This document introduces the concept of refined concept maps (RCM) as a way to make traditional concept maps more rigorous and less ambiguous. RCM focuses on using a finite set of well-defined semantic relation names instead of loose linking words. This allows knowledge to be represented in a more formal and logically consistent way while still being accessible to novices. The document provides examples of converting traditional concept maps to RCM and discusses how RCM could serve as a bridge between informal and formal knowledge representation.

2. Introducing Rigor in Concept Maps
Meena Kharatmal & Nagarjuna G.
{meena, nagarjuna}@hbcse.tifr.res.in
ICCS 2010, Malaysia
July 29, 2010
Homi Bhabha Centre for Science Education
(Tata Institute of Fundamental Research)
Mumbai, INDIA

3. Introduction
Concept map, a two-dimensional
representation of knowledge, is a simple
graphical form of knowledge representation
method comprising of nodes (concepts)
and arcs (linking phrases)

4. 4

5. Critique of concept maps
●
Informal (Sowa 2006)
●
undisciplined nature can be ambiguous (Kremer
1995;)
●
lack of knowledge representation (KR) methods
(Canas & Carvalho 2004)
●
the unlimited use of linking words, itself prevents
them from being a formal representation
●
loose usage of linking words leads to ambiguous
concept maps thereby lacking rigor in
representation of sceintific knowledge 5

6. Our critique on CM
● Loose usage of linking words
● Implicit
● No logical criteria for validating hierarchy
● Cross-links merely based on graphical repn
● No distinction between concepts and attributes
● scoring
Meena Kharatmal & Nagarjuna G. (2004):
A Proposal to Refine Concept Mapping for Science Learning 6

7. ●
Many relation types
1st level
2nd level ●
Hierarchy not validated
3rd level
●
Incorrect cross­links
4th level
●
Graphical
representation
5th level misleading
6th level ●
Not principled
Consists of / consists mainly of ; can be classified as ; of the ocean are ; aspects are
including ; like ; which are ; creates ; includes 4 orders ; can be either / are
either ; has 2 groups / have 3 groups / has 3 classes / includes 4 orders / include
phyla / have 3 types

8. Refined Example
Living things
Includes
Plants Animals
e.g. e.g.
An oak My dog
8

9. Objective
To propose a simple methodology of refine
concept mapping to make the representation
more clear and rigorous.
To demonstrate by re-representing concept
maps as refined concept maps.
To suggest how refined concept maps can be
a bridge for linking the informal models and
formal models of conceptual structures

10. Refined Concept Mapping
focuses on the nature of relation names
using a finite set of relation names
consistent usage of relation names
distinction between relations and attributes
Relation names used in RCM -- part of, includes, located in,
surrounded by, has role, has size, has color, etc.

11. Semantically defined relation names
(Open Biomedial Ontology Foundry)
is a =def. For continuants: C is_a C' if and only if: given
any c that instantiates C at a time t, c instantiates C' at
t. For processes: P is_a P' if and only if: that given any p
that instantiates P, then p instantiates P'.
part of =def. For continuants: C part of C if and only if:
given any c that instantiates C at a time t, there is some c
such that c instantiates C at time t, and c part of c at t.
located in =def. C located in C if and only if: given any c
that instantiates C at a time t, there is some c such that: c
instantiates C at time t and c located in c
contained in =def. C contained_in C' if and only if: given
any instance c that instantiates C at a time t, there is some
c' such that: c' instantiates C' at time t and c located_in
c' at t, and it is not the case that c *overlaps* c' at t.
(c' is a conduit or cavity).

14. Methodology
the loosely used ambiguous linking words
seen in TCM replaced with semantically
defined relation names, thus converting to
RCM

15. TCM
RCM

16. TCM
RCM

17. Examples showing the verbatim sentences
from text and the linking words, which
are replaced with the predicate terms and
are used while creating RCM propositions.

18. Verbatim sentences linking words predicate terms
mitochondria have DNA and ribosomes have consists of
mitochondria have 2 membrane covering have enveloped by
has number
plastids are present only in plant cells are present part of
materials such as starch, oils and protein granules such as includes
chloroplasts are important for photosynthesis in plants are important has function
plant cells have very large vacoules have has size
RCM Propositions
mitochondria consists of DNA and ribosomes
mitochondria enveloped by membrane
membrane has number 2
plastids are part of plant cells (only)
materials includes starch, oils and protein granules
chloroplasts has function photosynthesis in plants
vacoules has size large (in plant cells)

19. Mitochondria: * DNA: *
Consists of
Mitochondria: * ribosomes: *
Consists of
Mitochondria: * Membrane: *
Enveloped by
Golgi apparatus: * Storage: *
Has function
19

20. 20

21. 21

22. Semantic spectrum presented indicating the
inverse relation between ambiguity and rigor.
The KR models on the left are more ambiguous
and less rigorous whereas on the right are less
ambiguous and more rigorous

23. Ongoing Work
Applying RCM methodology to study the analysis
and the growth of scientific knowledge.
Class Concept Relation Attribute
8 75 10 5
9 195 15 6
11 430 12 10

24. Graph depicting the constancy in predicate terms
even when the number of concepts progressively
increase from class 8, 9, 11. (Note: the number of
concept names are scaled on secondary y-axis)

25. Graph depicting the proportion of
relation names and attribute names
linked to the concepts in class 8, 9, 11.

26. Predicate terms

27. Refined Concept Mapping in
Science Education

28. Claim of RCM for science education
during the course of development,
➢
knowledge gets added with just a few relation
names but with more of concepts
as the knowledge gets represented in more formal
➢
terms, the relation names decrease progressively
thus effectively all the concepts are handled by
➢
minimal relation names
parsimony therefore can be redefined in terms of
➢
relation names
28

29. RCM as a means for a novice on the way of expert
Profile of Novice Profile of Expert
Knowledge loose form, uneconomical, cohesive, integrated, parsimony,
Structure ambiguous relations unambiguous relations
Knowledge periphery core concepts
Organized
Refined Concept Maps
Approach superficial principled, accurate, deep
Theories concrete, fragmentary, abstract, global, consistent,
inconsistent, particular, diffuse universal, precise
Reasoning implicit and intuitive explicit and articulate
Networking poor in interconnetions rich in interconnections
focus on concepts focus on relations
repetitive refinements

30. RCM and Conceptual Change models
● Ausubel
● subsumption
● Carey
● accretion
● subsumption
● Mintzes
● strong
Restructuring
Karmillof-Smith
Representational
redescriptional

31. Research programs
Semantic holism (Quine)
Semantic network model (Quillians, Minsky)
Concept maps (Novak)
Conceptual graphs (Sowa)
Knowledge Representation Models (OBO, RO ; RDF, OWL)

32. References
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http://www.jfsowa.com/talks/cmapping.pdf
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Intelligence in Knowledge
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7. The Open Biological and Biomedical Ontologies, http://www.obofoundry.org
8. The OBO Relation Ontology, http://www.obofoundry.org/ro/
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biomedical ontologies. Genome Biology 6(5) (2005), http://genomebiology.com/2005/6/5/R46
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Novice to an Expert.
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Concept Mapping, Tallinn, Estonia & Helsinki, Finland (2008)
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Hoffman, Palermo (eds.) Cognition and the Symbolic Processes: Applied and Ecological Perspectives, pp. 209–232. Erlbaum, New
Jersey (1991)
16. Karmiloff-Smith, A.: Beyond Modularity: A Developmental Perspective on Cognitive Science. MIT Press, USA (1995)
17. Nagarjuna, G.: Layers in the Fabric of Mind: A Critical Review of Cognitive Ontogeny. In: Ramadas, J., Chunawala, S. (eds.) Research
Trends in Science, Technology and Mathematics Education. Homi Bhabha Centre for Science Education, Mumbai (2006)
18. McGuinness, D.: Ontologies Come of Age. In: Fensel, D., Hendler, J., Lieberman, J., Wahlster, W. (eds.) Spinning the Semantic Web:
Bringing the World Wide Web to Its Full Potential. MIT Press, USA (2003)

33. “i link, therefore i am”
! Thankyou !
meena@hbcse.tifr.res.in
nagarjun@gnowledge.org
http://okeanos.wordpress.com/publications
http://twitter.com/meena74