Multi-Context Models for Reasoning under Partial Knowledge: Generative Process and Inference Grammar

TL;DR

This paper introduces the Multi-Context Model (MCM), a graphical framework for reasoning with partial domain knowledge, enabling probabilistically consistent beliefs and inference despite incomplete information.

Contribution

The paper presents MCM as a novel graphical model that bridges probabilistic logic and graphical models for reasoning under partial knowledge.

Findings

MCM effectively represents partial domain knowledge.

It allows for contradiction-free belief updates.

Enables inference with incomplete information.

Abstract

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.