Changing Explanations in the Face of Anomalous Data in Abductive Reasoning

Changing Explanations in the Face of Anomalous Data in Abductive Reasoning Martin R. K. Baumann (martin.baumann@phil.tu-chemnitz.de) Franziska Bocklisch (franziska.bocklisch@phil.tu-chemnitz.de) Katja Mehlhorn (katja.mehlhorn@phil.tu-chemnitz.de) Josef F. Krems (krems@phil.tu-chemnitz.de) Chemnitz University of Technology, Department of Psychology, Wilhelm-Raabe-Str. 43, 09107 Chemnitz, Germany might happen that a new symptom contradicts this initial hypothesis. Such a situation is called an anomaly (Krems & Johnson, 1995). In this situation the physician has to change the current hypothesis to be able to integrate the contradicting symptom into a coherent explanation of all symptoms. There are two ways to do this. The physician can either modify the current explanation so that it explains both the new symptom and the previous ones, or select an alternative explanation for the new symptom that is compatible with the explanation for the previous observations. In our experiment we focused on situations where new observations enforce the reasoner to modify the current explanatory hypothesis as the new contradicting symptom could not be interpreted in a way compatible with the current explanation. The process of changing from an existing hypothesis to a new one is affected by several factors, such as the availability of alternative hypotheses (e.g., Burbules & Linn, 1988; Johnson & Krems, 2001; Krems & Johnson, 1995) or the entrenchment of the current explanation or the anomalous observation (Keinath & Krems, 1998). Given the importance of knowledge for real world abductive reasoning tasks, such as medical diagnosis, the structure of the domain knowledge should also affect the process of changing hypotheses. This knowledge is often organized into different levels of abstraction such that higher order concepts form categories under which lower level explanatory hypotheses are subsumed (e.g., Arocha & Patel, 1995). Previous studies on the generation of explanatory hypotheses in the domain of scientific discovery indicate that people need to encounter substantial negative outcomes of their hypothesis evaluations before they start to consider hypotheses from a different category as relevant explanations (Klahr & Dunbar, 1988). Hence, given these results it can be assumed that solving an anomaly is more difficult if it requires to change to a new category of explanatory hypotheses than to switch to a new hypothesis within the same category. Additionally, the relation of the contradicting observation to the current explanation’s category should also be relevant. The observation could be specific and linked specifically to the hypotheses of one category or it could be unspecific and linked to hypotheses of different categories. If an anomaly is caused by a specific observation that contradicts the current category of explanations it should facilitate solving the anomaly. This observation could be used to exclude all hypotheses of the current category from Abstract The integration of anomalous data is an essential subprocess of abductive reasoning. Abductive reasoning is viewed as a comprehension process by which observations are sequentially interpreted and explained in relation to existing knowledge. This emphasizes the importance of the reasoner’s knowledge structure also for the reaction to anomalous data. In this paper we investigated the effect of the specificity of anomalous data, that is whether they are related to only one category of causes or to different categories, on how hypotheses are changed to solve an anomaly. The results show that the specificity of observations facilitates the abductive reasoning process, especially in cases where the category of hypotheses must be changed. Keywords: abductive reasoning; anomaly; fuzzy pattern classification; changing explanations. Introduction Abductive reasoning is the process of finding the best explanation for a set of observations. In its simplest form this kind of reasoning can be described as follows: Given knowledge that A causes B, and B is observed, then A is hypothesized as the explanation for B (Josephson & Josephson, 1994). This kind of reasoning is part of many real world tasks such as scientific discovery, medical diagnosis, or software debugging. In these real world tasks there is often not only one observation that has to be explained but a whole set of observations and each of these observations is associated with different possible causes. For example, when a patient complains about headache the physician faces the problem that headache is a common symptom of many diseases. Furthermore, the patient often shows not only one symptom but a set of symptoms that all are associated with different causes and that become known to the physician sequentially. The physician’s task is to decide between the different possible causes of the symptoms during the reasoning process and to find the combination of causes that explains all the symptoms best. The generation of this explanation is in many cases a sequential process that can be viewed as a comprehension process by which observations are sequentially interpreted and integrated into the current explanation (Johnson & Krems, 2001). Hence, after recognizing the initially presented symptoms, the physician will generate an initial explanatory hypothesis that will be used as a context for the interpretation of following symptoms (Johnson & Krems, 2001). Because of the sequential nature of this process it