Abstract
Subjective logic is a formalism for reasoning under uncertain probabilistic information, with an explicit treatment of the uncertainty about the probability distributions. We introduce subjective networks as graph-based structures that generalize Bayesian networks to the theory of subjective logic. We discuss the perspectives of the subjective networks representation and the challenges of reasoning with them.
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Notes
- 1.
For simplicity, we make an abuse of the notation using the same type of letters for both elements of \(\mathbb {X}\) and elements of \(\mathcal {R}(\mathbb {X})\).
- 2.
If we think of \(u_{X}\) as of an amount of evidence assigned to the whole domain \(\mathbb {X}\), then \(b_X\) and \(u_X\) correspond to a basic belief assignment [12]. However, \(u_X\) is a measure for lack of evidence, not a belief, as will be further clarified in the next section.
- 3.
For this conditional probability to be always defined, it is enough to assume \(a_X (x_i) > 0\), for every \(x_i \in \mathbb {X}\). This amounts to assuming that everything we include in the domain has a non-zero probability of occurrence.
- 4.
This input information can be considered both a Bayesian subjective network with no evidence, or a fused subjective network with a subjective evidence on X.
- 5.
Note that in this section we use simplified notation for the projected probabilities, beliefs and base rates, for example \(\mathrm {P}(x_{i})\) is an abbreviation of \(\mathrm {P}_{\omega _X}(x_{i})\), \(b_{y\Vert X}\) is an abbreviation of \(b_{Y\Vert X}(y)\), etc.
- 6.
This case can only be classified as fused subjective network with a subjective evidence on Y.
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Acknowledgments
The research presented in this paper is conducted within the project ABRI (Advanced Belief Reasoning in Intelligence), partially funded by the US Army Research Laboratory.
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Ivanovska, M., Jøsang, A., Kaplan, L., Sambo, F. (2015). Subjective Networks: Perspectives and Challenges. In: Croitoru, M., Marquis, P., Rudolph, S., Stapleton, G. (eds) Graph Structures for Knowledge Representation and Reasoning. GKR 2015. Lecture Notes in Computer Science(), vol 9501. Springer, Cham. https://doi.org/10.1007/978-3-319-28702-7_7
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DOI: https://doi.org/10.1007/978-3-319-28702-7_7
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