Explanatory Reasoning for Image Understanding Using Formal Concept Analysis and Description Logics

In this paper, we propose an original way of enriching description logics with abduction reasoning services. Under the aegis of set and lattice theories, we put together ingredients from mathematical morphology, description logics, and formal concept analysis. We propose computing the best explanations of an observation through algebraic erosion over the concept lattice of a background theory that is efficiently constructed using tools from formal concept analysis. We show that the defined operators are sound and complete and satisfy important rationality postulates of abductive reasoning. As a typical illustration, we consider a scene understanding problem. In fact, scene understanding can benefit from prior structural knowledge represented as an ontology and the reasoning tools of description logics. We formulate model based scene understanding as an abductive reasoning process. A scene is viewed as an observation and the interpretation is defined as the best explanation, considering the terminological knowledge part of a description logic about the scene context. This explanation is obtained from morphological operators applied on the corresponding concept lattice.