Foundations For Temporal Reasoning Using Lower Previsions Without A Possibility Space Article Swipe
Matthias C. M. Troffaes
,
Michael Goldstein
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/978-3-031-15436-2_4
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1007/978-3-031-15436-2_4
We introduce a new formal mathematical framework for probability theory, \ntaking random quantities to be the fundamental objects of interest, without reference to \na possibility space, in spirit of de Finetti’s treatment of probability, Goldstein’s Bayes \nlinear analysis, and Williams’s treatment of lower and upper previsions. The aim of our \nframework is to formalize temporal reasoning, where we treat future beliefs as random \nquantities themselves. We do this by taking random quantities to form a linear space of \nexpressions, which we endow with structure through a linear projection operator. \nWe then use a version of the temporal sure preference principle as a basis for inference \nover time. We formulate the principle in terms of desirability, and explore its implications for lower previsions. We derive an explicit expression for the natural extension of \na lower prevision under the temporal sure preference principle. We establish consistency \nof the temporal sure preference principle with any given collection of assessments. We \nalso derive various bounds on the natural extension. Finally, we show how we can recover \nstandard Bayes linear calculus from our framework. \n
Related Topics
Concepts
Bayes' theorem
Preference
Extension (predicate logic)
Inference
Mathematics
Consistency (knowledge bases)
Space (punctuation)
Projection (relational algebra)
Basis (linear algebra)
Operator (biology)
Calculus (dental)
Spacetime
Computer science
Bayesian probability
Algorithm
Artificial intelligence
Discrete mathematics
Statistics
Operating system
Medicine
Quantum mechanics
Programming language
Biochemistry
Repressor
Geometry
Gene
Transcription factor
Physics
Dentistry
Chemistry
Metadata
- Type
- book-chapter
- Language
- en
- Landing Page
- https://doi.org/10.1007/978-3-031-15436-2_4
- OA Status
- gold
- References
- 12
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3216472582
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3216472582Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1007/978-3-031-15436-2_4Digital Object Identifier
- Title
-
Foundations For Temporal Reasoning Using Lower Previsions Without A Possibility SpaceWork title
- Type
-
book-chapterOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-01-01Full publication date if available
- Authors
-
Matthias C. M. Troffaes, Michael GoldsteinList of authors in order
- Landing page
-
https://doi.org/10.1007/978-3-031-15436-2_4Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
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goldOpen access status per OpenAlex
- OA URL
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https://durham-repository.worktribe.com/output/1625999Direct OA link when available
- Concepts
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Bayes' theorem, Preference, Extension (predicate logic), Inference, Mathematics, Consistency (knowledge bases), Space (punctuation), Projection (relational algebra), Basis (linear algebra), Operator (biology), Calculus (dental), Spacetime, Computer science, Bayesian probability, Algorithm, Artificial intelligence, Discrete mathematics, Statistics, Operating system, Medicine, Quantum mechanics, Programming language, Biochemistry, Repressor, Geometry, Gene, Transcription factor, Physics, Dentistry, ChemistryTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- References (count)
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12Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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