Multi-Context Models for Reasoning under Partial Knowledge: Generative Process and Inference Grammar
This addresses the challenge of making plausible inferences in domains where complete probabilistic knowledge is unavailable, which is incremental as it builds on existing graphical models and logic frameworks.
The paper tackles the problem of reasoning under partial knowledge by proposing the Multi-Context Model (MCM), a new graphical model that represents partial knowledge as a middle ground between Probabilistic Logic, Bayesian Logic, and Probabilistic Graphical Models, and discusses its construction and inference methods.
Arriving at the complete probabilistic knowledge of a domain, i.e., learning how all variables interact, is indeed a demanding task. In reality, settings often arise for which an individual merely possesses partial knowledge of the domain, and yet, is expected to give adequate answers to a variety of posed queries. That is, although precise answers to some queries, in principle, cannot be achieved, a range of plausible answers is attainable for each query given the available partial knowledge. In this paper, we propose the Multi-Context Model (MCM), a new graphical model to represent the state of partial knowledge as to a domain. MCM is a middle ground between Probabilistic Logic, Bayesian Logic, and Probabilistic Graphical Models. For this model we discuss: (i) the dynamics of constructing a contradiction-free MCM, i.e., to form partial beliefs regarding a domain in a gradual and probabilistically consistent way, and (ii) how to perform inference, i.e., to evaluate a probability of interest involving some variables of the domain.