Conservative Belief Change: A Gricean Approach James P. Delgrande School of Computing Science Simon Fraser University Burnaby, B.C., CANADA, V5A 1S6 jim@cs.sfu.ca Abhaya C. Nayak Department of Computing Macquarie University NSW 2109, AUSTRALIA abhaya@ics.mq.edu.au Maurice Pagnucco School of CSE The University of New South Wales NSW, 2052, AUSTRALIA morri@cse.unsw.edu.au Abstract A standard intuition underlying traditional ac- counts of belief change is the principle of minimal change. Briefly put, it states that an agent’s belief state should be modified minimally to incorporate new information. In this paper we introduce a novel account of belief change in which the agent’s belief state is modified minimally to incorporate exactly the new information. Thus a revision by will result in a new belief state in which is be- lieved, but a stronger proposition (such as ) is not, regardless of the initial form of the belief state. This form of belief change is termed conservative belief change and corresponds to a Gricean inter- pretation of the input formula. We investigate both belief revision and belief update in this framework and discuss both syntax independent as well as syn- tax sensitive methods. We show how this approach solves a recalcitrant problem in belief revision. A reasoning entity will need to maintain its stock of be- liefs in the face of new information. Such belief change is not arbitrary; rather belief change is generally taken to be guided by various rationality criteria. One of the most widely advocated rationality criterion is the principle of mini- mal change: that a belief state is modified minimally to incor- porate new information. This principle has many guises [16; 20]. Perhaps the most evident way in which a change in be- lief can be said to be minimal is in terms of standard con- structions such as systems of spheres [15; 7] or epistemic en- trenchment [4], i.e., orderings of possible worlds or orderings of sentences. We can also distinguish different fundamental forms of be- lief change. In the literature at least two are ubiquitous: re- vision and update. Intuitively, revision deals with the change that occurs when the reasoner’s beliefs about its environment are incomplete and possibly incorrect. Any new information fills in these gaps or rectifies mistaken beliefs. However, the environment is assumed static and does not change. Update on the other hand deals with dynamic environments in which the new information reflects changes brought about by actions Also affiliated with National ICT Australia and the ARC Centre of Excellence in Autonomous Systems. that have occurred. In this paper we introduce an account of belief change that is orthogonal to the notions of revision and update, and in which “minimal change” is taken with respect to the new information. We examine an account of belief change in which all we wish to accept is the new information itself—no more, no less. This is reminiscent of the Gricean principle of Conversational Implicature, that in interpreting a speaker we should assume that the speaker means no more, and no less, than what she says. We, of course, add as caveat that the lis- tener takes the speaker to be sincere (not trying to withhold information) and an expert in the domain of discourse. Our approach ensures that, in a sense to be specified, exactly the sentence accepted as evidence is incorporated. A modified knowledge base is a conservative extension (see Section 2) of the sentence for belief change; consequently we term this conservative belief change. We outline both syntax indepen- dent and syntax dependent methods for revision and update. The paper is organised as follows. In the next section we outline some motivating examples that highlight particular as- pects of our proposal; as well we examine related work. Sec- tion 2 provides the necessary background material. In Sec- tion 3 we outline our proposed method of belief change. Sec- tion 4 discusses the significance of these results and Section 5 presents our conclusions. 1 Motivation and Examples The following example illustrates the traditional account of integrating new information, in accord with the principle of minimal change. Example 1.1 (Exclusive disjunctive update) Leslie and Robin are two students who share an apartment above your’s. While they get along, they are independent and have their own circles of friends. You initially believe that for the upcoming weekend neither will be in the apartment, say . However, come the weekend you hear muted but unmistakable sounds of domestic activity. You modify your beliefs minimally to account for this new information, and consequently you conclude just that one of them has not gone away for the weekend, i.e. . 1 1 We use for material biconditional and for logical equiva- lence.