A Dempster-Shafer theory inspired logic

Issues of formalisirig and interpreting epistemic uncertainty have always played a prominent role in Artificial Intelligence. The Dempster-Shafer (DS) theory of partial beliefs is one of the most-well known formalisms to address the partial knowledge. Similarly to the DS theory, which is a généralisation of the classical probability theory, fuzzy logie provides an alternative reasoning apparatus as compared to Boolean logie. Both théories are featured prominently within the Artificial Intelligence domain, but the unified framework accounting for ali the aspects of imprecise knowledge is yet to be developed. Fuzzy logie apparatus is often used for reasoning based on vague information, and the beliefs are often processed with the aid of Boolean logie. The situation clearly calls for the development of a logie formalism targeted specifically for the needs of the theory of beliefs. Several frameworks exist based on interpreting epistemic uncertainty through an appropriately defined modal operator. There is an epistemic problem with this kind of frameworks: while addressing uncertain information, they also allow for non-constructive proofs, and in this sense the number of true statements within these frameworks is too large. In this work, it is argued that an inferential apparatus for the theory of beliefs should follow premises of Brouwer's intuitionism. A logie refuting tertium non daturìs constructed by deflning a correspondence between the support functions representing beliefs in the DS theory and semantic models based on intuitionistic Kripke models with weighted nodes. Without addional constraints on the semantic models and without modal operators, the constructed logie is equivallent to the minimal intuitionistic logie. A number of possible constraints is considered resulting in additional axioms and making the proposed logie intermediate. Further analysis of the properties of the created framework shows that the approach préserves the Dempster-Shafer beìief assignments and thus expresses modality through the belief assignments of the formulae within the developed logie.