In spite of a powerful tradition, more than two thousand years old, that in a valid argument the premises must be relevant to the conclusion, twentieth-century logicians neglected the concept of relevance until the publication of Volume I of this monumental work. Since that time relevance logic has achieved an important place in the field of philosophy: Volume II of Entailment brings to a conclusion a powerful and authoritative presentation of the subject by most of the top people working in (...) the area. Originally the aim of Volume II was simply to cover certain topics not treated in the first volume--quantification, for example--or to extend the coverage of certain topics, such as semantics. However, because of the technical progress that has occurred since the publication of the first volume, Volume II now includes other material. The book contains the work of Alasdair Urquhart, who has shown that the principal sentential systems of relevance logic are undecidable, and of Kit Fine, who has demonstrated that, although the first-order systems are incomplete with respect to the conjectured constant domain semantics, they are still complete with respect to a semantics based on "arbitrary objects." Also presented is important work by the other contributing authors, who are Daniel Cohen, Steven Giambrone, Dorothy L. Grover, Anil Gupta, Glen Helman, Errol P. Martin, Michael A. McRobbie, and Stuart Shapiro. Robert G. Wolf's bibliography of 3000 items is a valuable addition to the volume. (shrink)

An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of (...) the operations for belief change. Representation theorems are given for the local operators. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.

SUGGESTED COURSES Introductory level A (Requires very little background in logic .): 4: -9 - - -7 -2 Introductory level B: -9,:+-+ -,2:+,2: -,3:20+-22+ -7 -2 ...

In the middle of the 1980s, logical tools were discovered that make it possible to model changes in belief and knowledge in entirely new ways. These logical tools turned out to be applicable both to human beliefs and to the contents of databases. This is the first textbook in this new area. It contains both discursive chapters with a minimum of formalism and formal chapters in which proofs and proof methods are presented. By using different selections from the formal section (...) the book can be used on all levels of University education. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the putative conclusion and formulas in the sequence. The relevance relations are ternary (...) (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents. (shrink)

Change, Choice and Inference develops logical theories that are necessary both for the understanding of adaptable human reasoning and for the design of intelligent systems. The book shows that reasoning processes - the drawing on inferences and changing one's beliefs - can be viewed as belonging to the realm of practical reason by embedding logical theories into the broader context of the theory of rational choice. The book unifies lively and significant strands of research in logic, philosophy, economics and artificial (...) intelligence. It elaborates on the relevant theories and provides a mathematically precise foundation for the thesis that large parts of theoretical reason can be subsumed under practical reason. (shrink)

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.

This is a survey paper. Contents: 1 Introduction -- 2 The representation of belief -- 3 Kinds of belief change -- 4 Coherence constraints for belief revision -- 5 Different modes of belief change -- 6 Two strategies for characterizing rational changes of belief - 6.1 The postulates strategy - 6.2 The constructive strategy -- 7 An abstract view of the elements of belief change -- 8 Iterated changes of belief -- 9 Further developments - 9.1 Variants and extensions of (...) belief revision - 9.2 Updates - 9.3 Default inferences as expectation revision - 9.4 Belief merging -- 10 Concluding remarks. (shrink)

Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been perceived (...) as characterising idealised rational reasoners, and the corresponding belief change operations are considered unsuitable for implementable agents due to their high computational cost [3]. The main result of this paper is showing that an efficient (linear time) belief contraction operation nevertheless satisfies all but one of the AGM postulates for contraction. This contraction operation is defined for a realistic rule-based agent which can be seen as a reasoner in a very weak logic; although the agent’s beliefs are deductively closed with respect to this logic, checking consistency and tracing dependencies between beliefs is not computationally expensive. Finally, we give a non-standard definition of belief revision in terms of contraction for our agent. (shrink)

The AGM (Alchourrón-Gärdenfors-Makinson) model of belief change is extended to cover changes on sets of beliefs that are not closed under logical consequence (belief bases). Three major types of change operations, namely contraction, internal revision, and external revision are axiomatically characterized, and their interrelations are studied. In external revision, the Levi identity is reversed in the sense that one first adds the new belief to the belief base, and afterwards contracts its negation. It is argued that external revision represents an (...) intuitively plausible way of revising one's beliefs. Since it typically involves the temporary acceptance of an inconsistent set of beliefs, it can only be used in belief representations that distinguish between different inconsistent sets of belief. (shrink)

The standard theory for belief revision provides an elegant and powerful framework for reasoning about how a rational agent should change its beliefs when confronted with new information. However, the agents considered are extremely idealized. Some recent models attempt to tackle the problem of plausible belief revision by adding structure to the belief bases and using nonstandard inference operations. One of the key ideas is that not all of an agent's beliefs are relevant for an operation of belief change.In this (...) paper we incorporate the insights pertaining to local change and relevance sensitivity with the use of approximate inference relations. These approximate inference relations offer us partial solutions at any stage of the revision process. The quality of the approximations improves as we allow for more and more resources to be used. We are provided with upper and lower bounds to what would be obtained with the use of classical inference. (shrink)

The standard theory of belief revision was developed to describe how a rational agent should change his beliefs in the presence of new information. Many interesting tools were created, but the concept of rationality was usually assumed to be related to classical logics. In this paper, we explore the fact that the logical tools used can be extended to other sorts of logics, as proved in (Hansson and Wassermann, 2002), to describe models that are closer to the rationality of a (...) real agent. (shrink)

We propose a new relevance sensitive model for representing and revising belief structures, which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally tractable procedures for query answering and belief..

The standard theory of belief revision was developed to describe how a rational agent should change his beliefs in the presence of new information. Many interesting tools were created, but the concept of rationality was usually assumed to be related to classical logics.In this paper, we explore the fact that the logical tools used can be extended to other sorts of logics, as proved in (Hansson and Wassermann, 2002), to describe models that are closer to the rationality of a real (...) agent. (shrink)

An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of (...) the operations for belief change. Representation theorems are given for the local operators. (shrink)

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a (...) canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones. (shrink)