A Conceptual Framework for Secrecy-preserving Reasoning in Knowledge Bases

Abstract

In many applications, Knowledge Bases (KBs) contain confidential or private information (secrets). The KB should be able to use this secret information in its reasoning process but in answering user queries care must be exercised so that secrets are not revealed to unauthorized users. We consider this problem under the Open World Assumption (OWA) in a setting with multiple querying agents M 1 , . . . , M m that can pose queries against the KB K and selectively share answers that they receive from K with one or more other querying agents. We assume that for each M i , the KB has a prespecified set of secrets S i that need to be protected from M i . Communication between querying agents is modeled by a communication graph, a directed graph with self-loops. We introduce a general framework and propose an approach to secrecy-preserving query answering based on sound and complete proof systems. The idea is to hide the truthful answer from a querying agent M i by feigning ignorance without lying (i.e., to provide the answer 'Unknown' to a query q if it needs to be protected. Under the OWA, a querying agent cannot distinguish between the case that q is being protected (for reasons of secrecy) and the case that it cannot be inferred from K. In the pre-query stage we compute a set of envelopes E 1 , . . . , E m (restricted to a finite subset of the set of formulae that are entailed by K) so that S i ⊆ E i , and a query α posed by agent M i can be answered truthfully whenever α / ∈ E i and ¬α / ∈ E i . After the pre-query stage, the envelope is updated as needed. We illustrate this approach with two simple cases: the Propositional Horn KBs and the Description Logic AL KBs. ACM Reference Format:Jia Tao, Giora Slutzki, and Vasant Honavar. 2014. A conceptual framework for secrecy-preserving reasoning in knowledge bases.

Secrecy-preserving reasoning in simple description logic knowledge bases

“…With the advent of the semantic web and its increasingly pervasive usage, there is a lot of interest in studying this problem in knowledge base (KB) setting, see Bao et al (2007); Grau et al (2013); Tao et al (2010Tao et al ( , 2014. The concern here is that in view of the fundamental assumption that KBs possess incomplete knowledge, a situation could arise in which logical reasoning (used to produce implicit knowledge from the explicit one stored in the KB) may possibly lead to disclosure of secret information, see Grau et al (2013).…”

“…The notion of an envelope to hide secret information against logical inference was first defined and used in Tao et al (2010). In Tao et al (2014), the authors introduced a more elaborate conceptual framework for secrecy-preserving query answering (SPQA) under Open World Assumption (OWA) with multiple querying agents.…”

“…Specifically, in Bao et al (2007); Tao et al (2010Tao et al ( , 2014) the main idea was to utilize the secret information within the reasoning process, but then answering "Unknown" whenever the answer is truly unknown or in case the true answer could compromise confidentiality. Further, in Krishnasamy Sivaprakasam and Slutzki (2016), the authors extended the work of Tao et al, reported in Tao et al (2010), to the ELH language and studied secrecy in the context of assertions as well as general concept inclusions (GCIs).…”

“…(b) given Σ and a secrecy set S, we compute an envelope E of S by inverting the rules of tableau algorithm considered in (a), for more details see Tao et al (2010Tao et al ( , 2014. The idea behind the envelope concept is that no expression in the envelope can be logically deduced from information outside the envelope.…”

“…The framework introduced in Tao et al (2014), which we use here as well, was illustrated on very simple examples: the Propositional Horn Logic and the Description Logic AL. Here we consider the SPQA problem under OWA for DL-Lite R acyclic KBs.…”