The Canonical Structure as a Minimum Structure

Yasuhiko Takahara, Junichi Hjima, Shingo Takahashi

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)141-163
Number of pages23
JournalInternational Journal of General Systems
Volume15
Issue number2
DOIs
Publication statusPublished - 1989
Externally publishedYes

Fingerprint

Algebra
First-order Logic
Morphisms
Universality
Category Theory
Universal Algebra
Minimality
Homomorphisms
Completeness
Theorem

Keywords

  • canonical structure
  • freeness
  • language
  • minimality
  • model
  • stationary system
  • Structure
  • universality

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Systems Engineering
  • Modelling and Simulation
  • Theoretical Computer Science
  • Information Systems

Cite this

The Canonical Structure as a Minimum Structure. / Takahara, Yasuhiko; Hjima, Junichi; Takahashi, Shingo.

In: International Journal of General Systems, Vol. 15, No. 2, 1989, p. 141-163.

Research output: Contribution to journalArticle

Takahara, Yasuhiko ; Hjima, Junichi ; Takahashi, Shingo. / The Canonical Structure as a Minimum Structure. In: International Journal of General Systems. 1989 ; Vol. 15, No. 2. pp. 141-163.
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