Tuesday, November 2, 2010

Knowledge Maps – Part V: Propositions

   Unfortunately the richness of natural language goes above the capabilities of the current representational tools, for example the temporal, spatial, causal and conditional associations, or the associations between whole propositions are not so easy to represent in many of the K-maps available. Given the rules of syntax, in natural language a proposition is formed typically at minimum of a triple, while a typical proposition could be expressed as one or more such triples. On the other side, a chunk of meaning could be represented as one, two or more triples that span within one or more propositions, same as from a whole text only 2-3 triples could be relevant. As chunks could spread along several propositions, it is necessary to identify the meaningful triples and recombine them in more complex constructs, such a construct being the knowlet.

   Because has been discussed in several occasions about chunks of meaning, some examples are necessary in order to understand what is meant by this construct. The simplest chunk of meaning is the concept itself, for example “collective”, “intelligence”, “collective intelligence” and “harnessing collective intelligence” are such chunks. The next logical type of chunk of meaning is a simple triple formed actually from three concepts, for example “harnessing collective intelligence is a web 2.0 principle” is based on “harnessing collective intelligence”, “is a” and “web 2.0 principle”. A minimum of 4 concepts could result in two triples, for example “web as platform and harnessing collective intelligence are web 2.0 principles”, the two triples could be split in different propositions. By adding one more concept we arrive to three triples, and the logic could be followed, resulting several types of patterns.

     Is the latest example still a chunk of meaning? Yes, it is because they share together the same object within the same proposition, enclosed in a definition-like clause. Definitions are typically examples of such unitary chunks of meaning, for example let’s consider the definition of K-mapping given by Dr. Ann Hylton:

    "Knowledge Mapping is the process of surveying, assessing and linking the information, knowledge, competencies and proficiencies held by individuals and groups within an organization." [1]

     Proposition’s structure could be represented in a K-map resembling a Concept Map as follows:

 KM - example 5 - KM definition concept map Knowledge Mapping definition - Concept Map

     The representational language depends from person to person and from one KM to another, for example the same proposition could be rewritten as follows:

KM - example 5 - KM definition KMKnowledge Mapping definition - Knowledge Map

  Here’s another example following a similar structure, this time based on  D. Hyerle’s definition for K-mapping:

     Knowledge Mapping is “a rich synthesis of thinking processes, mental strategies, techniques and technologies, and knowledge that enables humans to investigate unknowns, show patterns of information, and then use the map to express, build, and assess new knowledge” [2].

KM - example 7 
   Which KM is better is a matter of personal taste, in theory the radial/hierarchical structures are easier to understand and navigate than the networked structures, though the later category of structures is closer to the structure of knowledge, the way concepts are structured. On the other side it could be problematic to represent the two definitions in the same K-map. Here’s an attempt based on propositions’ structure, respectively by restructuring concepts and associations:

KM - example 9 

KM - example 8

   Each of the two approaches comes with its advantages and disadvantages, the first K-map being closer to initial definitions’ formulation, highlighting the concepts found closer to the subject, but more difficult to represent, while the second, more condensed, closer to the representation of knowledge as triples, but keeping less from the initial structure. The maps are not necessarily representative, and neither too elaborate, they represent just the raw representation of two definitions. It would be useful to include multiple definitions in the same K-map, attempting to represent all the attributes of a concept and most representative associations. The downside of such K-maps is that they are more complex and all the consequences deriving from it.

References:
[1] M. Jafari, P. Akhavan, A. Bourouni, R. H. Amiri, (2009). A Framework For The Selection Of Knowledge Mapping Techniques. Journal of Knowledge Management Practice, Vol. 10, No. 1, [Online] Available from: http://www.tlainc.com/articl180.htm (Accessed:16 October 2010)
[2] Hyerle, D. (2008). Thinking Maps®: A Visual Language for Learning. In: Thinking Maps®: A Visual Language for Learning, ISBN: 978-1-84800-149-7. [Online] Available from: http://www.springerlink.com/content/x57121720731381j/ (Accessed: 23 June 2009)

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