An analysis of first-order logics of probability
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The paper is a brief summary of an invited talk given at the Discovery Science conference. The principal points are as follows: first, that probability theory forms the basis for connecting hypotheses and data; second, that the expressive power of the probability models used in scientific theory formation has expanded significantly; and finally, that still further expansion is required to tackle many problems of interest. This further expansion should combine probability theory with the expressive power of first-order logical languages. The paper sketches an approximate inference method for representation systems of this kind.