The theory of random propositions

The theory of random propositions is a theory of confirmation that contains the Bayesian and Shafer-Dempster theories as special cases, while extending both in ways that resolve many of their outstanding problems. The theory resolves the Bayesian "problem of the priors" and provides an extension of Dempster's rule of combination for partially dependent evidence. The standard probability calculus can be generated from the calculus of frequencies among infinite sequences of outcomes. The theory of random propositions is generated analogously from the calculus of frequencies among pairs of infinite sequences of suitably generalized outcomes and in a way that precludes the inclusion of contrived or ad hoc elements. The theory is also formulated as an uninterpreted calculus. © 1994 Kluwer Academic Publishers