# Splitting And Updating Hybrid Knowledge Bases (Extended Version)

MARTIN SLOTA∗ and JOAO LEITE ˜ †and TERRANCE SWIFT
CENTRIA & Departamento de Inform´atica Universidade Nova de Lisboa 2829-516 Caparica, Portugal submitted 1 January 2003; revised 1 January 2003; accepted 1 *January 2003*

## Abstract

Over the years, nonmonotonic rules have proven to be a very expressive and useful knowledge representation paradigm. They have recently been used to complement the expressive power of Description Logics (DLs), leading to the study of integrative formal frameworks, generally referred to as hybrid knowledge bases, where both DL axioms and rules can be used to represent knowledge. The need to use these hybrid knowledge bases in dynamic domains has called for the development of update operators, which, given the substantially different way Description Logics and rules are usually updated, has turned out to be an extremely difficult task.

In (Slota and Leite 2010b), a first step towards addressing this problem was taken, and an update operator for hybrid knowledge bases was proposed. Despite its significance - not only for being the first update operator for hybrid knowledge bases in the literature, but also because it has some applications - this operator was defined for a restricted class of problems where only the ABox was allowed to change, which considerably diminished its applicability. Many applications that use hybrid knowledge bases in dynamic scenarios require both DL axioms and rules to be updated.

In this paper, motivated by real world applications, we introduce an update operator for a large class of hybrid knowledge bases where both the DL component as well as the rule component are allowed to dynamically change. We introduce splitting sequences and splitting theorem for hybrid knowledge bases, use them to define a modular update semantics, investigate its basic properties, and illustrate its use on a realistic example about cargo imports.

KEYWORDS: hybrid knowledge base, update, splitting theorem, ontology, logic program

## 1 Introduction

Increasingly many real world applications need to intelligently access and reason with large amounts of dynamically changing, structured and highly interconnected information. The family of Description Logics (DLs) (Baader et al. 2003), generally characterised as decidable fragments of first-order logic, have become the established standard for representing ontologies, i.e. for specifying concepts relevant to a particular domain of interest. DLs can