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

On the local closedworld assumption of data-sources

Abstract. The Closed-World Assumption (CWA) on a database ex-presses that an atom not in the database is false. The CWA is only applicable in domains where the database has complete knowledge. In many cases, for example in the context of distributed databases, a data source has only complete knowledge about part of the domain of dis-course. In this paper, we introduce an expressive and intuitively appeal-ing method of representing a local closed-world assumption (LCWA) of autonomous data-sources. This approach distinguishes between the data that is conveyed by a data-source and the meta-knowledge about the area in which these data is complete. The data is stored in a relational database that can be queried in the standard way, whereas the meta-knowledge about its completeness is expressed by a first order theory that can be processed by an independent reasoning system (for example a mediator). We consider different ways of representing our approach, relate it to other methods of representing local closed-word assumptions of data-sources, and show some useful properties of our framework which facilitate its application in real-life systems.

Reducing inductive definitions to propositional satisfiability

Abstract. The FO(ID) logic is an extension of classical first-order logic with a uniform representation of various forms of inductive definitions. The definitions are represented as sets of rules and they are interpreted by two-valued well-founded models. For a large class of combinatorial and search problems, knowledge representation in FO(ID) offers a viable alternative to the paradigm of Answer Set Programming. The main reasons are that (i) the logic is an extension of classical logic and (ii) the semantics of the language is based on well-understood principles of mathematical induction. In this paper, we define a reduction from the propositional fragment of FO(ID) to SAT. The reduction is based on a novel characterization of two-valued well-founded models using a set of inequality constraints on level mappings associated with the atoms. We also show how the reduction to SAT can be adapted for logic programs under the stable model semantics. Our experiments show that when using a state of the art SAT solver both reductions are competitive with other answer set programming systems — both direct implementations and SAT based.