Abstract

We apply methods of abduction derived from propositional probabilistic reasoning to predicate probabilistic reasoning, in particular inductive logic, by treating nite predicate knowledge bases as potentially innite propositional knowledge bases. Full and detailed proofs are given to show that for a range of predicate knowledge bases (such as those typically associated with inductive reasoning) and several key propositional inference processes (in particular the Maximum Entropy Inference Process) this procedure is well dened, and furthermore yields an explanation for the validity of the induction in terms of `reasons'. Motivation Consider the following situation. I am sitting by a bend in a road and I start to wonder how likely it is that the next car which passes will skid on this bend. I have some knowledge which seems relevant, for example I know that if there is ice on the road then there is a good chance of a skid, and similarly if the bend is unsigned, the camber adverse, etc.. I possibly also have some knowledge of how likely it is that there is ice on the road, how likely it is that the bend is unsigned (possibly conditioned on the iciness of the road) etc.. Notice that this is generic knowledge which applies equally to any potential passing car. Supported by a EPRSC Research Associateship y Supported by an Egyptian Government Scholarship, File No. 7083 1 Armed with this knowledge base I may now form some opinion as to the likely outcome when the next car passes. Subsequently several cars pass by. I note the results and in consequence possibly revise my opinion as to the likelihood of the next car through skidding. Clearly we are all capable of forming opinions, or beliefs, in this way, but is it possible to formalize this inductive process, this pro...

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