Positive Agnosticism in Belief Revision
Rod Girle · 2002
Belief revision and dialogue logic overlap. There are ways of bringing both closer together and of making both more flexible and realistic. The classical AGM (Alchourrón, Gärdenfors and Makinson [1985]) account of belief revision is an account of the process of changing sets of beliefs by either adding beliefs consistent with a belief set (expansion), or giving up beliefs (contraction). Beliefs can be accepted, denied or left indetermined. Indetermined beliefs include beliefs never considered. The standard dialogue logic systems of Hamblin [1970], Walton [1984], and Walton and Krabbe [1995] attribute to each participant a commitment store which contains within it a store of beliefs. As a dialogue proceeds the store is expanded and contracted as items are added or withdrawn. When questions of the form "Is p true or false? " are asked, standard systems allow for only affirmation or rejection of the proposition, p, under consideration. We offer an alternate approach for both systems by drawing upon logics with the four values: both true and false, just true, just false, and neither true nor false (Belnap [1977]). These are taken to be "believed " values, and apply to considered propositions. Agents can then show that they are positively undecided, and do not believe a proposition to be either true or false. Differences between the AGM account and the multi-valued account are noted. The multi-valued account offers a subtler account than is presently available for a belief agent’s states and belief change options, and dialogue participants’ responses to true/false questions.