On compromising updates in labelled databases

Abstract

This paper presents a logical system, CIULDS, as a labelled realization to our approach of Compromising Interfering Updates. Basically, this approach proposes a method for handling logically conflicting inputs into knowledge bases, via restricting their consequences. The main idea is to update the database with as many consistent consequences of the inputs as possible, in the case that the inputs themselves are not allowed to be kept in it. And in the case that a revision applies, the idea is to keep as many as possible of the consistent consequences of the retracted sentences as a compromise.

Our approach caters for the specific case where compromised solutions for revising knowledge bases apply, when conflicts involving updates occur. In comparison with approaches that require preference between conflicting inputs, or that avoid them by cancelling them out completely, our approach fits as an alternative which provides more informative results, and is directed to some specific applications. Hence, instead of preventing updates to be performed, when they introduce inconsistency to the system, our approach proposes to generate the consequences of the conflicting inputs, and to get rid of the inconsistency, via a minimal number of retractions of those consequences. We expect the resulting database to be consistent w.r.t. the integrity constraints, and to retain a safe-maximal subset of the consistent non-supported consequences. This reconciliation of conflicting inputs follows some specified postulates for compromised revision.

CIULDS is based on the Labelled Deductive Systems framework (LDS). This framework deals with labelled formulae as its basic units of information. By labelling the formulae, we are provided with a way of including in the labels extra information to the system. The main motivation for adopting LDS as the underlying framework of this formalization was to take advantage of its labelling facility, to control the derivation process of the compromised consequences. We embed in the labelling propagation conditions, which act on the inference rules, part of the control mechanism for the compromised approach. This control mechanism helps the update operations to perform the reconciliation of conflicting inputs. The update operations invoke a compromised revision on the labelled database, whenever conflicts arise.

In this paper, we present briefly our main motivations and we discuss the general issue of conflict resolution and theory revision. We introduce the basic specification of our approach CIU, for the case of database updates, describing the adopted policies for reconciling conflicting updates under a compromised reasoning perspective. We introduce the CIULDS system, by describing informally its main features and definitions. In CIULDS, we propose a specific revision method which applies some compromising criteria for achieving the revised database. Finally, we summarize the system's main properties.