Causal approximations

摘要

Adequate models require the identification of abstractions and approximations that are well suited to the task at hand. In this paper we analyze the problem of automatically selecting adequate models for the task of generating parsimonious causal explanations. We make three important contributions. First, we develop a precise formalization of this problem. In this formalization, models are defined as sets of model fragments, causal explanations are generated using causal ordering, and model simplicity is based on the intuition that using more approximate descriptions of fewer phenomena leads to simpler models. Second, we use this formalization to show that the problem is intractable (NP-hard) and identify three sources of intractability: (a) deciding what phenomena to model; (b) deciding how to model the chosen phenomena; and (c) satisfying domain-dependent constraints. Third, we introduce a new class of approximations called causal approximations that are commonly found in modeling the physical world. Causal approximations are based on the idea that more approximate descriptions usually explain less about a phenomenon than more accurate descriptions. Hence, when all approximations are causal approximations, the causal relations entailed by a model decrease monotonically as models become simpler, leading to an efficient, polynomial-time algorithm for finding adequate models.