  The study of representations is of fundamental importance to any form of
communication, and our ability to exploit them effectively is paramount. This
article presents a novel theory -- Representational Systems Theory -- that is
designed to abstractly encode a wide variety of representations from three core
perspectives: syntax, entailment, and their properties. By introducing the
concept of a construction space, we are able to encode each of these core
components under a single, unifying paradigm. Using our Representational
Systems Theory, it becomes possible to structurally transform representations
in one system into representations in another. An intrinsic facet of our
structural transformation technique is representation selection based on
properties that representations possess, such as their relative cognitive
effectiveness or structural complexity. A major theoretical barrier to
providing general structural transformation techniques is a lack of terminating
algorithms. Representational Systems Theory permits the derivation of partial
transformations when no terminating algorithm can produce a full
transformation. Since Representational Systems Theory provides a universal
approach to encoding representational systems, a further key barrier is
eliminated: the need to devise system-specific structural transformation
algorithms, that are necessary when different systems adopt different
formalisation approaches. Consequently, Representational Systems Theory is the
first general framework that provides a unified approach to encoding
representations, supports representation selection via structural
transformations, and has the potential for widespread practical application.
