A Conceptual Approach to Meaning Composability

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A Conceptual Approach to Meaning Composability
James R. McCracken, Ph.D.The Design Knowledge
CompanyRobert G. Eggleston, Ph.D.AFRL/HECS
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Introduction

• Semantic vs. syntactic composability
• Semantic composability
• Conceptual space
• Dimensions
• Isomorphism
• Standard
• W3C XTM 1.0
• ISO/IEC 13250
• Application of XTM and XFML to Individual and
• Organizational Modeling (AXIOM)

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Introduction (cont.)

• Conceptual space (Gardenfors)
• Relation to other modeling techniques
• Centrality of questions
• In modeling and simulation
• In AXIOM
• In human cognition

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Assumptions and Foundations

• Conceptual space
• Dimensions
• Similarity judgments
• Isomorphism
• Shared conceptual meaning
• Biological foundations
• Linguistic foundations

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Similarity Judgments (biological)

• All perceptions are of difference. Bateson,
• 1979
• Comparison of incoming perceptual streams to
• previous experience
• Judgments of degree of similarity
• Distance on dimensional continuum
• ? Apples to apples?
• Abstract judgments

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Structural coupling(biological)

• Mutual changes effected via the interaction of
• organisms with their environment
• Kittens
• Olympic training
• Mountain running (low altitude)
• Computer games Green and Bavelier, 2003

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Structural coupling(biological)

• We admit knowledge whenever we observe an
• effective (or adequate) behavior in a given
• context, i.e., in a realm or domain which
  we
• define by a question (explicit or
  implicit).
• Maturana and Varela, 1988

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Concept Mapping(linguistic token)

• Externalization of internal state
• Beaver (non-verbal warning)
• Human (verbal warning can specify type)
• Science education
• Concept map/XTM link
• Knowledge representation/machine knowledge

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Conceptual Spaces

• Composability as challenge
• There is a single level of mental
  representation, conceptual structure, at which
  linguistic, sensory and motor information are
  compatible. Jackendoff, 2002
• Conceptual Spaces The Geometry of Thought
• Gardenfors, 2002
• Topic map operations
• Merges
• Pruning
• Chunking

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Dimensions

• The structure of dimensions enables a conceptual
• space model in which distance in conceptual
  space
• is tightly coupled to judgments of similarity.
• Judgments of similarity are also tightly coupled
  to
• the quality structure of objects in/composing
  the
• environment.
• Estimation of place along these dimensions leads
• to the development of multi-dimensional
  concepts
• that have a spatial structure.

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Dimensions
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Isomorphism and Dimensional Structure

• Isomorphism comparisons can be made at the object
  (AXIOM XTM node) level, XTM (object/relation)
  level, and at the conceptual process (AXIOM
  model) (object/relation/control) level.

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Integral vs. Separable Dimensions

• Integral dimensions are those for which one
  cannot assign
• a conceptual object a value on one dimension
  without
• assigning a value on another dimension (hue
  and
• brightness, pitch and loudness).
• Separable dimensions are those for which one can
  assign
• a conceptual object a value on one dimension
  without
• assigning a value on another dimension (size
  and hue, size
• and taste).
• Relations among dimensions can vary, that is,
  dimensions
• can be treated as either integral or
  separable, depending
• on the context of use.

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Model Composition
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Composition of Knowledge Structures

• The underlying concept dimensions and the XTM
• merge of existing AXIOM models enable the
• composition of new knowledge and a structural
• matching of models in response to novel
  question
• elements.
• Matching can occur at multiple levels of
• abstraction.

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Dimension-based Generation of Knowledge
What is the slot size for a G200 following a
757?
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Concept-based Generation of Knowledge
What is the slot size for a Citation following a
B-1?
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Methods and Tools

• Approaches to generate the dimensions and
• metrics for conceptual spaces
• back-of-the-envelope
• SME-generated dimensions
• Self-generated Likert scales
• Multidimensional scaling techniques
• Proximity analyses
• Direct dissimilarity scaling (pair-wise
  comparisons of all possible pairs, one at a time)

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Methods and Tools

• Protégé ontology development tool available
• from Stanford http//protege.stanford.edu/
• Topic Mapping for Java (TM4J)
• Java cloud (pub/sub)
• Java messaging service
• Service-Oriented Architecture (SOA)
• Universal Description, Discovery and Integration
  
• (UDDI)

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Summary

• The AXIOM approach to composability links
  experiential and linguistic meaning in a
  biologically grounded, progressively externalized
  method of modeling human cognition, embodied in
  standards-based, platform-independent technology.

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Questions?
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