On Mathematical Semantics: A Pattern Theoretic View.

Abstract

Mathematical semantics is introduced as the study of mappings between configuration spaces and image algebras. An image algebra is synthesized using generators that are relations. This will serve as the semantic counterpart of a formal language. The image algebra is analyzed in terms of its similarity group, bond relations and connection type. The semantic map is studied in terms of the morphisms of a category, the term used in its algebraic sense. We present strategies for constructing semantic maps with special properties related to memory requirements. Some examples are given, showing how the semantic categories can be constructed. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1978
Accession Number
ADA061592

Entities

People

  • Ulf Grenander

Organizations

  • Brown University

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programs
  • Computer Science
  • Computers
  • Connectors
  • Coordinate Systems
  • Formal Languages
  • Generators
  • Language
  • Linguistics
  • Mathematics
  • Natural Languages
  • Permutations
  • Rhode Island
  • Semantics
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Computational Linguistics
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space