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Knowledge Bases and Preferred Update Actions : Searching for Consistency through Dynamic Logic Programs

Christos Rantsoudis 1
1 IRIT-LILaC - Logique, Interaction, Langue et Calcul
IRIT - Institut de recherche en informatique de Toulouse
Abstract : In the database literature it has been proposed to resort to active integrity constraints in order to restore database integrity. Such active integrity constraints consist of a classical constraint together with a set of preferred update actions that can be triggered when the constraint is violated. In the first part of this thesis, we review the main repairing routes that have been proposed in the literature and capture them by means of Dynamic Logic programs. The main tool we employ for our investigations is the recently introduced logic DL-PA, which constitutes a variant of PDL. We then go on to explore a new, dynamic kind of database repairing whose computational complexity and general properties are compared to the previous established approaches. In the second part of the thesis we leave the propositional setting and pursue to adapt the aforementioned ideas to higher level languages. More specifically, we venture into Description Logics and investigate extensions of TBox axioms by update actions that denote the preferred ways an ABox should be repaired in case of inconsistency with the axioms of the TBox. The extension of the TBox axioms with these update actions constitute new, active TBoxes. We tackle the problem of repairing an ABox with respect to such an active TBox both from a syntactic as well as a semantic perspective. Given an initial ABox, the syntactic approach allows us to construct a set of new ABoxes out of which we then identify the most suitable repairs. On the other hand, for the semantic approach we once again resort to a dynamic logic framework and view update actions, active inclusion axioms and repairs as programs. Given an active TBox aT , the framework allows to check (1) whether a set of update actions is able to repair an ABox according to the active axioms of aT by interpreting the update actions locally and (2) whether an ABox A' is the repair of a given ABox A under the active axioms of aT using a bounded number of computations by interpreting the update actions globally. After discussing the strong points of each direction, we conclude by combining the syntactic and semantic investigations into a cohesive approach.
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Christos Rantsoudis. Knowledge Bases and Preferred Update Actions : Searching for Consistency through Dynamic Logic Programs. Databases [cs.DB]. Université Paul Sabatier - Toulouse III, 2018. English. ⟨NNT : 2018TOU30286⟩. ⟨tel-02479121⟩

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