if it makes one of the disjuncts true—which classically implies totality—for each proposition, a world either makes the proposition true or makes its negation true. This chapter surveys a more general approach to logical semantics, known as possibility semantics, which replaces possible worlds with possibly partial "possibilities." In classical possibility semantics, propositions are interpreted as regular open sets of a poset, as in set-theoretic forcing, or as compact regular open sets of an upper Vietoris space, as in the recent theory of "choice-free Stone duality." The elements of these sets, viewed as possibilities, may be partial in the sense of making a disjunction true without settling which disjunct is true. We explain how possibilities may be used in semantics for classical logic and modal logics and generalized to semantics for intuitionistic logics. The goals are to overcome or deepen incompleteness results for traditional semantics, to avoid the nonconstructivity of traditional semantics, and to provide richer structures for the interpretation of new languages.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Buy the book Find it on Amazon.com
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,784
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Another Problem in Possible World Semantics.Yifeng Ding & Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 13. London: College Publications.
A Simple Logic of Functional Dependence.Alexandru Baltag & Johan van Benthem - 2021 - Journal of Philosophical Logic 50 (5):939-1005.

Add more citations

Similar books and articles

A Bimodal Perspective on Possibility Semantics.Johan van Benthem, Nick Bezhanishvili & Wesley H. Holliday - 2017 - Journal of Logic and Computation 27 (5):1353–1389.
Another Problem in Possible World Semantics.Yifeng Ding & Wesley H. Holliday - 2020 - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 13. London: College Publications.
Partiality and Adjointness in Modal Logic.Wesley H. Holliday - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Vol. 10. College Publications. pp. 313-332.
Partiality and Adjointness in Modal Logic.Wesley H. Holliday - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 313-332.
Inquisitive Intuitionistic Logic.Wesley H. Holliday - forthcoming - In Nicola Olivetti & Rineke Verbrugge (eds.), Advances in Modal Logic, Vol. 11. London: College Publications.
“Four-Valued” Semantics for the Relevant Logic R.Edwin D. Mares - 2004 - Journal of Philosophical Logic 33 (3):327-341.
Probability Modals and Infinite Domains.Adam Marushak - 2020 - Journal of Philosophical Logic 49 (5):1041-1055.
Representing Counterparts.Andrew Bacon - 2014 - Australasian Journal of Logic 11 (2):90-113.
A Note on Algebraic Semantics for S5 with Propositional Quantifiers.Wesley H. Holliday - 2019 - Notre Dame Journal of Formal Logic 60 (2):311-332.
Restricted Classical Modal Logics.Cezar Mortari - 2007 - Logic Journal of the IGPL 15 (5-6):741-757.
The Dynamification of Modal Dependence Logic.Pietro Galliani - 2013 - Journal of Logic, Language and Information 22 (3):269-295.

Analytics

Added to PP index
2021-09-28

Total views
0

Recent downloads (6 months)
0

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes