Kevin T. Kelly

Iterated belief revision, reliability, and inductive amnesia

Belief revision theory concerns methods for reformulating an agents epistemic state when the agents beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agents epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning methods reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the reliability of several proposed belief revision operators. Stringent conceptions of “minimal change” are shown to occasion a limitation called inductive amnesia: they can predict the future only if they cannot remember the past. Avoidance of inductive amnesia can therefore function as a plausible and hitherto unrecognized constraint on the design of belief revision operators.

Reliable Belief Revision

Philosophical logicians proposing theories of rational belief revision have had little to say about whether their proposals assist or impede the agent’s ability to reliably arrive at the truth as his beliefs change through time. On the other hand, reliability is the central concern of formal learning theory. In this paper we investigate the belief revision theory of Alchourron, Gardenfors and Makinson from a learning theoretic point of view.

Propositional Reasoning that Tracks Probabilistic Reasoning

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method

A New Solution to the Puzzle of Simplicity

{\sf B}_{p}

Justification as truth-finding efficiency: how Ockham's Razor works

, which specifies an initial belief state

Ockham's razor, empirical complexity, and truth-finding efficiency

{\sf B}_{p}(\top)

Learning Theory and the Philosophy of Science

that is revised to the new propositional belief state

Simplicity, Truth, and Probability

{\sf B}(E)

HOW SIMPLICITY HELPS YOU FIND THE TRUTH WITHOUT POINTING AT IT

upon receipt of information E. An acceptance rule tracks Bayesian conditioning when

Theory Discovery from Data with Mixed Quantifiers

{\sf B}_{p}(E) = {\sf B}_{p|_{E}}(\top)