Equations as knowledge

Mathematical formulas as knowledge subjects

Formulas in ontologies

In mathematics-heavy domains, equations and theorems should be first-class knowledge: not only PDF or LaTeX blobs, but structured subjects that link symbols to concepts, units, and proofs. The canonical chapter describes formal representation, web presentation, and publication workflows. Logical background for combining equations with ontologies touches description logics and concrete domains [BaMc2003]; RDF-oriented practice [AlHe2020].

Pythagorean theorem

See the mirror page Pythagorean theorem for a worked ontological encoding example.

deriver.app

The workbench is not a computer algebra system; use triples and rules to record constraints and trigger checks appropriate to your deployment.

Source: taoke.de — Equations.

References

  1. [BaMc2003] Franz Baader, Deborah L. McGuiness, Daniele Nardi, Peter F. Patel-Schneider (eds.), The Description Logic Handbook: Theory, Implementation and Applications, Cambridge University Press , 2003, ISBN: 978-0521781763, pp. 574
  2. [AlHe2020] Dean Allemang, Jim Hendler, Fabien Gandon, Semantic Web for the Working Ontologist - Effective Modeling in RDFS and OWL, Third Edition, ACM Books series, Nbr. 33 , 2020, ISBN: 978-1-4503-7614-3