Kee** Secrets in $\mathcal {EL}^{+}$ Knowledge Bases

Abstract

In this paper we study Secrecy-Preserving Query Answering problem under Open World Assumption (OWA) for $\mathcal {EL}^+$ Knowledge Bases (KBs). First we compute some consequences of ABox ($\mathcal {A}$) and TBox ($\mathcal {T}$) denoted by $\mathcal {A}^*$ and $\mathcal {T}^*$ respectively. A secrecy set of a querying agent is subset $\mathbb {S}$ of $\mathcal {A}^*\cup \mathcal {T}^*$ which the agent is not allowed to access. Next we compute envelopes which provide logical protection to the secrecy set against the reasoning of the querying agent. Once envelopes are computed, they are used to efficiently answer assertional and GCI queries without compromising the secret information in $\mathbb {S}$. When the querying agent asks a query q, the reasoner answers “Yes” if KB $\models q$ and q does not belong to the envelopes; otherwise, the reasoner answers “Unknown”. Being able to answer “Unknown” plays a key role in protecting secrecy under OWA. Since we are not computing all the consequences of the KB, answers to the queries based on just $\mathcal {A}^*$ and $\mathcal {T}^*$ could be erroneous. To fix this problem, we further augment our algorithms to make the query answering procedure foolproof.