Cut-free sequent systems for temporal logic

Currently known sequent systems for temporal logics such as linear time temporal logic and computation tree logic either rely on a cut rule, an invariant rule, or an infinitary rule. The first and second violate the subformula property and the third has infinitely many premises. We present finitary cut-free invariant-free weakening-free and contraction-free sequent systems for both logics mentioned. In the case of linear time all rules are invertible. The systems are based on annotating fixpoint formulas with a history, an approach which has also been used in game-theoretic characterisations of these logics.     

The basic constructive logic for a weak sense of consistency

In this paper, consistency is understood as the absence of the negation of a theorem, and not, in general, as the absence of any contradiction. We define the basic constructive logic B_Kc1 adequate to this sense of consistency in the ternary relational semantics without a set of designated points. Then we show how to define a series of logics extending B_Kc1 within the spectrum delimited by contractionless minimal intuitionistic logic. All logics defined in the paper are paraconsistent logics.     

Event calculus and temporal action logics compared

We compare the event calculus and temporal action logics (TAL), two formalisms for reasoning about action and change. We prove that, if the formalisms are restricted to integer time, inertial fluents, and relational fluents, and if TAL action type specifications are restricted to definite reassignment of a single fluent, then the formalisms are not equivalent. We argue that equivalence cannot be restored by using more general TAL action type specifications. We prove however that, if the formalisms are further restricted to single-step actions, then they are logically equivalent.     

Spatial reasoning in a fuzzy region connection calculus

Although the region connection calculus (RCC) offers an appealing framework for modelling topological relations, its application in real-world scenarios is hampered when spatial phenomena are affected by vagueness. To cope with this, we present a generalization of the RCC based on fuzzy set theory, and discuss how reasoning tasks such as satisfiability and entailment checking can be cast into linear programming problems. We furthermore reveal that reasoning in our fuzzy RCC is NP-complete, thus preserving the computational complexity of reasoning in the RCC, and we identify an important tractable subfragment. Moreover, we show how reasoning tasks in our fuzzy RCC can also be reduced to reasoning tasks in the original RCC. While this link with the RCC could be exploited in practical reasoning algorithms, we mainly focus on the theoretical consequences. In particular, using this link we establish a close relationship with the Egg-Yolk calculus, and we demonstrate that satisfiable knowledge bases can be realized by fuzzy regions in any dimension.     

Condition-based diagnosis of mechatronic systems using a fractional calculus approach

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model’s complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.     

Fast decision procedure for propositional Dummett logic based on a multiple premise tableau calculus

We present a procedure to decide propositional Dummett logic. Such a procedure relies on a tableau calculus with a multiple premise rule and optimizations. The resulting implementation outperforms the state of the art graph-based procedure.     

Coquand's calculus of constructions: A mathematical foundation for a proof development system

The calculus of constructions of Coquand, which is a version of higher order typed-calculus based on the dependent function type, is considered from the perspective of its use as the mathematical foundation for a proof development system. The paper considers formulations of the calculus, the underlying consistency of the formalism (i.e., the strong normalisation theorem), and the proof theory of adding assumptions for notions from logic and set theory. Proofs are not given, but references to them are.A preliminary version of this paper was presented at the Third Banff Higher Order Workshop, 23–28 September 1989.     

Numerical solution of a calculus of variations problem using the feedforward neural network architecture

It is demonstrated, through theory and numerical example, how it is possible to construct directly and noniteratively a feedforward neural network to solve a calculus of variations problem. The method, using the piecewise linear and cubic sigmoid transfer functions, is linear in storage and processing time. The L₂ norm of the network approximation error decreases quadratically with the piecewise linear transfer function and quartically with the piecewise cubic sigmoid as the number of hidden layer neurons increases. The construction requires imposing certain constraints on the values of the input, bias, and output weights, and the attribution of certain roles to each of these parameters.

All results presented used the piecewise linear and cubic sigmoid transfer functions. However, the noniterative approach should also be applicable to the use of hyperbolic tangents and radial basis functions.     

多方向模板变分模型的单幅图像超分辨率重建

目的 为了增强图像超分辨率重建的准确性,克服传统插值所产生的边缘模糊与边缘锯齿等负面效果,提出一种基于多方向模板变分模型的单幅图像超分辨率重建方法。方法 首先构建体现28个方向的多方向模板对输入图像的轮廓方向进行计算,同时通过将TV模型引入到图像轮廓的估计中来确定边缘轮廓的最优方向;在此基础上通过进行基于所提出的多方向模板的图像插值来实现图像的超分辨率重建。结果 对比基于活动轮廓的图像边缘插值方法重建的经典高分辨率测试图像,本文方法在平均峰值信噪比和平均结构相似度方面分别提高了1.578 dB和 0.030 02 dB。结论 本文方法可以有效地克服传统插值方法所产生的边缘模糊和边缘锯齿化等负面效果,也避免了较少方向模板所带来的边缘和纹理丰富区域的纹理失真现象,可以取得较好的重建效果。     

On a generalization of Bernstein polynomials and Bézier curves based on umbral calculus

In Winkel (2001) a generalization of Bernstein polynomials and Bézier curves based on umbral calculus has been introduced. In the present paper we describe new geometric and algorithmic properties of this generalization including: (1) families of polynomials introduced by Stancu (1968) and Goldman (1985), i.e., families that include both Bernstein and Lagrange polynomial, are generalized in a new way, (2) a generalized de Casteljau algorithm is discussed, (3) an efficient evaluation of generalized Bézier curves through a linear transformation of the control polygon is described, (4) a simple criterion for endpoint tangentiality is established.     

Technology adoption as process: A case of integrating an information-intensive website into a patient education helpline

This study followed the introduction of the Arthritis Source website into the existing teaching practices of Arthritis Foundation Helpline volunteers. The goal was to examine what factors may affect a particular group of educators adopt a potentially valuable Internet tool into an existing instructional environment. Defining the possible uses of the website in reference to the volunteers' actual job duties helped provide a clearer understanding of how the volunteers might use this new technology. The researchers used qualitative techniques to focus on three volunteers who experienced different physical, environmental and cognitive means that impacted their use of the new tool. Each volunteer experienced varying levels of motivation in areas of learning, satisfaction and responses to outside influences. Each volunteer also had varying amounts of opportunity prompts in which to interact or refer the website. Consequently, Helpline volunteers experienced different rates of adopting the information-intensive website into their traditional work system.