Secrecy logic: S-secrecy structures

Authors: GEORGE VOUTSADAKIS

Abstract: Let S = \lan L,\vdash_S\ran be a deductive system. An S-secrecy logic is a quadruple K = \lan Fm_L(V),K,B,S\ran, 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_A\ran, 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_A\cap 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.

Keywords: Secrecy-preserving reasoning, abstract algebraic logic, logical matrices, protoalgebraic logics, first-order structures, homomorphism theorems, regular categories, subdirect products, subdirectly irreducible structures

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