Modeling Primitives as Music Keys

Johann Sebastian Bach’s ‘The Art of Fugue’ Original Manuscript


In music, keys are set of notes that form an harmonic foundation for musical pieces. They are not constitutive of music itself but socially defined constructs which vary with cultures and kinds of music. As far as Western music is concerned, seven basic keys (noted A-G) can be applied to music pieces, with pieces often played in more keys than their native one.

Applying the same principle to systems modeling, models would be compared to musical pieces, composed according to a set (or key) of modeling axioms (or notes) ensuring their validity (or harmony). And like musical pieces, models could be expressed or translated (played) using different sets of axioms (or key) without unwarranted assumptions with regard to the truth of representations.

Applying the principle to systems modeling brings clear benefits:

  • It circumscribes semantics controversies to small sets of clear-cut definitions meant to be either accepted or rejected as they are.
  • Axioms can serve as firebreaks in thesauruses preventing circular definitions.
  • Like keys for music variations, axioms enable open-ended definitions, facilitate translations, and can serve as semantic bridges between alternative representations.

To that end, and assuming standard logic, seven axioms are proposed to support the kernel semantics.

Axioms as Modeling Keys

Caminao Kernel (CaKe) Axioms


Physical or symbolic occurrences of objects or phenomena (both accepted as postulates): The distinction between physical and symbolic instances is not exclusive (consider hybrids); additionally, fictional instances are instances (physical or symbolic) that are not meant to be realized. Instances are represented by individuals in OWL.

Symbolic Account of Physical instances


Set of instances managed uniformly, independently of their nature.

Collection & Container


Unique value associated with an instance: External identities are defined independently of the organization or system under consideration. External identities can be biological, social, or designed; they are not exclusive (e.g., social security number and fingerprints). Internal identities are used to manage systems components independently of environments. 

Biological, Social, & Fictional Identities

Symbolic Representations

  1. A symbol is a sign pointing to something else (referent).
  2. A symbolic representation is a symbol pointing to a set of instances.
  3. A symbolic object is an object representing a referent; this means that symbolic objects can be physical, as they usually are.


The ability of an instance to change the state of instances, including itself: Objects are either active (with behavior) or passive (without behavior), and the propriety is exclusive.

Asynchronous (placid) & Synchronous (acid) Behaviors


Named sets of values that characterize instances of objects (actual or symbolic), processes, or representations, between events. Stateful objects and activities come with a finite number of discrete states; stateless ones don’t have this limited array, and may indeed have an infinite number of discrete states.

Physical & Expectations States


Change in the state of objects and phenomena: External events are changes triggered from outside the organization or system under consideration.

Digital, Symbolic, & Physical Events


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