2013/03/20 by Robert Kennes, Kennes, Robert
Arts and Humanities · Computer Science · #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #Epistemology, Ethics, and Metaphysics #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #cs.AI
paper · pdf · doi:10.48550/arxiv.1303.5725
Appears in Proceedings of the Seventh Conference on Uncertainty in Artificial Intelligence (UAI1991)
arxiv created 2013/03/20 · openalex publication_date 2013/03/20 · arxiv updated 2013/03/26 · openalex created_date 2022/08/18 · openalex updated_date 2026/07/28
The categorial approach to evidential reasoning can be seen as a combination of the probability kinematics approach of Richard Jeffrey (1965) and the maximum (cross-) entropy inference approach of E. T. Jaynes (1957). As a consequence of that viewpoint, it is well known that category theory provides natural definitions for logical connectives. In particular, disjunction and conjunction are modelled by general categorial constructions known as products and coproducts. In this paper, I focus mainly on Dempster-Shafer theory of belief functions for which I introduce a category I call Dempster?s category. I prove the existence of and give explicit formulas for conjunction and disjunction in the subcategory of separable belief functions. In Dempster?s category, the new defined conjunction can be seen as the most cautious conjunction of beliefs, and thus no assumption about distinctness (of the sources) of beliefs is needed as opposed to Dempster?s rule of combination, which calls for distinctness (of the sources) of beliefs.