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Yes / In this paper, we discuss a framework for synthesising manufacturing process controllers using situation calculus, a well-known second-order logic for reasoning about actions in AI. Using a library of high-level ConGolog programs and logical action theories for production resources, we demonstrate how to efficiently synthesise an ‘optimal’ plan, i.e. the plant that minimises the number of actions for a target high-level program of a process recipe. / University of Bradford / The full-text of this conference paper will be released for public view at the end of the publisher embargo on 8 Nov 2025.

This work develops theoretical and applied results for variational convex analysis. First we present the basic tools of analysis necessary to develop the core theory and applications. New results concerning duality principles for systems originally modeled by non-linear differential equations are shown in chapters 9 to 17. A key aspect of this work is that although the original problems are non-linear with corresponding non-convex variational formulations, the dual formulations obtained are almost always concave and amenable to numerical computations. When the primal problem has no solution in the classical sense, the solution of dual problem is a weak limit of minimizing sequences, and the evaluation of such average behavior is important in many practical applications. Among the results we highlight the dual formulations for micro-magnetism, phase transition models, composites in elasticity and conductivity and others. To summarize, in the present work we introduce convex analysis as an interesting alternative approach for the understanding and computation of some important problems in the modern calculus of variations. / Ph. D.

A transition calculus is developed for describing and analyzing the dynamic behavior of logic circuits. Boolean partial derivatives are introduced that are more powerful and applicable to a wider class of problems than the Boolean difference. The partial derivatives are used to define a Boolean differential which provides a concise method for describing the effect on a switching function of changes in its variables. It is shown that a nonconstant function is uniquely determined by its differential, and integration techniques are developed for finding a function when its differential is known. The useful concepts of exact integrals, compatible integrals, and integration by parts are introduced and the conditions for their existence are established. Algorithms for both differentiation and integration are simply implemented using Karnaugh maps. / Ph. D.

The purpose of this paper is to present proofs for six cases of L'Hospital's Rule for the evaluation of indeterminate forms. It is also a purpose to reduce to one of these six cases some other indeterminate forms to which L'Hospital's Rule is applicable. In the course of presenting these proofs several theorems and definitions will be used without proof.

We study minimizers of the Landau-de Gennes energy in the exterior region around a smooth 2-manifold in R3 with a constant external magnetic field present. Uniaxial boundary data and a strong tangential anchoring are imposed on the surface of the manifold and we consider the large particle limit in a regime where the magnetic field is relatively weak. Before studying the general manifold, we analyze a more simple case in which the manifold is spherical. After deriving a lower bound for the energy in this limiting regime, we prove that a director field on the boundary which maximizes its vertical component yields a minimal lower bound. We then construct a recovery sequence to show that this lower bound is in fact the optimal energy bound. These steps are later repeated in more generality for a larger class of smooth manifolds. / Thesis / Master of Science (MSc)

The Internet and Web have brought in a new era of information sharing and opened up countless opportunities for people to rethink and redefine communication. With the development of network-related technologies, a Client/Server architecture has become dominant in the application layer of the Internet. Nowadays network nodes are behind firewalls and Network Address Translations, and the centralised design of the Client/Server architecture limits communication between users on the client side. Achieving the conflicting goals of data privacy and data openness is difficult and in many cases the difficulty is compounded by the differing solutions adopted by different organisations and companies. Building a more decentralised or distributed environment for people to freely share their knowledge has become a pressing challenge and we need to understand how to adapt the pervasive Client/Server architecture to this more fluid environment. This thesis describes a novel framework by which network nodes or humans can interact and share knowledge with each other through formal service-choreography specifications in a decentralised manner. The platform allows peers to publish, discover and (un)subscribe to those specifications in the form of Interaction Models (IMs). Peer groups can be dynamically formed and disbanded based on the interaction logs of peers. IMs are published in HTML documents as normal Web pages indexable by search engines and associated with lightweight annotations which semantically enhance the embedded IM elements and at the same time make IM publications comply with the Linked Data principles. The execution of IMs is decentralised on each peer via conventional Web browsers, potentially giving the system access to a very large user community. In this thesis, after developing a proof-of-concept implementation, we carry out case studies of the resulting functionality and evaluate the implementation across several metrics. An increasing number of service providers have began to look for customers proactively, and we believe that in the near future we will not search for services but rather services will find us through our peer communities. Our approaches show how a peer-to-peer architecture for this purpose can be obtained on top of a conventional Client/Server Web infrastructure.

I present a simple Simultaneous Abstraction Calculus, where the familiar lambda-abstraction over single variables is replaced by abstraction over whole sets of them. Terms are applied to partial assignments of objects to variables. Variants of the system are investigated and compared, with respect to their semantic and proof theoretic properties. The system overcomes the strict ordering requirements of the standard lambda-calculus,and is shown to provide the kind of "non-selective" binding needed for Dynamic Montague Grammar and Discourse Representation Theory. It is closely related to a more complex system, due to Peter Aczel and Rachel Lunon, and can be used for Situation Theory in a similar way. I present versions of these theories within an axiomatic, property-theoretic framework, based on Aczels Frege Structures. The aim of this work is to provide the means for integrating various semantic theories within a formal framework,so that they can share what is common between them, and adopt from each other what is compatible with them.

Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

The Maple V package Vessiot is an extensive set of procedures for performing computations in variational and tensor calculus. Vessiot is an extension of a previous package, Helmholtz, which was written by Cinnamon Hillyard for performing operations in the calculus of variations. The original set of commands included standard operators on differential forms, Euler-Lagrange operators, the Lie bracket operator, Lie derivatives, and homotopy operators. These capabilities are preserved in Vessiot, and enhanced so as to function in a multiple coordinate frame context. In addition, a substantial number of general tensor operations have been added to the package. These include standard algebraic operations such as the tensor product, contraction, raising and lowering of indices, as well covariant and Lie differentiation. Objects such as connections, the Riemannian curvature tensor, and Ricci tensor and scalar may also be easily computed. A synopsis of the command syntax appears in Appendix A on pages 194 through 225, and a complete listing of the Maple procedural code is given in Appendix B, beginning on page 222.