On the completeness of incidence calculus (Q1923826)

This paper is concerned with an approach to reasoning with uncertainity. Reasoning with uncertainity is a subfield of artificial intelligence. In classical logic a proposition may be true or false. This is not suitable for all purposes of knowledge representation in artificial intelligence. There are situations where one may need to represent and reason about uncertain knowledge. In the presence of uncertainity the classical semantics is not sufficient, because the truth value of a proposition may be uncertain. Thus, the field of reasoning with uncertainity investigates non-classic logics whose semantics may capture notions of truth different than the classical one. The incidence calculus, the approach studied in this paper, is one such logic. Its semantics is a possible-worlds semantics. The truth of a proposition is characterized by a lower bound and an upper bound of the set of possible worlds where the proposition is true. This paper treats in particular the completeness of an inference system for this logical calculus in the propositional case. The inference system itself was proposed in previous work (referenced in the paper), and this article contains a proof of completeness.