Verification of model transformations

Model transformations are a central element of model-driven development (MDD) approaches such as the model-driven architecture (MDA). The correctness of model transformations is critical to their effective use in practical software development, since users must be able to rely upon the transformations correctly preserving the semantics of models. In this paper we define a formal semantics for model transformations, and provide techniques for proving the termination, confluence and correctness of model transformations

A cognitive exploration of the “non-visual” nature of geometric proofs

Why are Geometric Proofs (Usually) “Non-Visual”? We asked this question as a way to explore the similarities and differences between diagrams and text (visual thinking versus language thinking). Traditional text-based proofs are considered (by many to be) more rigorous than diagrams alone. In this paper we focus on human perceptual-cognitive characteristics that may encourage textual modes for proofs because of the ergonomic affordances of text relative to diagrams. We suggest that visual-spatial perception of physical objects, where an object is perceived with greater acuity through foveal vision rather than peripheral vision, is similar to attention navigating a conceptual visual-spatial structure. We suggest that attention has foveal-like and peripheral-like characteristics and that textual modes appeal to what we refer to here as foveal-focal attention, an extension of prior work in focused attention

An Information-Geometric Reconstruction of Quantum Theory, I: The Abstract Quantum Formalism

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few elementary features of quantum phenomena, such as the statistical nature of measurements, complementarity, and global gauge invariance. It is shown that these features can be traced to experimental observations characteristic of quantum phenomena and to general theoretical principles, and thus can reasonably be taken as a starting point of the derivation. When appropriately formulated within an information geometric framework, these features lead to (i) the abstract quantum formalism for finite-dimensional quantum systems, (ii) the result of Wigner's theorem, and (iii) the fundamental correspondence rules of quantum theory, such as the canonical commutation relationships. The formalism also comes naturally equipped with a metric (and associated measure) over the space of pure states which is unitarily- and anti-unitarily invariant. The derivation suggests that the information geometric framework is directly or indirectly responsible for many of the central structural features of the quantum formalism, such as the importance of square-roots of probability and the occurrence of sinusoidal functions of phases in a pure quantum state. Global gauge invariance is seen to play a crucial role in the emergence of the formalism in its complex form.Comment: 26 page