A model of inductive inquiry is defined within a first-order context. Intuitively, 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 players along with a partition of a class of structures for that vocabulary. Next, Nature secretly chooses one structure ("the real world") from some cell of the partition. She then presents the scientist with a sequence of atomic facts about the chosen structure. With (...) each new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his inquiry, the scientist's 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 revision allows scientists to solve a wide class of problems. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

In this incisive new book one of Britain's most eminent philosophers explores the often overlooked tension between voluntariness and involuntariness in human cognition. He seeks to counter the widespread tendency for analytic epistemology to be dominated by the concept of belief. Is scientific knowledge properly conceived as being embodied, at its best, in a passive feeling of belief or in an active policy of acceptance? Should a jury's verdict declare what its members involuntarily believe or what they voluntarily accept? And (...) should statements and assertions be presumed to express what their authors believe or what they accept? Does such a distinction between belief and acceptance help to resolve the paradoxes of self-deception and akrasia? Must people be taken to believe everything entailed by what they believe, or merely to accept everything entailed by what they accept? Through a systematic examination of these problems, the author sheds new light on issues of crucial importance in contemporary epistemology, philosophy of mind, and cognitive science. (shrink)

This paper is concerned with formal aspects of the logic of theory change, and in particular with the process of shrinking or contracting a theory to eliminate a proposition. It continues work in the area by the authors and Peter Gärdenfors. The paper defines a notion of safe contraction of a set of propositions, shows that it satisfies the Gärdenfors postulates for contraction and thus can be represented as a partial meet contraction, and studies its properties both in general and (...) under various natural constraints. (shrink)

Eric Martin and Daniel N. Osherson present a theory of inductive logic built on model theory. Their aim is to extend the mathematics of Formal Learning Theory to a more general setting and to provide a more accurate image of empirical inquiry. The formal results of their study illuminate aspects of scientific inquiry that are not covered by the commonly applied Bayesian approach.

SUGGESTED COURSES Introductory level A (Requires very little background in logic .): 4: -9 - - -7 -2 Introductory level B: -9,:+-+ -,2:+,2: -,3:20+-22+ -7 -2 ...

This book is devoted to a different proposal--that the logical structure of the scientist's method should guarantee eventual arrival at the truth given the scientist's background assumptions.