A Generic Module System forWeb Rule Languages: Divide and Rule

An essential feature in practically usable programming languages is the ability to encapsulate functionality in reusable modules. Modules make large scale projects tractable by humans. For Web and Semantic Web programming, many rule-based languages, e.g. XSLT, CSS, Xcerpt, SWRL, SPARQL, and RIF Core, have evolved or are currently evolving. Rules are easy to comprehend and specify, even for non-technical users, e.g. business managers, hence easing the contributions to the Web. Unfortunately, those contributions are arguably doomed to exist in isolation as most rule languages are conceived without modularity, hence without an easy mechanism for integration and reuse. In this paper a generic module system applicable to many rule languages is presented. We demonstrate and apply our generic module system to a Datalog-like rule language, close in spirit to RIF Core. The language is gently introduced along the EU-Rent use case. Using the Reuseware Composition Framework, the module system for a concrete language can be achieved almost for free, if it adheres to the formal notions introduced in this paper

Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant synthesis (obtained as the dual of backward reachability), again, under suitable hypotheses on the theories. We also present a pragmatic approach to interleave invariant synthesis and backward reachability so that a fix-point for the set of backward reachable states is more easily obtained. Finally, we discuss heuristics that allow us to derive an implementation of the techniques in the model checker MCMT, showing remarkable speed-ups on a significant set of safety problems extracted from a variety of sources.Comment: Accepted for publication in Logical Methods in Computer Scienc

The Vadalog System: Datalog-based Reasoning for Knowledge Graphs

Over the past years, there has been a resurgence of Datalog-based systems in the database community as well as in industry. In this context, it has been recognized that to handle the complex knowl\-edge-based scenarios encountered today, such as reasoning over large knowledge graphs, Datalog has to be extended with features such as existential quantification. Yet, Datalog-based reasoning in the presence of existential quantification is in general undecidable. Many efforts have been made to define decidable fragments. Warded Datalog+/- is a very promising one, as it captures PTIME complexity while allowing ontological reasoning. Yet so far, no implementation of Warded Datalog+/- was available. In this paper we present the Vadalog system, a Datalog-based system for performing complex logic reasoning tasks, such as those required in advanced knowledge graphs. The Vadalog system is Oxford's contribution to the VADA research programme, a joint effort of the universities of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the main contribution of this paper, we illustrate the first implementation of Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive termination control strategy. We also provide a comprehensive experimental evaluation.Comment: Extended version of VLDB paper <https://doi.org/10.14778/3213880.3213888

Bott periodicity for Z2Z_2 symmetric ground states of gapped free-fermion systems

Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a "Bott clock" topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d+1)-dimensional system in symmetry class s+1. This relation gives a new vantage point on topological insulators and superconductors.Comment: 55 pages; one figure added; corrections in Section 8; proofs in Section 6 expande

Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory

Our primary task is to demonstrate that the logarithmic nonlinearity in the quantum wave equation can cause the spontaneous symmetry breaking and mass generation phenomena on its own, at least in principle. To achieve this goal, we view the physical vacuum as a kind of the fundamental Bose-Einstein condensate embedded into the fictitious Euclidean space. The relation of such description to that of the physical (relativistic) observer is established via the fluid/gravity correspondence map, the related issues, such as the induced gravity and scalar field, relativistic postulates, Mach's principle and cosmology, are discussed. For estimate the values of the generated masses of the otherwise massless particles such as the photon, we propose few simple models which take into account small vacuum fluctuations. It turns out that the photon's mass can be naturally expressed in terms of the elementary electrical charge and the extensive length parameter of the nonlinearity. Finally, we outline the topological properties of the logarithmic theory and corresponding solitonic solutions.Comment: Dedicated to memory of V. L. Ginzburg (1916-2009). Updates: (v2) chapter on BEC/fluid/gravity correspondence; (v3) comments on BEC-vacuum thermodynamics, induced relativity postulates, Mach's principle, Weyl curvature hypothesis, BEC-vacuum cosmology and origin of fundamental scalar field; (v4) appendix with quantum-informational arguments towards LogSE; (v5 [pub]) refs about superfluid vacuu

Configurable Input Devices for 3D Interaction using Optical Tracking

Three-dimensional interaction with virtual objects is one of the aspects that needs to be addressed in order to increase the usability and usefulness of virtual reality. Human beings have difficulties understanding 3D spatial relationships and manipulating 3D user interfaces, which require the control of multiple degrees of freedom simultaneously. Conventional interaction paradigms known from the desktop computer, such as the use of interaction devices as the mouse and keyboard, may be insufficient or even inappropriate for 3D spatial interaction tasks. The aim of the research in this thesis is to develop the technology required to improve 3D user interaction. This can be accomplished by allowing interaction devices to be constructed such that their use is apparent from their structure, and by enabling efficient development of new input devices for 3D interaction. The driving vision in this thesis is that for effective and natural direct 3D interaction the structure of an interaction device should be specifically tuned to the interaction task. Two aspects play an important role in this vision. First, interaction devices should be structured such that interaction techniques are as direct and transparent as possible. Interaction techniques define the mapping between interaction task parameters and the degrees of freedom of interaction devices. Second, the underlying technology should enable developers to rapidly construct and evaluate new interaction devices. The thesis is organized as follows. In Chapter 2, a review of the optical tracking field is given. The tracking pipeline is discussed, existing methods are reviewed, and improvement opportunities are identified. In Chapters 3 and 4 the focus is on the development of optical tracking techniques of rigid objects. The goal of the tracking method presented in Chapter 3 is to reduce the occlusion problem. The method exploits projection invariant properties of line pencil markers, and the fact that line features only need to be partially visible. In Chapter 4, the aim is to develop a tracking system that supports devices of arbitrary shapes, and allows for rapid development of new interaction devices. The method is based on subgraph isomorphism to identify point clouds. To support the development of new devices in the virtual environment an automatic model estimation method is used. Chapter 5 provides an analysis of three optical tracking systems based on different principles. The first system is based on an optimization procedure that matches the 3D device model points to the 2D data points that are detected in the camera images. The other systems are the tracking methods as discussed in Chapters 3 and 4. In Chapter 6 an analysis of various filtering and prediction methods is given. These techniques can be used to make the tracking system more robust against noise, and to reduce the latency problem. Chapter 7 focusses on optical tracking of composite input devices, i.e., input devices 197 198 Summary that consist of multiple rigid parts that can have combinations of rotational and translational degrees of freedom with respect to each other. Techniques are developed to automatically generate a 3D model of a segmented input device from motion data, and to use this model to track the device. In Chapter 8, the presented techniques are combined to create a configurable input device, which supports direct and natural co-located interaction. In this chapter, the goal of the thesis is realized. The device can be configured such that its structure reflects the parameters of the interaction task. In Chapter 9, the configurable interaction device is used to study the influence of spatial device structure with respect to the interaction task at hand. The driving vision of this thesis, that the spatial structure of an interaction device should match that of the task, is analyzed and evaluated by performing a user study. The concepts and techniques developed in this thesis allow researchers to rapidly construct and apply new interaction devices for 3D interaction in virtual environments. Devices can be constructed such that their spatial structure reflects the 3D parameters of the interaction task at hand. The interaction technique then becomes a transparent one-to-one mapping that directly mediates the functions of the device to the task. The developed configurable interaction devices can be used to construct intuitive spatial interfaces, and allow researchers to rapidly evaluate new device configurations and to efficiently perform studies on the relation between the spatial structure of devices and the interaction task

Higher Segal spaces I

This is the first paper in a series on new higher categorical structures called higher Segal spaces. For every d > 0, we introduce the notion of a d-Segal space which is a simplicial space satisfying locality conditions related to triangulations of cyclic polytopes of dimension d. In the case d=1, we recover Rezk's theory of Segal spaces. The present paper focuses on 2-Segal spaces. The starting point of the theory is the observation that Hall algebras, as previously studied, are only the shadow of a much richer structure governed by a system of higher coherences captured in the datum of a 2-Segal space. This 2-Segal space is given by Waldhausen's S-construction, a simplicial space familiar in algebraic K-theory. Other examples of 2-Segal spaces arise naturally in classical topics such as Hecke algebras, cyclic bar constructions, configuration spaces of flags, solutions of the pentagon equation, and mapping class groups.Comment: 221 page

Cartesian institutions with evidence: Data and system modelling with diagrammatic constraints and generalized sketches

Data constraints are fundamental for practical data modelling, and a verifiable conformance of a data instance to a safety-critical constraint (satisfaction relation) is a corner-stone of safety assurance. Diagrammatic constraints are important as both a theoretical concepts and a practically convenient device. The paper shows that basic formal constraint management can well be developed within a finitely complete category (hence the reference to Cartesianity in the title). In the data modelling context, objects of such a category can be thought of as graphs, while their morphisms play two roles: of data instances and (when being additionally labelled) of constraints. Specifically, a generalized sketch $S$ consists of a graph $G_S$ and a set of constraints $C_S$ declared over $G_S$, and appears as a pattern for typical data schemas (in databases, XML, and UML class diagrams). Interoperability of data modelling frameworks (and tools based on them) very much depends on the laws regulating the transformation of satisfaction relations between data instances and schemas when the schema graph changes: then constraints are translated co- whereas instances contra-variantly. Investigation of this transformation pattern is the main mathematical subject of the paperComment: 35 pages. The paper will be presented at the conference on Applied Category Theory, ACT'2