Modeling Belief in Dynamic Systems, Part II: Revision and Update

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.Comment: See http://www.jair.org/ for other files accompanying this articl

How to do things with modals

Mind &Language, Volume 35, Issue 1, Page 115-138, February 2020

Coherent Integration of Databases by Abductive Logic Programming

We introduce an abductive method for a coherent integration of independent data-sources. The idea is to compute a list of data-facts that should be inserted to the amalgamated database or retracted from it in order to restore its consistency. This method is implemented by an abductive solver, called Asystem, that applies SLDNFA-resolution on a meta-theory that relates different, possibly contradicting, input databases. We also give a pure model-theoretic analysis of the possible ways to `recover' consistent data from an inconsistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. This allows us to characterize the `recovered databases' in terms of the `preferred' (i.e., most consistent) models of the theory. The outcome is an abductive-based application that is sound and complete with respect to a corresponding model-based, preferential semantics, and -- to the best of our knowledge -- is more expressive (thus more general) than any other implementation of coherent integration of databases

A Potpourri of Reason Maintenance Methods

We present novel methods to compute changes to materialized views in logic databases like those used by rule-based reasoners. Such reasoners have to address the problem of changing axioms in the presence of materializations of derived atoms. Existing approaches have drawbacks: some require to generate and evaluate large transformed programs that are in Datalog - while the source program is in Datalog and significantly smaller; some recompute the whole extension of a predicate even if only a small part of this extension is affected by the change. The methods presented in this article overcome these drawbacks and derive additional information useful also for explanation, at the price of an adaptation of the semi-naive forward chaining

Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases composed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve. In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties. To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010 Cambridge University Pres