Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Algebraic calculi for weighted ontology alignments

inants2016bInternational audienceAlignments between ontologies usually come with numerical attributes expressing the confidence of each correspondence. Semantics supporting such confidences must generalise the semantics of alignments without confidence. There exists a semantics which satisfies this but introduces a discontinuity between weighted and non-weighted interpretations. Moreover, it does not provide a calculus for reasoning with weighted ontology alignments. This paper introduces a calculus for such alignments. It is given by an infinite relation-type algebra, the elements of which are weighted taxonomic relations. In addition, it approximates the non-weighted case in a continuous manner

Robust spatial memory maps encoded in networks with transient connections

The spiking activity of principal cells in mammalian hippocampus encodes an internalized neuronal representation of the ambient space---a cognitive map. Once learned, such a map enables the animal to navigate a given environment for a long period. However, the neuronal substrate that produces this map remains transient: the synaptic connections in the hippocampus and in the downstream neuronal networks never cease to form and to deteriorate at a rapid rate. How can the brain maintain a robust, reliable representation of space using a network that constantly changes its architecture? Here, we demonstrate, using novel Algebraic Topology techniques, that cognitive map's stability is a generic, emergent phenomenon. The model allows evaluating the effect produced by specific physiological parameters, e.g., the distribution of connections' decay times, on the properties of the cognitive map as a whole. It also points out that spatial memory deterioration caused by weakening or excessive loss of the synaptic connections may be compensated by simulating the neuronal activity. Lastly, the model explicates functional importance of the complementary learning systems for processing spatial information at different levels of spatiotemporal granularity, by establishing three complementary timescales at which spatial information unfolds. Thus, the model provides a principal insight into how can the brain develop a reliable representation of the world, learn and retain memories despite complex plasticity of the underlying networks and allows studying how instabilities and memory deterioration mechanisms may affect learning process.Comment: 24 pages, 10 figures, 4 supplementary figure

Quantitative evaluation of Pandora Temporal Fault Trees via Petri Nets

© 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Using classical combinatorial fault trees, analysts are able to assess the effects of combinations of failures on system behaviour but are unable to capture sequence dependent dynamic behaviour. Pandora introduces temporal gates and temporal laws to fault trees to allow sequence-dependent dynamic analysis of events. Pandora can be easily integrated in model-based design and analysis techniques; however, the combinatorial quantification techniques used to solve classical fault trees cannot be applied to temporal fault trees. Temporal fault trees capture state and therefore require a state space solution for quantification of probability. In this paper, we identify Petri Nets as a possible framework for quantifying temporal trees. We describe how Pandora fault trees can be mapped to Petri Nets for dynamic dependability analysis and demonstrate the process on a fault tolerant fuel distribution system model