The aim of this paper is twofold: (i) to introduce the framework of update semantics and to explain what kind of semantic phenomena may successfully be analysed in it: (ii) to give a detailed analysis of one such phenomenon: default reasoning.

In this paper I offer an account of the meaning of must and can within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like must and can in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in (...) the first part, which arise from the ex falso quodlibet paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of must and can. (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)

This paper is on the update semantics for might of Veltman. Threeconsequence relations are introduced and studied in an abstract setting.Next we present sequent-style systems for each of the consequence relations.We show the logics to be complete and decidable. The paper ends with asyntactic cut elimination result.

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Of course, although this view on meaning was the prevailing one for almost a century, many of the people who initiated the enterprise of logical semantics, including people like Frege and Wittgenstein, had an open eye for all that it did not catch. However, the logical means which Frege, Wittgenstein, Russell, and the generation that succeeded them, had at their disposal were those of classical mathematical logic and set-theory, and these indeed are not very suited for an analysis of other (...) aspects of meaning than those which the slogan covers. A real change in view then had to await the emergence of other concepts, which in due course became available mainly under the influence of developments in computer science and cognate disciplines such as artificial intelligence. And this is one of the reasons why it took almost a century before any serious and successful challenge of the view that meaning equals truthconditions from within logical semantics could emerge. (shrink)

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency'' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) buys (...) us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all. (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 dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of Gärdenfors''s (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions (additions) are to be equated with logical expansions. If negated or might conditionals are interpreted on the basis of (...) autoepistemic omniscience, or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as parasitic (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect monotonic revisions in languages including conditionals. (shrink)