Semantics of Dempster-Shafer Inspired Si-Logic

A new interpretation of Dempster-Shafer theory using Kripke models was recently proposed. The map between frames of discernment and Kripke models preserves Dempster-Shafer evidence combination rule and thus allows to use Kripke models for calculating beliefs in different propositions. The procedure induces a logic (as a set of true formulas). In the present paper we analyze the semantic of this logic. By representing the logic of interest through commutative lattices we show that it is a complete and sound logic, which does not have a finite independent axiomatization. The results can be used for choosing a propositional language for such logic and thus contribute towards building a fuzzy logic for Dempster-Shafer theory.