Compositional Models in Valuation-Based Systems
Compositional models were initially described for discrete probability theory, and later extended for possibility theory, and Dempster-Shafer (D-S) theory of evidence. Valuation-based systems (VBS) can be considered as a generic uncertainty framework that has many uncertainty calculi, such as probability theory, a version of possibility theory where combination is the product t-norm, Spohn’s epistemic belief theory, and D-S belief function theory, as special cases. In this paper, we describe compositional models for the VBS framework using the semantics of no-double counting. We show that the compositional model defined here for belief functions differs from the one studied by Jiroušek, Vejnarová, and Daniel. The latter model can be described in the VBS framework, but with a combination operation that is different from Dempster’s rule.
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