### REL — a logic for relative evidential support

Z. An, D.A. Bell, J.G. Hughes
1993 International Journal of Approximate Reasoning
A formal logic--588~ for Relative Evidential Support is proposed based on the following ideas: 1. Arguments are represented direct(y and are taken as the terms for ~5 °. By arguments we mean the relationships between two judgments expressing that one supports or refutes the other, ie, evidential supports; 2. Comparisons between arguments are used as carriers for their relative strengths. By comparisons we mean relationships between two arguments with respect to their strengths. 3. Uncertainty
more » ... asoning is viewed as a process of three phases of." • evidence structure construction; • evidence accumulation; • decision-making. Some examples are presented showing how ~qZ~S: can be used to represent various kinds of uncertain information such as: • the relative strengths of evidential supports, eg, evidence e 1 supports conclusion PI better than evidence e 2 supports P2; • belief functions, eg. evidence e I is exhausted by stating a belief function with mass function m l; • necessity assertions, eg, the necessity function derived from the membership function f of predicate F on domain D; • probability assertions, eg, the probability that statement s is true is. 99. These examples illustrate the advantages off,S: over other representations of uncertain information and evidential reasoning, eg, 1. it is based on relative strengths of arguments that cannot be represented using any absolute measures; 2. It is capable of representing explicitly the design of evidence [21]; 3. It can represent many kinds of absolute measures--in doing so it has the merit 205 206 Z. Anet al. that it explicates the assumptions and requirements for using different kinds of measurements of uncertainty; 4. it provides a natural common base for a hybrid system. Our conclusion is that~qPS"S a is a suitable formalization for uncertain information.