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123
Transforming Data by Calculation
 IN GTTSE’07, VOLUME 5235 OF LNCS
, 2008
"... This paper addresses the foundations of datamodel transformation. A catalog of data mappings is presented which includes abstraction and representation relations and associated constraints. These are justified in an algebraic style via the pointfreetransform, a technique whereby predicates are lif ..."
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This paper addresses the foundations of datamodel transformation. A catalog of data mappings is presented which includes abstraction and representation relations and associated constraints. These are justified in an algebraic style via the pointfreetransform, a technique whereby predicates are lifted to binary relation terms (of the algebra of programming) in a twolevel style encompassing both data and operations. This approach to data calculation, which also includes transformation of recursive data models into “flat ” database schemes, is offered as alternative to standard database design from abstract models. The calculus is also used to establish a link between the proposed transformational style and bidirectional lenses developed in the context of the classical viewupdate problem.
The Objects and Arrows of Computational Design
 In MoDELS
, 2008
"... Abstract. Computational Design (CD) is a paradigm where both program design ..."
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Cited by 13 (3 self)
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Abstract. Computational Design (CD) is a paradigm where both program design
Granulation for Graphs
 Spatial Information Theory. Cognitive and Computational Foundations of Geographic Information Science. International Conference COSIT'99, volume 1661 of Lecture Notes in Computer Science
, 1999
"... . In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure ..."
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. In multiresolution data handling, a less detailed structure is often derived from a more detailed one by amalgamating elements which are indistinguishable at the lower level of detail. This gathering together of indistinguishable elements is called a granulation of the more detailed structure. When handling spatial data at several levels of detail the granulation of graphs is an important topic. The importance of graphs arises from their widespread use in modelling networks, and also from the use of dual graphs of spatial partitions. This paper demonstrates that there are several quite different kinds of granulation for graphs. Four kinds are described in detail, and situations where some of these may arise in spatial information systems are indicated. One particular kind of granulation leads to a new formulation of the boundarysensitive approach to qualitative location developed by Bittner and Stell. Vague graphs and their connection with granulation are also discusse...
Functorial data migration
 Information and Computation 2012, DOI: 10.1016/j.ic.2012.05.001. ePrint available: http://arxiv.org/abs/1009.1166
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Fibered Manifolds, Natural Bundles, Structured Sets, GSets and all that: The Hole Story from Space Time to Elementary Particles, grqc/0505138 12
 Isenberg, J., Marsden
, 2005
"... [M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol ..."
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Cited by 8 (3 self)
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[M]athématiciens et physiciens ont pris conscience, depuis longtemps déjà, du fait que les espaces fibrés constituent un cadre de pensée fondamental pour la relativité, comme ils le font d’ailleurs aussi pour la mécanique analytique classique. (Lichnerowicz, Espaces Fibres et EspaceTemps, GRG, vol 1. No. 3, pp 235245) In this paper we review the hole argument for the spacetime points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract from differentiability and even continuity, the hole argument is applied to a much wider class of mathematical objects. We discuss the problem concerning the individuation of the objects in more general settings such that fibered manifolds, fibered
Ologs: a categorical framework for knowledge representation
 PLoS ONE
, 2011
"... In this paper we introduce the olog, or ontology log, a categorytheoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and crosscompared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relationa ..."
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In this paper we introduce the olog, or ontology log, a categorytheoretic model for knowledge representation (KR). Grounded in formal mathematics, ologs can be rigorously formulated and crosscompared in ways that other KR models (such as semantic networks) cannot. An olog is similar to a relational database schema; in fact an olog can serve as a data repository if desired. Unlike database schemas, which are generally difficult to create or modify, ologs are designed to be userfriendly enough that authoring or reconfiguring an olog is a matter of course rather than a difficult chore. It is hoped that learning to author ologs is much simpler than learning a database definition language, despite their similarity. We describe ologs carefully and illustrate with many examples. As an application we show that any primitive recursive function can be described by an olog. We also show that ologs can be aligned or connected together into a larger network using functors. The various methods of information flow and institutions can then be used to integrate local and global worldviews. We finish by providing several different avenues for future research.
Introduction to categories and categorical logic
 In: New Structures for Physics, B. Coecke (ed), Springer Lecture Notes in Physics
, 2009
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Ordinals and Interactive Programs
, 2000
"... The work reported in this thesis arises from the old idea, going back to the origins of constructive logic, that a proof is fundamentally a kind of program. If proofs can be ..."
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Cited by 5 (2 self)
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The work reported in this thesis arises from the old idea, going back to the origins of constructive logic, that a proof is fundamentally a kind of program. If proofs can be