Some Connections Between Epistemic Logic and the Theory of Nonadditive Probability

Abstract

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (D.S.) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions a Ja Shafer is made. Then it is shown that the Alchourr6n-Ciirdenfors-Makinson (A.C.M.) logic of belief change is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine.