Advancing the Use of Sparse Knowledge for Qualitative Models and Simulations
Stefania Ionescu

Abstract:
The fundamental problem of process-oriented qualitative models and simulations is to extract as much useful information as possible from sparse or incomplete descriptions. These qualitative reasoning approaches address the gap between the infinite complexity of the world and our partial knowledge of it, which defies traditional numerical modelling and generalises the reasoning to the qualitative behaviour capturing the key aspects. We take a theoretical approach to this problem, and make the following contributions. First, we develop a new partial axiomatisation that is better suited for simulation analysis. Second, using this axiomatisation, we identify inconsistencies of state graphs resulted from the use of sparse knowledge, and suggest solutions for these. Third, we introduce the problem of early inconsistency detection, requiring non-trivial inequality reasoning in the context of partial knowledge. Fourth, we formulate a generalisation of this problem, called the “combining changes problem”, and analyse it from a complexity theoretic perspective, proving it to be polynomial under reasonable assumptions. Fifth, we derive a practical procedure for the early identification of contradictory relations, making qualitative reasoning more efficient by reducing the number of eligible compound terminations. As a general result, our work demonstrates the value of a theoretical approach to this problem when grounded by practical examples, realised using Garp3, clarifying the concepts and problems, and motivating the methods we developed.