Theory ABSTRACT-ALGEBRA

• Last modified: Monday, 2 May 1994
• Source code: abstract-algebra.lisp
• List of other known theories

Theory documentation:

Defines the basic vocabulary for describing algebraic operators, domains, and structures such as fields, rings, and groups.

Notes:

• Originally based on the example given as an appendix to the KIF3.0 manual. Modified to work over classes instead of sets, to be consistent with the frame-ontology.

Cross Reference Report:

Theories included by Abstract-Algebra:

  Frame-Ontology

Theories that include Abstract-Algebra:

  Physical-Quantities

No classes defined.

25 relations defined:

  Abelian-Group
  Abelian-Semigroup
  Antisymmetric
  Associative
  Asymmetric
  Binary-Operator-On
  Commutative
  Commutative-Ring
  Distributes
  Division-Ring
  Field
  Group
  Identity-Element-For
  Integral-Domain
  Invertible
  Irreflexive
  Linear-Order
  Linear-Space
  Partial-Order
  Reflexive
  Ring
  Semigroup
  Symmetric
  Transitive
  Trichotomizes

No functions defined.

No instances defined.

The following constants were used from included theories:

• Arity defined as a function in theory Frame-Ontology
• Binary-Function defined as a class in theory Kif-Relations
• Binary-Relation defined as a class in theory Kif-Relations
• Class defined as a class in theory Frame-Ontology
• Documentation defined as a relation in theory Frame-Ontology
• Domain defined as a relation in theory Frame-Ontology
• Holds defined as a relation in theory Kif-Relations
• Instance-Of defined as a relation in theory Frame-Ontology
• Nth-Domain defined as a relation in theory Frame-Ontology
• Relation defined as a class in theory Kif-Relations
• Subrelation-Of defined as a relation in theory Frame-Ontology
• Value defined as a function in theory Kif-Relations

All constants that were mentioned were defined.