2013/10/04 by Ernest Davis, Davis, Ernest · 1 citation
Computer Science · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1310.1328
openalex publication_date 2013/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A number of well-known theorems, such as Cox's theorem and de Finetti's\ntheorem. prove that any model of reasoning with uncertain information that\nsatisfies specified conditions of "rationality" must satisfy the axioms of\nprobability theory. I argue here that these theorems do not in themselves\ndemonstrate that probabilistic models are in fact suitable for any specific\ntask in automated reasoning or plausible for cognitive models. First, the\ntheorems only establish that there exists some probabilistic model; they do not\nestablish that there exists a useful probabilistic model, i.e. one with a\ntractably small number of numerical parameters and a large number of\nindependence assumptions. Second, there are in general many different\nprobabilistic models for a given situation, many of which may be far more\nirrational, in the usual sense of the term, than a model that violates the\naxioms of probability theory. I illustrate this second point with an extended\nexamples of two tasks of induction, of a similar structure, where the\nreasonable probabilistic models are very different.\n