We study the problem of answering queries when
(part of) the data may be sensitive and should not be leaked to the querier. Simply restricting the computation to non-sensitive part of the data may leak sensitive data through inference based on data dependencies. While inference control from data dependencies during query processing has been studied in the literature, existing solution either detect and deny queries causing leakage, or use a weak security model that only protects against exact reconstruction of the sensitive data. In this paper, we adopt a stronger security model based on full deniability that prevents any information about sensitive data to be inferred from query answers. We identify conditions under which full deniability can be achieved and develop an efficient algorithm that minimally hides non-sensitive cells during query processing to achieve full deniability. We experimentally show that our approach is practical and scales to increasing proportion of sensitive data, as well as, to increasing database size.