The closely connected fields of belief revision and of nonmonotonic reasoning attract researchers in artificial intelligence, logic and philosophy. The reviewed book is aiming at a philosophical contribution to the field. The author opens a new, choice-theoretic perspective on the formation and transformation of belief.
The basic attitudes of the author are characterized in Chapter 1 (Doxastic states and their representation). The use of the term “belief” in the book is explained: beliefs as states, attitudes, or dispositions to utter certain linguistic expressions or to act in certain ways are discussed. Moreover, belief is viewed as defeasible, open to revision, and degrees of retractability (certainty) are considered. Therefore, very week forms of belief or acceptance (hidden premises, expectations) and inference operations with features of nonmonotonicity and paraconsistency are accounted. It is stressed that abstract choice functions for processes of belief change are employed in the book. It is argued that it is important to distinguish belief bases from coherent systems of belief (belief sets, theories). Belief sets are derived from bases by a process of inferential closure. Operations of changing expectations and beliefs are needed in the inference machinery, and orderings of priority or entrenchment are associated with belief bases or belief sets.
Chapter 2 (Epistemology and belief change) advocates the thesis that problems of epistemology and problems of belief change are tightly interwoven. A good theory of belief revision is necessary for a proper development of a theory of knowledge. On the other hand, the analysis of belief revision can profit from a proper understanding of the notion and representation of knowledge.
The third chapter (Changing doxastic states: two complementary perspectives) offers a general philosophical underpinning of the presented approach. Two dimensions of belief change, a static one and a dynamic one, are characterized. Five maxims for the dynamics of belief are introduced. Two of them (consistency, inferential closure) are logical constraints, the other two represent economic constraints specific to the dynamics of belief (the minimality of a change, and minimality with respect to an ordering of priority on beliefs). A new principle is introduced, a criterion of coherent choices. Next, two orthogonal perspectives on belief change are discussed – foundationalist and coherentist belief change. The third chapter includes also a discussion of the connections between belief revision and nonmonotonic reasoning.
Chapter 4 presents and comments the rationality postulates known in the literature: AGM postulates for rational contraction and for rational revisions. Also the postulates for rational nonmonotonic reasoning are discussed. The three sets of postulates exhibit close parallels. This enables the author to treat contraction, revision and nonmonotonic reasoning as three aspects of essentially the same subject matter (theoretical reason).
The central foundationalist part of the book is expounded in Chapter 5 (Foundational belief change using nonmonotonic inference). A direct mode of belief revision which operates on the level of belief bases (explicitly given sets of sentences) is studied in the chapter. The changes of the belief base are made in an uncomplicated fashion, and then a sophisticated inferential closure of the new base is taken. First some methods with serious shortcomings are discussed. The first method implements revisions and contractions by set-theoretic addition and subtraction, respectively. The second method replaces set-theoretical addition and subtraction by two change operations, by the operations of full meet contraction and revision, respectively. When performing a revision (or contraction) by \(\phi\), we keep only those sentences which are contained in all maximal subsets of the belief base that are consistent with (that do not imply) \(\phi\). Both methods do not satisfy some postulates of rationality, the second allows implicit expectations to override explicit data. A solution of the foundational belief change is proposed. A prioritized expectation base \(\mathcal E\) and a prioritized information base \(\mathcal H\) are considered and an operation of Consolidation over them is introduced.
The remainder of the book is devoted to a presentation of the view that principles of reasoning and of revising beliefs are derivable from principles of rational choice. It is shown that there are close and pointwise correspondences between the postulates for practical reason and the postulates of theoretical reason (nonmonotonic reasoning and belief change are treated as “one package”).
The general theory of rational choice is developed in Chapter 6. The author pays special attention to limiting cases: to agents that do not really have to choose, to agents that refuse to choose and agents whose choices are not rationalizable by an underlying, context-independent pattern of preferences, but still show a form of rationality which is captured by a condition of path independence. No mention of inferences or revisions is made in Chapter 6.
Coherentist belief change is presented in Chapter 7 (being the central coherentist part of the book) as a problem of rational choice. The problem consists in the general specification which parts of the background theory must be given up in response to which information input. It is shown that all postulates of theoretical reason are derived from more general principles of rational choice.
The last chapter is devoted to the problem of providing a systematic justification of the postulates for the entrenchment relations. Epistemic entrenchment is reconstructed from belief change or choice behaviour. The notion of epistemic entrenchment turns out to be constructible as a preference relation revealed by an agent’s actual or potential choices. Purely choice-theoretic and logic components in the theory of entrenchment are separated.
According to the author “The book is intended to satisfy the needs of the philosopher interested in general conceptual analyses as well as the more specialized logician or AI researcher. It is perhaps the best to read it as an essay on the notion of rationality, which in turn is explicated mainly by means of various concepts of coherence”.