A Formal Approach to Aggregated Belief Formation

Abstract

Abstract. This paper introduces a formal method to aggregate over basic beliefs, in order to deduce aggregated or complex beliefs as often used in applications. Complex beliefs can represent several things, such as a belief about a period in which other beliefs held or the minimal or maximal certainty with which a belief held. As such they contain richer information than the basic beliefs they are aggregated from and can be used to optimize an agent's search through its memory and its reasoning processes. The developed method can also aggregate over aggregated beliefs, hence nested aggregations are possible. An implementation in Prolog demonstrates its operationality.

An Agent Memory Model Enabling Rational and Biased Reasoning

“…The approach introduced in [3] allows for the formation of arbitrary aggregations over beliefs, which result in aggregated beliefs. In this approach an aggregated belief is defined as an aggregation that takes the form of a constraint (e.g., highest) that must hold for a certain variable (e.g., T) of a partially specified belief (e.g., belief(identity, contact1, friendly, T, S, C) in which the P, O, and V are specified while the T, S, and C are left variable).…”

“…Its clauses execute the aggregations as which the complex beliefs are defined that are in task focus, but could not be retrieved. For the details concerning the execution of these aggregations, see [3]. Note that when an aggregation requires a complex belief as input, it is first attempted to retrieve it.…”

“…Which perspective and level of aggregation is needed, is application and task dependent. For that reason, an algebraic approach was developed in [3] that can form arbitrary aggregations over beliefs. For this, it uses a general aggregation operator parameterized by a specific constraint that can be used in a recursive manner.…”