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12 Mar Building a Concept Hierarchy

Existential knowledge, our knowledge of things that exist, is hierarchical. In other words, we categorize things into classes. Objects in these classes form the content of our thoughts. We have heard about the phylogenetic tree, the “tree of life” or the system of biological classification. This is a beautiful example of a regular taxonomy (irregular might have squiggles that circle back and cross lines of ancestry). I like pictures that illustrate the regularity. This one is from

Tree of Life

Understanding Context Cross-Reference
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Section 5 #16

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Table of Context

Learn Categorize ConnectNoted psychologist William James, in his elucidation of the sequence of cognitive processes (1890, Chapters 12 and 13), interprets learning and cognitive capabilities as synthesizing class membership and hierarchical relations and analyzing part-whole relations. These capabilities both associate and dissociate objects in the concept hierarchy as new data are processed. James’ dynamic model of knowledge and learning resembles connectionist models (see Section 7) in that positive and negative feedback cause adjustments in connection weights. “The truth is that EXPERIENCE is trained by both association and dissociation,” James writes (1890, Chapter 13). He describes a human psychology based on both synthetic and analytic abilities in which discriminative attention and agency govern our impressions and responses.

The link to connectionism is strengthened later in Chapter 13 when Weber’s and Leipzig’s theories on the measurement of discriminative sensibility are discussed and integrated, to some degree, into James’ model of cognition. Class Subclass InstanceThis illustration shows a hierarchy. If the class is “animals,” for example, the tier of circles underneath animals might be dogs and cats. The next level down might be another subclass, such as breeds of dogs and cats, and or it may be specific instances, such as Fido the mutt and Fluffy the longhaired cat.

Units of Thought

The essential meaning of a proposition is a critical issue, so we will consider it for a moment. It has been suggested that “propositions are the simplest complete units of thought” (Stillings, et al., 1987, p. 23). A “complete unit of thought” can be said to have a truth value, whether that value be TRUE or FALSE or somewhere on a multi-valued continuum. An easy way to think of a proposition is as having two components linked by a relation of some sort. The component entities could equate to labeled concepts such as JOHN and BALL and the relationship to the concept HIT. Obviously, HIT expresses an active relationship. A proposition might be hierarchical, as in the relationship PART_OF between HOUSE and WINDOW.

Tile MosaicPropositional relationships may also be CAUSAL, such as that between EXERCISE and FATIGUE, or PROCEDURAL, such as those relationships that exist between REACH, GRASP and LIFT. The introduction of procedural knowledge in the context of propositions punctuates the fact that all knowledge is so interrelated that clear (as opposed to “fuzzy” or multi-valued) distinctions fail to capture the interplay and interdependencies of all knowledge. Conceptual dependencies (Shank, 1986, p. 172) are a core element of cognition.

Dependency, hierarchy, causality and a host of other intricate relationships link the concepts in our knowledge reservoir into a mosaic that leads back to those first introspective feelings that were the sparks of intelligence. Propositions are often described in linguistic terms. Though less expressive than images, these are generally the only kind of terms we can deal with efficiently. They are easily stored as objects in a flat structure, such as an ontology, to represent ideas of multiple dimensions and arbitrary complexity. In my upcoming posts in Understanding Context I will use examples from language acquisition, storage, interpretation, and generation to represent cognitive activities. By the way, please check out the links on Cathy Law’s science site.

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