Can Information Theory Help Us Remove Outdated Beliefs
Erik J Olsson · 1995
Abstract: It is argued that a rational agent should not be able to gain information simply by removing a previously accepted proposition, i.e. a proposition having probability 1. An example is given showing that the Gärdenfors axioms for probabilistic contraction in fact do not exclude that the agent’s uncertainty is decreased as a result of contraction. The concept of entropy is borrowed from statistical information theory and used as a tool for measuring the uncertainty pertaining to a belief state. Entropy is then used to formulate a new axiom in addition to the Gärdenfors axioms. The new axiom explicitly rules out the possibility of agents getting more informed as a result of belief removal.