33 research outputs found
The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence
Intelligent systems based on first-order logic on the one hand, and on
artificial neural networks (also called connectionist systems) on the other,
differ substantially. It would be very desirable to combine the robust neural
networking machinery with symbolic knowledge representation and reasoning
paradigms like logic programming in such a way that the strengths of either
paradigm will be retained. Current state-of-the-art research, however, fails by
far to achieve this ultimate goal. As one of the main obstacles to be overcome
we perceive the question how symbolic knowledge can be encoded by means of
connectionist systems: Satisfactory answers to this will naturally lead the way
to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page
Categoricity and covering spaces
This thesis develops some of the basic model theory of covers of algebraic
curves. In particular, an equivalence between the good model-theoretic
behaviour of the modular j-function, and the openness of certain Galois
representations in the Tate-modules of abelian varieties is described.Comment: DPhil Thesi
Multicoloured Random Graphs: Constructions and Symmetry
This is a research monograph on constructions of and group actions on
countable homogeneous graphs, concentrating particularly on the simple random
graph and its edge-coloured variants. We study various aspects of the graphs,
but the emphasis is on understanding those groups that are supported by these
graphs together with links with other structures such as lattices, topologies
and filters, rings and algebras, metric spaces, sets and models, Moufang loops
and monoids. The large amount of background material included serves as an
introduction to the theories that are used to produce the new results. The
large number of references should help in making this a resource for anyone
interested in beginning research in this or allied fields.Comment: Index added in v2. This is the first of 3 documents; the other 2 will
appear in physic