Secrecy logic: S-secrecy structures

Let S = lan L,vdash_Sran be a deductive system. An S-secrecy logic is a quadruple K = lan Fm_L(V),K,B,Sran, where Fm_L(V) is the algebra of L-formulas, K,B are S-theories, with B subseteq K and S subseteq K such that S cap B = emptyset. K corresponds to information deducible from a knowledge base, B to information deducible from the publicly accessible (or browsable) part of the knowledge base and S is a secret set, a set of sensitive or private information that the knowledge base aims at concealing from its users. To provide models for this context, the notion of an S-secrecy structure is introduced. It is a quadruple A = lan A,K_A,B_A,S_Aran, consisting of an L-algebra A, two S-filters K_A,B_A on A, with B_A subseteq K_A, and a subset S_A subseteq K_A, such that S_Acap B_A = emptyset. Several model theoretic/universal algebraic and categorical properties of the class of S-secrecy structures, endowed with secrecy homomorphisms, are studied relating to various universal algebraic and categorical constructs.