CKML: Conceptual Knowledge Markup Language

Conceptual Knowledge Markup Language

Version 0.2

~ Under Construction ~

Main Entry: con·cept
Pronunciation: 'kän-"sept
Function: noun
Etymology: Latin conceptum, neuter of conceptus,
past participle of concipere to conceive -- more at CONCEIVE
Date: 1556
1 : something conceived in the mind : THOUGHT, NOTION
2 : an abstract or generic idea generalized from particular instances
synonym see IDEA.
Information Flow
Ontological Structure
Conceptual Scaling
CKML Grammar
CKML Examples
Simple OML
OML Version 0.2
CKML Base Ontology
Frame Systems


Earlier versions of CKML followed rather exclusively the philosophy of Conceptual Knowledge Processing (CKP), a principled approach to knowledge representation and data analysis that "advocates methods and instruments of conceptual knowledge processing which support people in their rational thinking, judgement and acting and promote critical discussion." The new version of CKML continues to follow this approach, but also incorporates various principles, insights and techniques from the logical design of Information Flow (IF) and distributed systems, as being developed by Jon Barwise, Jerry Seligman and colleagues. For more information on the IF approach, see the 1997 book Information flow: The logic of distributed systems authored by Barwise and Seligman. CKML is an extension of OMLAmong other things, this will allow diverse communities of discourse to compare their own information structures, as coded in logical theories a la IF, with that of other communities that share a common generic ontology. Integration of IF theory is current work-in-progress.

The Conceptual Knowledge Markup Language (CKML), an application of XML, is an extension of OML. But the new idea in this version is that CKML is not just an extension of OML, it is a "better" OML in the sense that by using ideas from Information Flow it provides a rigorous, logical semantics for OML.

Where OML had two language parts
Ontology: represents structured intent; is a container of types; registers collections that use the ontology.
Collection: represents structured extent; is a container of instances; points to the associated ontology.
CKML has extra (more refined) language parts
Theory: represents any controlled vocabulary - nested theories represent nested vocabularies; represents ontological structure specified by any (ontology, type) pair which embeds as a theory; specifies an abstract conceptual scale; is carried within an ontology; registers local logics that use the theory.
Theory Interpretation: represents any state space; represents ontological extension which embeds as a theory interpretation; specifies a concrete conceptual scale; is a component of a theory.
Local Logic: in direct conceptual scaling represents any binary relation to a controlled vocabulary; represents ontological structure specified by any collection which embeds as a local logic; represents a realized conceptual scale which is often regarded as a facet of the information space; is carried within a collection; points to the associated theory.
Infomorphism: used somewhat more implicitly; for example, in simple conceptual scaling the state space description function forms the token part of an infomorphism that is split to get a local logic, and in relational conceptual scaling the argument functions of relations form the token part of channel infomorphisms.

Conceptual Interface

Conceptual knowledge processing (CKP) is a principled approach to knowledge management. At the heart of CKP is a basic theorem that establishes the equivalence between the non-hierarchical structure of an incidence relation and the hierarchical structure of a (concept) lattice. The WAVE system provides a conceptual interface that smoothly integrates the basic theorem into the user-level.

Basic Theorem of FCA   WAVE Conceptual Interface
Basic Theorem: Formal Context
Formal Context
or Classification
Basic Theorem: equiv
Basic Theorem: Concept Lattice
Concept Lattice
  WAVE Interface


Please send questions, comments and
suggestions about this page to:
Robert E. Kent

Last modification date: November 1998