Foundational Belief Change* Foundational Belief Change

anonymous referee for the Journal of Philosophical Logic for their insightful comments on earlier versions of this paper. I also thank Prasanta Bandy-opadhyay, Jim Cain, Francis Jeery Pelletier and Ted Sider for their sugges tions and encouragement, and acknowledge the help of my friend Ramkrish-nan Nambimadom in the construction of a crucial proof. Abstract: This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation , even under quite strong restrictions, fails to satisfy the \supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modiied so as to yield the desired properties. The new construction may be described as involving a modiication of safe (base) contraction so as to make it maxichoice. We often change our beliefs. We learn new things, occasionally things that connict with our current beliefs. On such occasions new beliefs replace the old ones. It is as if this process is completed in two steps: (1) rst we identify and throw out the beliefs that connict with the new information and then (2) we accept the new information. In the literature (1) is referred to as the problem of \belief contraction", and (2) as the problem of \belief expansion". The combination of (1) followed by (2) is called \belief revision". Though this account of belief change is very intuitive, 1 its logic is not understood very well. If it is assumed that a rational epistemic (doxastic) agent wants to minimize unnecessary loss of information, then belief contraction becomes a very diicult problem. 2 This paper is about belief revision seen from a foundationalist perspective. We show that in order to satisfy GG ardenfors postulates on belief revision in a founda-tionalist framework, we need to radically revise Fuhrmann's Fuhrmann 91] construction of a reject-set. This result makes an interesting connection between Nebel's Nebel 89] theory revision based on maxichoice base revision and his Nebel 91] unambiguous partial meet revision. This contraction operation also bridges the gap between Fuhrmann's Fuhrmann 88, Fuhrmann 91] minimal theory revision approach and Nebel's approach. 1 Background We assume that the objects of beliefs are propositions, which may be represented as equivalence classes of sentences, or as sets of worlds. The believer's language L is assumed to contain the usual propositional …