Sensitivity analysis in probabilistic argumentation systems

摘要

A sensitivity analysis method is built upon a PAS framework that includes a knowledge base defined by a set of propositions, a set of logical statements over the propositions, a set of assumptions for each statement and the corresponding assumption probabilities. The knowledge base is queried to determine the quasi-support qs(H) and qs(⊥). Disjoint arguments of the quasi-support are then found for both the hypothesis H and contradiction ⊥. Symbolic formulas dqs(H) and dqs(⊥) are formed for the degree of quasi-support for hypothesis H and contradiction ⊥, respectively, based on these disjoint arguments. The partial derivatives $$ D_{H,j}\equiv \frac{\partial \mathrm{dqs}\left(H\right)}{\partial r_j}\mathrm{of}\mathrm{dqs}\left(H\right)\mathrm{and}{D}_{\perp ,j}\equiv \frac{\partial \mathrm{dqs}(\perp )}{\partial r_j}$$of dqs(⊥) are computed with respect to the assumption probability r_j. Sensitivity analysis formulas ƒ(H,D_H,j,D_⊥,j,r_j,δr_j) are then formed from the partial derivatives to establish the relationship between a PAS output, such as the degree of support dsp( ), degree of doubt ddb( ), and degree of possibility dps( ), for hypothesis H, and the assumption probabilities under a given input condition. The formulas can be used to determine how to tune the assumption probabilities to achieve the desired PAS output values, to identify key assumption probabilities, to measure the sensitivity of the system to the assumption probabilities, to account for input variability, to identify contradictions in the knowledge base and so forth.