We introduce reference structures - a basic mathematical model of a data organization capable of storing and utilizing information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming languages is presented as an example of a reference structure building.
Artëmov, S., & Krupski, V. (1996). Data storage interpretation of labeled modal logic. Annals of Pure and Applied Logic, 78(1–3), 57–71. https://doi.org/10.1016/0168-0072(95)00062-3