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Quick Completeness Proofs for some Logics of Conditionals
Open accessAbstract
Vx e W\/y e W x RxyyVx e W Vj/, z, w e W x (Rxyz & Rxzw D Rxyw).A model-class is any 71/ C. Tfty closed under isomorphism; the interesting examples are obtained by imposing certain characteristic restrictions on R.Next, we fix a notion of satisfaction/validity.A valuation in(W, R)e7ft/ is a map F assigning each variable p, a subset of W. K can be extended to all of Ji by treating truth-functions in the usual way (e.g.,and defining V(a -• j8) as the set of all x e W such that: VyeW x Γ) Via) 3z e W x Π F(α) [Λxzy & Vr e H/ x Π F(α)(Λx^z D t e V(β))]
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“The analogy is so close that conditional belief on reflexive transitive plausibility models satisfies exactly the principles of the minimal conditional logic (Burgess 1981, Veltman 1985).”
From THE STORIES OF LOGIC AND INFORMATION (2008) · cites this paper as Burgess 1981
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Research works printed but not linked: 2
- Lewis, D. K., "Intensional logics without iterative axioms," Journal of Philosophical Logic, vol. 3 (1974), pp. 457-466.
- Lewis, D. K., Count erf actuals, Harvard University Press, Cambridge, 1973.
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THE STORIES OF LOGIC AND INFORMATION
van Benthem, J., & Martinez, M. (2008) · Philosophy of Information · doi:10.1016/b978-0-444-51726-5.50012-1 · Cited by 80
Metadata
- Authors
- Burgess, J. P.
- Corresponding author
- Burgess, John P.
- ORCID
- Burgess, John P.
- Venue
- Notre Dame Journal of Formal Logic
- Publisher
- Duke University Press
- Published
- 1981-01-01
- Volume
- 22
- Issue
- 1
- Pages
- 76-84
- ISSN
- 0029-4527 (ISSN-L)
- 1939-0726
- OpenAlex
- W2159304001
- Cited by
- 147
- References
- 0
- Citations by year
- 2026: 1 · 2025: 10 · 2024: 2 · 2023: 9 · 2022: 3 · 2021: 10 · 2020: 4 · 2019: 5 · 2018: 4 · 2017: 5 · 2016: 7 · 2015: 6 · 2014: 2 · 2013: 9 · 2012: 3
- FWCI
- 3.43
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Notre Dame Journal of Formal Logic (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Logic, Reasoning, and Knowledge
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Algebra and Logic
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Topology and Set Theory
- Keywords
- completeness proof, model classes, isomorphism, valuation, truth functions, validity, modal logic
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