Ernest Davis — Page 2

arXiv2015

The Scope and Limits of Simulation in Cognitive Models

It has been proposed that human physical reasoning consists largely of running "physics engines in the head" in which the future trajectory of the physical system under consideration is computed precisely using accurate scientific theories. In such models, uncertainty and incomplete knowledge is dealt with by sampling probabilistically over the space of possible trajectories ("Monte Carlo simulation"). We argue that such simulation-based models are too weak, in that there are many important aspects of human physical reasoning that cannot be carried out this way, or can only be carried out very inefficiently; and too strong, in that humans make large systematic errors that the models cannot account for. We conclude that simulation-based reasoning makes up at most a small part of a larger system that encompasses a wide range of additional cognitive processes.

cs.AI↗

arXiv2013

The Relevance of Proofs of the Rationality of Probability Theory to Automated Reasoning and Cognitive Models

A number of well-known theorems, such as Cox's theorem and de Finetti's theorem. prove that any model of reasoning with uncertain information that satisfies specified conditions of "rationality" must satisfy the axioms of probability theory. I argue here that these theorems do not in themselves demonstrate that probabilistic models are in fact suitable for any specific task in automated reasoning or plausible for cognitive models. First, the theorems only establish that there exists some probabilistic model; they do not establish that there exists a useful probabilistic model, i.e. one with a tractably small number of numerical parameters and a large number of independence assumptions. Second, there are in general many different probabilistic models for a given situation, many of which may be far more irrational, in the usual sense of the term, than a model that violates the axioms of probability theory. I illustrate this second point with an extended examples of two tasks of induction, of a similar structure, where the reasonable probabilistic models are very different.

cs.AI↗