Bernard M. Diaz

KRAFT: knowledge fusion from distributed databases and knowledge bases

The KRAFT project aims to investigate how a distributed architecture can support the transformation and reuse of a particular class of knowledge, namely constraints, and to fuse this knowledge so as to gain added value, by using it for constraint solving or data retrieval.

Resolving Ontological Heterogeneity in the KRAFT Project

KRAFT is an agent architecture for the integration of heterogeneous information systems. The focus in KRAFT is on the integration of knowledge in the form of constraints. In this article we describe the architecture from an ontological perspective. We start by introducing the agent architecture and illustrate its application in the telecommunication-network design. We then describe how we assess the ontological heterogeneity in the domain, which problems the integration of constraint knowledge pose, and how we construct a shared ontology. Also, we describe the mapping, functions that are used to translate information between the shared and the local ontologies. Finally, we look at the direction our research is taking hereafter.

Classical Behavior of the Dirac Bispinor

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current. Previous attempts to provide this form of transformational behavior have foundered because a satisfactory current could not be derived.(14)

The Two-Body Interaction with a Circle in Time

We complete our previous(1, 2) demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,(4) including fine structure. We complete our previous derivation(2) of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.

Spatial Reasoning for GIS Using a Tesseral Data Representation

A technique for spatial reasoning is described which is directly compatible with the data representation techniques used by Geographical Information Systems (GIS). GIS may be thought of as specialised forms of database systems which are distinguished by their ability to handle spatial data and are widely used to aid environmental planners to make decisions and predictions. However, their application is limited by their lack of support for any spatio-temporal reasoning capability. The technique described here provides GIS with this capability. It is based on a quad tesseral addressing representation of space supported by a constraint based reasoning mechanism. The technique has been incorporated into a tesseral spatial reasoning system (SPARTA) which has been used successfully to resolve two-dimensional reasoning scenarios.

Spatial Reasoning Using the Quad Tesseral Representation

A review of the application of the quad tesseral representation tosupport spatial reasoning is presented. The principal feature of therepresentation is that it linearises multi-dimensional space, while stillproviding for the description of individual objects within that space andthe relationships that may exist between those objects (in any directionand through any number of dimensions). In addition the representation issupported by an arithmetic which allows the manipulation (translation etc.)of spatial objects. Consequently, when incorporated into a spatialreasoning system, all necessary processing can be implemented as if in onlyone dimension. This offers two significant advantages over moreconventional multi-directional approaches to spatial reasoning. Firstly,many of the concerns associated with the exponential increase in the numberor relations that need to be considered (as the number of dimensions underconsideration increases) are no longer relevant. Secondly, the computationalcost of manipulating and comparing spatial objects remains static at itsone dimensional level, regardless of the number of dimensions underconsideration.

An Ontology for Linear Spatial Reasoning

An ontology for spatial reasoning based on a tesseral representation of space is presented. The principal advantage offered is that the representation has the effect of linearising multi-dimensional space while still supporting translation through the space in any direction and through any number of dimensions. Consequently, all multi-dimensional spatial reasoning can be implemented using one dimensional (temporal) reasoning techniques. As a result, many of the concerns associated with conventional multi-dimensional spatial reasoning systems, based on more traditional representations, no longer apply.

A Tesseral Approach to n-Dimensional Spatial Reasoning

A qualitative multi-dimensional spatial reasoning system is described founded on a tesseral representation of space. Spatial problems are presented to this system in the form of a script describing the nature of the N-dimensional space (the object space), the spatial objects of interest and the relations that are desired to exist between those objects. Objects are defined in terms of classes and instances of classes with locations and shapes defined as sets of tesseral addresses. Relations are expressed in terms of topological set relations which may be quantified through the application of tesseral offsets. Solutions to spatial problems are generated using a heuristically guided constraint satisfaction mechanism. The heuristics are directed at limiting the growth of the search tree through a constraint selection strategy applied at each stage of the satisfaction process. The general advantages of the system are that it is conceptually simple, computationally effective and universally applicable to N-dimensional problem solving.

Temporal reasoning using tesseral addressing: towards an intelligent environmental impact assessment system

A temporal reasoning system is described which uses a tesseral addressing referencing system. The tesseral addressing techniques used are directly compatible with raster based Geographic Informatiori Systems (GIS) and by extension vector based GIS. As a result the temporal reasoning mechanism can be integrated into GIS systems and provide a temporal reasoning capability for such systems. Although the target application of the system described is the production of Environmental Impact Assessment reports it is considered that the advantages offered have a much wider field of application. The temporal reasoning approach advocated has similarities with Kowalskis event calculus in that the principal entities under consideration are temporally displaced events which have temporal attributes associated with them. Events are considered to be instantaneous; non-instantaneous events are described in terms of instantaneous start and end events. The temporal attributes which can be associated with events comprise sets of one or more ranges. Ranges may define a time period during which an event can be said to occur, in which case they are defined in terms of their earliest and latest times (tesseral address), or they may be used to allocate an absolute reference to an event, i.e. a range comprising a single tesseral address. Experiments to date have indicated that the system provides an excellent foundation on which to base further, multi-dimensional reasoning, work.

QED Derived from the Two-Body Interaction

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.(1) In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.