A Combinatorial Bit Bang Leading to Quaternions

This paper describes in detail how (discrete) quaternions - ie. the abstract structure of 3-D space - emerge from, first, the Void, and thence from primitive combinatorial structures, using only the exclusion and co-occurrence of otherwise unspecified events. We show how this computational view supplements and provides an interpretation for the mathematical structures, and derive quark structure. The build-up is emergently hierarchical, compatible with both quantum mechanics and relativity, and can be extended upwards to the macroscopic. The mathematics is that of Clifford algebras emplaced in the homology-cohomology structure pioneered by Kron. Interestingly, the ideas presented here were originally developed by the author to resolve fundamental limitations of existing AI paradigms. As such, the approach can be used for learning, planning, vision, NLP, pattern recognition; and as well, for modelling, simulation, and implementation of complex systems, eg. biological.Comment: 23 pages, 4 figure

Issues about the Adoption of Formal Methods for Dependable Composition of Web Services

Web Services provide interoperable mechanisms for describing, locating and invoking services over the Internet; composition further enables to build complex services out of simpler ones for complex B2B applications. While current studies on these topics are mostly focused - from the technical viewpoint - on standards and protocols, this paper investigates the adoption of formal methods, especially for composition. We logically classify and analyze three different (but interconnected) kinds of important issues towards this goal, namely foundations, verification and extensions. The aim of this work is to individuate the proper questions on the adoption of formal methods for dependable composition of Web Services, not necessarily to find the optimal answers. Nevertheless, we still try to propose some tentative answers based on our proposal for a composition calculus, which we hope can animate a proper discussion

Distributed Computation as Hierarchy

This paper presents a new distributed computational model of distributed systems called the phase web that extends V. Pratt's orthocurrence relation from 1986. The model uses mutual-exclusion to express sequence, and a new kind of hierarchy to replace event sequences, posets, and pomsets. The model explicitly connects computation to a discrete Clifford algebra that is in turn extended into homology and co-homology, wherein the recursive nature of objects and boundaries becomes apparent and itself subject to hierarchical recursion. Topsy, a programming environment embodying the phase web, is available from www.cs.auc.dk/topsy.Comment: 16 pages, 3 figure

Web Information Systems: Usage, Content, and Functionally Modelling

The design of large-scale data-intensive web information systems (WIS) requires a clear picture of the intended users and their behaviour in using the system, a support of various access channels and the technology used with them, and an integration of traditional methods for the design of data-intensive information systems with new methods that address the challenges arising from the web-presentation and the open access. This paper presents the conceptual modelling parts of a methodology for the design of WISs that is based on an abstract abstraction layer model (ALM). It concentrates on the two most important layers in this model: a business layer and a conceptual layer. The major activities on the business layer deal with user profiling and storyboarding, which addresses the design of an underlying application story. The core of such a story can be expressed by a directed multi-graph, in which the vertices represent scenes and the edges actions by the users including navigation. This leads to story algebras which can then be used to personalise the WIS to the needs of a user with a particular profile. The major activities on the conceptual layer address the support of scenes by modelling media types, which combine links to databases via extended views with the generation of navigation structures, operations supporting the activities in the storyboard, hierarchical presentations, and adaptivity to users, end-devices and channels. Adding presentation style options this can be used to generate the web-pages that will be presented to the WIS users

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Towards Systematic Personalization of Information Spaces

Web information systems often have large and complex information spaces. These spaces serve as a conceptual framework for all user-system interactions. Their complexity is likely to cause users having trouble carrying out with these systems the business cases in their portfolio. Aiding users therefore requires a view of reduced complexity on the information space being defined and made accessible to the users. Such a view is called a story. Working out the stories that best help users beneficially use Web information systems is the task of information space personalization. This paper analyses a Web information system. A Kleene algebra is used as a mathematical model of a story of this system. We illustrate that formal manipulation of Kleene algebras can be used for personalizing information spaces. This paper thus supports the proposal of using Kleene algebras as mathematical model of Web information system usage

Mathematical knowledge management is needed

In this lecture I discuss some aspects of MKM, Mathematical Knowledge Management, with particuar emphasis on information storage and information retrieval.Comment: Keynote speech at the November, 2003 MKM meeting ar Herriott-Watt, Edinburg, UK. Nine pages, one figur