An Integer 0-1 Linear Programming Approach for Computing Inconsistency Degree in Product-Based Possibilistic DL-Lite

This paper considers the problem of computing inconsistency degree of uncertain knowledge bases expressed in product-based possibilistic DL-Lite, which is an extension of DL-Lite to deal with uncertainty in the product-based possibility theory framework. Indeed, computing the inconsistency degree is at the heart of any query answering process in such knowledge bases. Unlike previous work where uncertainty is only considered at the ABox level, in the present work both ABox and TBox may be uncertain. We discuss the new form of conflicts and how to obtain them by a generalized negative closure procedure. Then, we model the inconsistency degree computation as an integer 0-1 linear programming problem and we show the efficiency of this choice by a comparison with two other solutions, using the weighted Max-SAT and the approximate greedy algorithm for the weighted set cover problem, respectively.