Conservation Law

A conservation law states that a particular quantity remains unchanged as a system evolves. It may be transferred or transformed within the system, but it is neither created nor destroyed.

An invariant is a quantity, relationship, or property that remains unchanged under the allowed transformations of a system.

A conservation law describes what is conserved. An invariant is the mathematical expression of that conservation. A conservation law is a principle; an invariant is the quantity or equation that stays unchanged because of that principle. Here are three examples of systems that adhere to the notion of conservation law:

  • Physics: conservation of energy; energy is not created or destroyed; the energy just moves; the invariant is total energy.
  • Chemistry: conservation of mass (atoms); the inventory of atoms does not change; the count of each atomic species is the invariant.
  • Accounting: conservation of resources and obligations; the resources must always equal the claims on those resources (e.g. obligations); the invariant is the relationship between resources and obligations, they must always be equal.

A useful way to think about these three domains is that they are all state-transition systems constrained by conservation laws.

Energy does not appear out of thin air in physics. Atoms don't appear out of thin air in chemistry.  Resources and claims don't appear out of thin air in accounting. All these state-transitions are explainable.

I have noticed this same pattern being explained in different ways.

Law of Requisite Variety

Requisite variety, in the context of computer science, refers to the principle that in order to effectively regulate a system, the regulator of that system must possess a sufficient range of actions to counter act the variety of important potential disturbances that system might encounter.  The principle of requisite variety ensures that the system's internal state remains as close as possible to the desired goal state of the system.

Effectively, the Law of Requisite Variety requires that there be a balance or "matching" between the potential "perturbance variety" or potential possible disturbances which may occur within a system and the "control variety" which is the information such as rules available to the system to make sure the "residual variety" is as close to 0 as possible, preferably equal to zero.

Ontology Engineering

As I explained in another post on completeness; in her book An Introduction to Ontology Engineering (PDF page 23), C. Maria Keet, PhD, provides discussion about what constitutes a good and perhaps a not-so-good ontology.  There are three categories of errors she discusses and these three ideas are applicable to models:

  • Syntax errors (syntactic quality): If the expression of the model is of some specific machine-readable language, having a syntax error is similar to computer code not being able to compile.
  • Logic errors (semantic quality): If the expression of the model has an error in logic then the model does not reflect what is being modeled and the  model will not work as would be expected.
  • Precision and coverage errors (pragmatic quality, fitness for purpose): If the expression of a model precisely reflect what is being modeled with a high enough level of precision and a high enough level of coverage of the area of interest being modeled then the model might not be adequate enough to meet the needs of the stakeholder of a system that has been modeled. For example, when you neglect to represent a rule and therefore something that should not be permissible appears in the model to be permissible because you neglected to include that rule; then you might not get the result you expect from the model.

Completeness (a.k.a. fitness of purpose, pragmatic quality) of a model is determined by the level of precision (high or low) and the level of coverage (high or low) relative to the specific goal or objective or range of goals/objective that a community of stakeholders has agreed to  with respect to some system of interest. Completeness must match the needs of the workflow.

Completeness is declared by the rules of governance.

Algebraic Semantics of Governed Execution

The paper, Algebraic Semantics of Governed Execution: Monoidal Categories, Effect Algebras, and Coterminous Boundaries, (PDF, page 17), discusses the notion of a "governance algebra" that provides safe, transparent, and proper governance for artificial intelligence agents.  That algebra has the notion of a fragment of information coinciding to the governance information for that fragment.

KROG Rules

KROG is formal semantics and rule language for rights, obligations, and governance. KROG specializes in the legal industry. KROG expresses a conservation law for the relationship between knowledge, rights, obligations, and governance which effectively says:  (K ∩ R ∩ O) ⊆ G (Every valid action satisfies Knowledge (K) intersection Rights (R), and intersection Obligations (O); and remains contained within Governance (G).

Pattern

The pattern that I am seeing is that accounting, governance, and accountability all fit together and that "bunch of capabilities" is generally applicable and not simply for the accounting of money in an enterprise.  While, perhaps, not needed for all artificial intelligence agents; if it is the case that there is zero tolerance for error, you need traceability/trackability, you need an audit trail, and there needs to be someone to blame if something goes wrong; there is a way to achieve that.

Information does not appear from thin air on the internet. Either a human or a machine created it. It should always be clear not only by which, but also by whom; which human, which agent, which organization. And that creator should be held accountable for that information.  That is the price, the responsibility, that provides you with the right of free speech.

If you use information there there is no trust or confidence; your injury, it seems to me, can be considered self inflicted.  Good governance, good accounting, and good accountability can minimize that injury.

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