The liberalized δ-rule in free variable semantic tableaux

In this paper we have a closer look at one of the rules of the tableau calculus presented by Fitting [4], called the -rule. We prove that a modification of this rule, called the ⁺-rule, which uses fewer free variables, is also sound and complete. We examine the relationship between the ⁺-rule and variations of the -rule presented by Smullyan [9]. This leads to a second proof of the soundness of the ⁺-rule. An example shows the relevance of this modification for building tableau-based theorem provers.     

Polite Combination of Algebraic Datatypes

Journal of Automated Reasoning - Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its...     

Model-based inversion of speckle interferometer fringe patterns

Micrometer-scale rigid-body translations are determined fromelectronic speckle interferometric fringe patterns. An iterativeminimum error procedure employs the relative fringe order of pickedpositions of fringe maxima and minima within a single interferogram tocalculate the displacement field directly. The method does notcalculate the displacement at a single point but relies on theassumption that the character, but not the magnitudes or directions, ofthe displacements over the viewing area of the interferogram isknown. That is, a model of the displacements exists. Onperfect, noise-free forward modeled fringe patterns calculated for an 8.0-mum displacement, the phase error is less than 2 x10(-6) fringe orders (1.3 x 10(-5) rad)and probably results only from numerical noise in the inversion. Onreal fringe patterns obtained in electronic speckle interferometricexperiments, mean phase errors are generally less than 5 x10(-5) fringe orders (3.2 x 10(-4)rad), suggesting that the technique is robust despite errorsresulting from speckle noise, lack of accuracy in positioning ofexperimental components, and image-distortion corrections.     

Stable splitting scheme for general form of associated plasticity including different scales of space and time

An efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model. We start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple (quadratic) form, and the elasticity tensor does not have constant entries. We then turn to the multi-scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation. We also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time. We proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge, for any such general form of associated plasticity. Moreover, we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global Newton’s iteration, such as the consistent elastoplastic tangent.     

Robust M-estimation of multivariate GARCH models

The Gaussian quasi-maximum likelihood estimator of Multivariate GARCH models is shown to be very sensitive to outliers in the data. A class of robust M-estimators for MGARCH models is developed. To increase the robustness of the estimators, the use of volatility models with the property of bounded innovation propagation is recommended. The Monte Carlo study and an empirical application to stock returns document the good robustness properties of the M-estimator with a fat-tailed Student t loss function.     

Combination of convex theories: Modularity,deduction completeness,and explanation

Decision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories.     

Co-constructing with stakeholders a role-playing game to initiate collective management of erosive runoff risks at the watershed scale

Erosive runoff is a recurring problem and is a source of sometimes deadly muddy floods in the Pays de Caux (France). The risk results from a conjunction of natural factors and human activity. Efficient actions against runoff in agricultural watersheds are well known. However they are still difficult to implement as they require co-operation between stakeholders. Local actors thus need tools to help them understand the collective consequences of their individual decisions and help to initiate a process of negotiation between them. We decided to use a participatory approach called companion modelling (ComMod), and, in close collaboration with one of the first group of local stakeholders, to create a role-playing game (RPG) to facilitate negotiations on the future management of erosive runoff. This paper describes and discusses the development of the RPG and its use with other groups of local stakeholders within the framework of two game sessions organized by two different watershed management committees. During the joint construction step, stakeholders shared their viewpoints about the environment, agents, rules, and how to model runoff in preparation for the creation of the RPG. During the RPG sessions, two groups of eight players, including farmers, mayors and watershed advisors, were confronted with disastrous runoff in a fictive agricultural watershed. Results showed that they managed to reduce runoff by 20–50% by engaging a dialogue about grass strips, storage ponds and management of the intercrop period. However, further progress is still needed to better control runoff through the implementation of better agricultural practices because, during the RPG sessions, the watershed advisors did not encourage farmers to do so. Because of the complexity of management problems, results of jointly constructing the game and the RPG sessions showed that modelling and simulation can be a very useful way of accompanying the collective learning process. This new way of working was welcomed by the participants who expressed their interest in organizing further RPG sessions.     

An Efficient Newton-Krylov Implementation of the Constrained Runs Scheme for Initializing on a Slow Manifold

The long-term dynamic behavior of many dynamical systems evolves on a low-dimensional, attracting, invariant slow manifold, which can be parameterized by only a few variables (“observables”). The explicit derivation of such a slow manifold (and thus, the reduction of the long-term system dynamics) is often extremely difficult or practically impossible. For this class of problems, the equation-free framework has been developed to enable performing coarse-grained computations, based on short full model simulations. Each full model simulation should be initialized so that the full model state is consistent with the values of the observables and close to the slow manifold. To compute such an initial full model state, a class of constrained runs functional iterations was proposed (Gear and Kevrekidis, J. Sci. Comput. 25(1), 17–28, 2005; Gear et al., SIAM J. Appl. Dyn. Syst. 4(3), 711–732, 2005). The schemes in this class only use the full model simulator and converge, under certain conditions, to an approximation of the desired state on the slow manifold. In this article, we develop an implementation of the constrained runs scheme that is based on a (preconditioned) Newton-Krylov method rather than on a simple functional iteration. The functional iteration and the Newton-Krylov method are compared in detail using a lattice Boltzmann model for one-dimensional reaction-diffusion as the full model simulator. Depending on the parameters of the lattice Boltzmann model, the functional iteration may converge slowly or even diverge. We show that both issues are largely resolved by using the Newton-Krylov method, especially when a coarse grid correction preconditioner is incorporated.