1. www.nomencurator.org What name can do alone An Application of Formal Concept Analysis with Rough Set Approximation to Multiple Hierarchies Visualisation by TaxoNote Comparator Nozomi Ytow 1, David R. Morse 2, Akira Sato 1, David McL. Roberts 4 1 University of Tsukuba, Japan 2 Open University, UK 3 The Natural History Museum, UK ©2003 team Nomencurator. All rights reserved.

2. www.nomencurator.org Multiple taxonomies Similar data models accept multiple taxon concepts, multiple hierarchies We also need a method to compare concepts and hierarchies Prometheus/II: specimen/character based LITCHI, MoReTaX: rule based Nomencurator: annotation captures historical relationships, but need more Does set theory help us?

3. www.nomencurator.org Two Major Set Theories Axiomatic set theory Explicit list of elements in the set Naïve set theory Collection of items satisfies conditions

4. www.nomencurator.org Axiomatic Set Theory Logically well-established Defines a set as an explicit list of elements, e.g. specimen or taxa Addition of a new identified specimen modifies the set, and hence the concept represented by the set? Too stiff for taxonomy, because it requires a complete list

5. www.nomencurator.org Naïve set theory Collection of items satisfying conditions Flexible than axiomatic set Too flexible, e.g. Russell's paradox, or, Too stiff, with Russell's type theory Theoretically more problematic than axiomatic set theory, but sounds better as taxon concept

6. www.nomencurator.org Elements of taxon “set” Axiomatic set theory assumes specimen or lower taxa as elements Naïve set theory uses not only “ordinary” elements but a list of conditions to be satisfied; it is an implicit set of character states Trick: using two sets to capture a concept

7. www.nomencurator.org Formal concept analysis Axiomatic set theory extensional set Naïve set theory intensional set (of objects) Formal concept Defined as a pair of its extension and intension sets

8. www.nomencurator.org Taxon concept and name Specimen circumscription “Character” circumscription Taxon Concept circumscription

9. www.nomencurator.org Rough set theory Not a genuine set theory, but an application of set theory Uses two sets to approximate a concept; positive and negative sets Set to be included in the concept Set to be excluded from the concept Boundary between these two sets gives a flexibility

10. www.nomencurator.org Concept approximation

11. www.nomencurator.org Rough comparison of concepts Cross evaluation

12. www.nomencurator.org Comparison of hierarchies A taxonomy looks like a tree… A tree can be divided into nodes and linkages between nodes Can a taxonomy divided as in tree? Looks like inseparable A taxon concept closely relate to its members, i.e. links included in a node Rough set enables the separation

13. www.nomencurator.org From Taxon to Taxonomy A hierarchy of names works as whole

14. www.nomencurator.org Difference in concepts Rough set detects difference in concepts

15. www.nomencurator.org Difference in hierarchies Separation of concept and hierarchy

16. www.nomencurator.org Hierarchies of compatible concepts

17. www.nomencurator.org Hierarchies of incompatible concepts

18. www.nomencurator.org Team Nomencurator David McL Roberts Zoological Department The Natural History Museum David M. Morse Faculty of Mathematics and Computing The Open University, UK Akira Sato Information Processing Center University of Tsukuba, Japan

19. www.nomencurator.org Acknowledgement Initial exploration of the problem domain was made by Dr Marion Edwards, generously supported by The Cadbury Trust. Development of Nomencurator and its specification (so called Mk II) was initiated as part of a foreign scholarship funded by the Ministry of Education, Culture, Sports Science and Technology of Japan (November 1998 - November 1999) to one of us (NY). It's development was partly funded by University of Tsukuba (2000) and by the Ministry of Education, Culture, Sports Science and Technology of Japan (Grant-in-Aid for Exploratory Research, 13878069, 2001-2003 to NY and Science and Technology Special Coordination Funds to NY with Juno Shimura at NIES). Travel has been partly supported by the National Institute of Environmental Sciences, Japan, as part of collaboration of NY with Junko Shimura at NIES focusing on GBIF. The Nomencurator website is hosted under name of www.nomencurator.org by courtesy of University of Tsukuba

20. www.nomencurator.org

21. Revisiting name A name is not a string Name is the relationship between a string and the designated object A tag removed from the object is not the tag anymore Name (and hence database) can not manage object directly Giving a name to a set containing single object enables unified management both specimen and taxa

22. www.nomencurator.org Nested subsets, not members Treat each specimen as a sat Each lower taxon is not a member of lower taxa, but a subset

23. www.nomencurator.org Common Data Structure

24. www.nomencurator.org Revisiting name A name is not a string Name is the relationship between a string and the designated object A tag removed from the object is not the tag anymore Name (and hence database) can not manage object directly Giving a name to a set containing single object enables unified management both specimen and taxa