# Towards Closed World Reasoning In Dynamic Open Worlds (Extended Version)

MARTIN SLOTA∗ **and JOAO LEITE** ˜
CENTRIA & Departamento de Inform´atica Universidade Nova de Lisboa 2829-516 Caparica, Portugal Note**: This is an extended version containing all proofs of the article published**
in Theory and Practice of Logic Programming, 10 (4-6): 547 - 564, July. c **2010**
Cambridge University Press.

Changes on July 23, 2010**: some minor substitutions and additions to be in line**
with the TPLP version; full reference to the journal version added.

## Abstract

The need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics for hybrid knowledge bases **composed of** both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules.

These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve.

In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties.

To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

KEYWORDS**: belief change, belief update, hybrid knowledge bases, ontologies, rules, description logics, answer set programming, semantic web**

## 1 Introduction

In this paper we address updates of hybrid knowledge bases composed of a Description Logic ontology and Logic Programming rules. We propose an operator to be used when a hybrid theory is updated by new observations of a changing world, examine its properties, and discuss open problems pointing to future research.

∗ **Supported by FCT Scholarship SFRH/BD/38214/2007. Participation on conference supported**
by FLoC 2010 Student Travel Support and by APPIA Study Scholarship.

arXiv:1004.4342v2 [cs.AI] 23 Jul 2010