In this paper we consider two points of views to the problem of coherent integration of distributed data. First we give a pure model-theoretic analysis of the possible ways to repair' a database. We do so by characterizing the possibilities 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. Then we introduce an abductive application to restore the consistency of a given database. This application is based on an abductive solver (A-system) that implements an SLDNFA-resolution procedure, and computes a list of data-facts that should be inserted to the database or retracted from it in order to keep the database consistent. The two approaches for coherent data integration are related by soundness and completeness results.
Coherent integration and proper representation of amalgamated data is extensively studied in the literature (see, e.g., @cite_40 @cite_36 @cite_2 @cite_19 @cite_27 @cite_21 @cite_37 @cite_10 @cite_12 @cite_6 @cite_33 ). Common approaches for dealing with this task are based on techniques of belief revision @cite_21 , methods of resolving contradictions by quantitative considerations (such as majority vote'' @cite_37 ) or qualitative ones (e.g., defining priorities on different sources of information or preferring certain data over another @cite_24 @cite_34 ), and approaches that are based on rewriting rules for representing the information in a specific form @cite_27 . As in our case, abduction is used for database updating in @cite_23 and an extended form of abduction is used in @cite_17 @cite_18 to explain modifications in a theory.
@cite_37 @cite_18 @cite_33 @cite_36 @cite_21 @cite_6 @cite_24 @cite_19 @cite_40 @cite_27 @cite_23 @cite_2 @cite_34 @cite_10 @cite_12 @cite_17
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Horn clause logic programming can be extended to include abduction with integrity constraints. In the resulting extension of logic programming, negation by failure can be simulated by making negative conditions abducible and by imposing appropriate denials and disjunctions as integrity constraints. This gives an alternative semantics for negation by failure, which generalises the stable model semantics of negation by failure. The abductive extension of logic programming extends negation by failure in three ways: (1) computation can be perfonned in alternative minimal models, (2) positive as well as negative conditions can be made abducible, and (3) other integrity constraints can also be accommodated. * This paper was written while the first author was at Imperial College. 235 Introduction The tenn "abduction" was introduced by the philosopher Charles Peirce [1931] to refer to a particular kind of hypothetical reasoning. In the simplest case, it has the fonn: From A and A fB infer B as a possible "explanation" of A. Abduction has been given prominence in Charniak and McDennot's [1985] "Introduction to Artificial Intelligence", where it has been applied to expert systems and story comprehension. Independently, several authors have developed deductive techniques to drive the generation of abductive hypotheses. Cox and Pietrzykowski [1986] construct hypotheses from the "dead ends" of linear resolution proofs. Finger and Genesereth [1985] generate "deductive solutions to design problems" using the "residue" left behind in resolution proofs. Poole, Goebel and Aleliunas [1987] also use linear resolution to generate hypotheses. All impose the restriction that hypotheses should be consistent with the "knowledge base". Abduction is a fonn of non-monotonic reasoning, because hypotheses which are consistent with one state of a knowledge base may become inconSistent when new knowledge is added. Poole [1988] argues that abduction is preferable to noh-monotonic logics for default reasoning. In this view, defaults are hypotheses fonnulated within classical logic rather than conclusions derived withln some fonn of non-monotonic logic. The similarity between abduction and default reasoning was also pointed out in [Kowalski, 1979]. In this paper we show how abduction can be integrated with logic programming, and we concentrate on the use of abduction to generalise negation by failure. Conditional Answers Compared with Abduction In the simplest case, a logic program consists of a set of Horn Clauses, which are used backward to_reduce goals to sub goals. The initial goal is solved when there are no subgollls left; Abstract During the process of knowledge acquisition from different experts it is usual that contradictions occur. Therefore strategies are needed for dealing with divergent statements and conflicts. We provide a formal framework to represent, process and combine distributed knowledge. The representation formalism is many-valued logic, which is a widely accepted method for expressing uncertainty, vagueness, contradictions and lack of information. Combining knowledge as proposed here makes use of the bilattice approach, which turns out to be very flexible and suggestive in the context of combining divergent information. We give some guidelines for choosing truth value spaces, assigning truth values and defining global operators to encode integration strategies. The process of integrating knowledge coming from different sources has been widely investigated in the literature. Three distinct conceptual approaches to this problem have been most succesful: belief revision, merging and update. In this paper we present a framework that integrates these three approaches. In the proposed framework all three operations can be performed. We provide an example that can only be solved by applying more than one single style of knowledge integration and, therefore, cannot be addressed by anyone of the approaches alone. The framework has been implemented, and the examples shown in this paper (as well as other examples from the belief revision literature) have been successfully tested. This paper investigates, several methods for coping with inconsistency caused by multiple source information by introducing suitable consequence relations capable of inferring non trivial conclusions from an inconsistent stratified knowledge base. Some of these methods presuppose a revision step, namely a selection of one or several consistent subsets of formulas, and then classical inference is used for inferring from these subsets. Two alternative methods that do not require any revision step are studied: inference based on arguments and a new approach called safely supported inference, where inconsistency is kept local. These two last methods look suitable when the inconsistency is due to the presence of several sources of information. The paper offers a comparative study of the various inference modes under inconsistency.