H-Complexity Metric for Qualitative Spatial and Temporal Reasoning Applications

Commonsense reasoning, in particular qualitative spatial and temporal reasoning (QSTR), provides flexible and intuitive methods for reasoning about vague and uncertain information including temporal duration and ordering, and spatial orientation, topology and distance. Despite significant theoretical advances in QSTR, there is a distinct absence of applications that employ these methods. The central problem is a lack of application-level standards and metrics that developers can use to measure the effectiveness of their QSTR applications. To address this we present a fundamental metric called H-complexity that quantifies the expressiveness of QSTR systems according to the number of distinct scenario classes that can be encoded. In this paper we show that H-complexity can be employed in a range of powerful and practical ways that support QSTR application development. To illustrate this, we present two examples: calculating test coverage for validation, and quantifying the reduction in expressiveness due to constraints. We thereby demonstrate that H-complexity is a useful tool for determining whether a QSTR system meets the needs of a specific application.