Reasoning with Graph Operations

Problem solving is an analog to scientific method, wherein abduction and deduction operate in a cyclic fashion to generate and refine a series of hypotheses that purport to explain the observed data. Model Generative Reasoning implements this cycle through a family of operations on representations based on conceptual graphs. Specialize, the operator that implements abduction generates alternative hypotheses. Fragment removes potential incoherences from hypotheses, while preserving coherence with the observations. This is seen as a form of deduction with the aim of allowing more hypotheses to be generated in the next cycle. 1. Problem solving and noisy data In essence, problem solving is a two-part process. There is a data-driven side, where making observations, filtering them and generating hypotheses from them is important. There is also another side, that is more goal-driven; evaluation of hypotheses against new data can, and does lead to reformulation or even rejection of these hypotheses. Typically problem solving machines are good at the first but less so at the second part. Heuristic search enables this sort of efficient generation, leading to excellent systems for planning, where the prime aim is to reach some desired goal without interference from the environment (Chapman, 87). When, however, data are incomplete, incoherent (i.e. unexpected), or just irrelevant, such techniques will fail. In these difficult cases, what is needed is a principled way of handling noisy data. The gaps in incomplete data should be filled, the incoherencies removed and the irrelevancies ignored. We will present, in this paper, mechanisms for doing all of these, and place these mechanisms in a problem solving framework. In order to do this we will contrast our approach with that based on theorem proving. In particular the nonmonotonic approach to noisy data through the ATMS (Reiter and de Kleer, 87) can be seen as only solving one of the problems associated with noisy data: incoherence that presents itself through logical inconsistency.