Hypothesis Discrimination with Abstractions based on Observation and Action Costs Gianluca Torta 1 , Daniele Theseider Dupr´ e 2 , Luca Anselma 1 (1) Universit` a di Torino, Italy, email: {torta,anselma}@di.unito.it (2) Universit` a del Piemonte Orientale, Italy, email: dtd@mfn.unipmn.it Abstract Several explanation and interpretation tasks, such as diagnosis, plan recognition and image interpre- tation, can be formalized as abductive and consis- tency reasoning. Some proposals address the prob- lem based on a task-independent representation of a domain which includes an ontology or taxonomy of hypotheses. In this paper we rely on the same type of representation, and we address cost trade- offs in abduction intended as an iterative process where, like in model-based diagnosis, further ob- servations are proposed to discriminate among can- didates. Discrimination is performed up to an ap- propriate level which depends on the cost of actions (e.g. repair actions or therapy) to be taken based on the results of abduction, and on the cost of addi- tional observations, which should be balanced with the benefits, in terms of more suitable actions, of better discrimination. Abstractions have a signifi- cant impact on this trade-off, given that the cost of observing the same phenomenon at different levels of abstraction may be quite different. 1 Introduction Several explanation and interpretation tasks, such as diagno- sis, plan recognition and image interpretation, can be formal- ized as abductive reasoning or related forms of nonmonotonic reasoning. A number of approaches [Chu and Reggia, 1991; Console and Theseider Dupr´ e, 1994; Kautz, 1991], includ- ing recent ones [Besnard et al., 2007; Neumann and M¨ oller, 2006], address the problem based on a representation of a domain which includes an ontology or taxonomy of hypothe- ses. Such a representation may have been developed inde- pendently of the reasoning task (in perspective, it may even be available on the Web in a shared ontology for different rea- soning tasks), i.e., the structure reflects a natural representa- tion of the domain, but it does not necessarily provide directly the best structure for diagnosis or interpretation. In this paper we adopt a similar representation, and con- centrate on the following issues: • Dealing with abduction as an iterative process where, as in model-based diagnosis, further observations are pro- posed to discriminate among candidate explanations; • Balancing the costs of observations with (reduced) costs or (increased) benefits of the results of abduction. The costs/benefits associated with the results of abduction, in a diagnostic setting, correspond to the cost of repair ac- tions or therapy, and are expected to decrease as long as more information is available on hypotheses; in a plan recognition or in an interpretation task, the human or software agent us- ing the results should similarly achieve some benefit from a better discrimination of hypotheses or from more specific hy- potheses, leading to a more focused action: this could either imply a reduced cost — e.g. if hypotheses are threats to the agent with costly defense actions — or an increased benefit — e.g. if the agent might use the results to earn money. In all settings, we intend that some action has to be taken based, in general, on the remaining candidate hypotheses. If the set of candidates is too broad or too abstract, the agent may incur into higher action costs due to (a combination of) the follow- ing reasons: • more actions to be taken, to account for all possibilities, e.g. in component-oriented diagnosis, replacing all sus- pect components; • selecting, for example, the action associated with the most probable explanation, with an expected cost which takes into account the cost of making, with a smaller probability, the wrong action (repairing the wrong part, taking the wrong therapy, defending from the wrong threat); and similarly, in the benefit case, making an ac- tion which will probably (but not certainly) be the right one for achieving the benefit. The different issues are related: discrimination may be per- formed among hypotheses at the same level of abstraction, but it could also involve refining hypotheses. In any case, dis- crimination requires more observations, whose cost should be balanced with the benefits, in terms of more suitable actions, of better discrimination. The presence of a domain representation with abstractions has a significant impact on this trade-off. The cost of observ- ing the same phenomenon at different levels of abstraction may vary significantly; in fact, it may range from subjective information from a human (patient or user) to more or less costly medical or technical tests, or, in an image interpretation task, it may involve computationally complex image process- ing, to be performed interactively with the reasoning task, as