Scientific discovery on positive data via belief revision

A model of inductive inquiry is defined within a first-order context. Intui tively, the model pictures inquiry as a game between Nature and a scientist . To begin the game, a nonlogical vocabulary is agreed upon by the two play ers along with a partition of a class of structures for that vocabulary. Ne xt, Nature secretly chooses one structure (the real world) from some cell o f the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With each new datum the scientist announc es a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientists successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. A special kind of scientist selects his hypotheses on the basis of a belief revision operator. We show that reliance on belief revis ion allows scientists to solve a wide class of problems.