Semiotics 1980 pp 523-532 | Cite as

Symbolic Configurations and Two-Dimensional Mathematical Notation

  • W. E. Underwood


In this paper a mathematical model is presented for defining the morphology and syntax of displayed mathematical expressions -- two-dimensional mathematical notation such as matrices, stacked fractions, and summation notation that are not usually written on a single line but displayed in text. A mathematical object, called a configuration, is used to model the spatial patterns or shapes in displayed mathematics. A rewriting system, called a configuration grammar, enables the description of the syntactic structure of displayed mathematics. Parsing procedures can be used with context-free configuration grammars and automatic character recognizers to interpret two-dimensional notations appearing in digitized images.


Mathematical Expression Mathematical Object Lower Left Hand Corner Symbolic Configuration Integral Symbol 


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  1. Anderson, R. H., 1977, Two-Dimensional Mathematical Notation, in: “Syntactic Pattern Recognition Applications,” K.S. Fu, ed., Springer-Verlag, New York.Google Scholar
  2. Rosenfeld, A., 1979, “Picture Languages: Formal Models for Picture Recognition,” Academic Press, New York.Google Scholar
  3. Underwood, W. E., 1980, “Configuration Grammars and Automata for the Definition of Displayed Mathematical Expressions,” Ph.D. Dissertation, University of Maryland, College Park.Google Scholar

Copyright information

© Plenum Press, New York 1982

Authors and Affiliations

  • W. E. Underwood
    • 1
  1. 1.School of Information and Computer ScienceGeorgia Institute of TechnologyAtlantaUSA

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