A logic of diagnosis proceeds in terms of a set of data and one or more (prioritized) sets of expectancies. In this paper we generalize the logics of diagnosis from [27] and present some alternatives. The former operate on the premises and expectancies themselves, the latter on their consequences.

. In this paper, adaptive logics are studied from the viewpoint of universal logic (in the sense of the study of common structures of logics). The common structure of a large set of adaptive logics is described. It is shown that this structure determines the proof theory as well as the semantics of the adaptive logics, and moreover that most properties of the logics can be proved by relying solely on the structure, viz. without invoking any specific properties of the (...) logics themselves. (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)

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)

In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is $\Pi _1^1 - complete$ . So, the complexity results in (Horsten and Welch, Synthese 158:41–60,2007) are mistaken for adaptive logics using the minimal abnormality strategy.

This article discusses the proof theory, semantics and meta-theory of a class of adaptive logics, called hierarchic adaptive logics. Their specific characteristics are illustrated throughout the article with the use of one exemplary logic HKx, an explicans for reasoning with prioritized belief bases. A generic proof theory for these systems is defined, together with a less complex proof theory for a subclass of them. Soundness and a restricted form of completeness are established with respect to a non-redundant semantics. It is (...) shown that all hierarchic adaptive logics are reflexive, have the strong reassurance property and that a subclass of them is a fixed point for a broad class of premise sets. Finally, they are compared to a different yet related class of adaptive logics. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

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)

The splitting theorem says that any set of formulae has a finest representation as a family of letter-disjoint sets. Parikh formulated this for classical propositional logic, proved it in the finite case, used it to formulate a criterion for relevance in belief change, and showed that AGMpartial meet revision can fail the criterion. In this paper we make three further contributions. We begin by establishing a new version of the well-known interpolation theorem, which we call parallel interpolation, use it to (...) prove the splitting theorem in the infinite case, and show how AGM belief change operations may be modified, if desired, so as to ensure satisfaction of Parikh’s relevance criterion. (shrink)

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...) can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus. (shrink)

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 ...

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..

In this paper dedicated to Carlos Alchourrón, we review an issue that emerged only after his death in 1996, but would have been of great interest to him: To what extent do the formal operations of AGM belief change respect criteria of relevance? A natural criterion was proposed in 1999 by Rohit Parikh, who observed that the AGM model does not always respect it. We discuss the pros and cons of this criterion, and explain how the AGM account may be (...) refined, if we so desire, so that it is always respected. En este trabajo dedicado a Carlos Alchourrón consideramos un problema que surgió recién después de su muerte en 1996 pero que seguramente habría sido de gran interés para él: ¿hasta dónde las operaciones formales sobre el cambio de creencias de AGM respetan el criterio de relevancia? Un criterio natural ha sido propuesto en 1999 por Rohit Parikh quien asimismo observó que el modelo AGM no siempre lo respeta. Nosotros discutimos los pros y los contras de este criterio y explicamos cómo podría refinarse AGM para que, si así lo deseáramos, lo respetara siempre. (shrink)

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)