Modelling Uncertainty in Agent Programming

Existing cognitive agent programming languages that are based on the BDI model employ logical representation and reasoning for implementing the beliefs of agents. In these programming languages, the beliefs are assumed to be certain, i.e. an implemented agent can believe a proposition or not. These programming languages fail to capture the underlying uncertainty of the agent’s beliefs which is essential for many real world agent applications. We introduce Dempster-Shafer theory as a convenient method to model uncertainty in agent’s beliefs. 1 Mapping agent beliefs to Dempster-Shafer sets In Dempster-Shafer theory[4], a frame of discernment Ω is defined as the set of all hypotheses in a certain domain. On the power set 2, a mass function m(X) is defined for every X ⊆ Ω, with m(X) ≥ 0 and ∑ X⊆Ω m(X) = 1. If there is no information available with respect to Ω, m(Ω) = 1, and m(X) = 0 for every subset of Ω. A simple support function is a special case of a mass function, where the evidence supports one set of hypotheses A, and zero mass value is assigned to any subset of Ω other than A. Mass functions can be combined using Dempster’s Rule of Combination. This combination rule for mass function m1 and m2 is denoted as m1 ⊕ m2 and is defined, for X, Y, Z ⊆ Ω, as: