On Mathematical Semantics: A Pattern Theoretic View.
Pattern analysis rept. no. 71,
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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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
- Theoretical Mathematics