The Canonical Structure as a Minimum Structure

Yasuhiko Takahara, Junichi Hjima, Shingo Takahashi

研究成果: Article査読

抄録

In this paper a structure of a syslem is defined as a mathematical structure [formula omitted], where [formula omitted]is a first-order logic language and Σ is a set of sentences of the given first-order logic. It is shown that a canonical structure determined by I, which is similar to those used in proving the Gödel's completeness theorem, satisfies a universality in the sense of category theory when homomorphisms are used as morphisms, and a freeness in the sense of universal algebra when Σ-morphisms, which preserve Σ, are used. The universality and the freeness give the minimality of the canonical structure.As an example, a structure of a stationary system is defined as a pair [formula omitted] Its canonical structure is actually constructed. In a sense this canonical structure accords with models constructed by Nerode realization.

本文言語English
ページ(範囲)141-163
ページ数23
ジャーナルInternational Journal of General Systems
15
2
DOI
出版ステータスPublished - 1989 6
外部発表はい

ASJC Scopus subject areas

  • 制御およびシステム工学
  • 理論的コンピュータサイエンス
  • 情報システム
  • モデリングとシミュレーション
  • コンピュータ サイエンスの応用

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