Understanding and Expressing Logical Systems
Wednesday, September 25, 2019 at 07:37AM
Charlie in Becoming an XBRL Master Craftsman

A general purpose financial report (or business report) is a type of man-made logical system (a.k.a. logical theory).  There is nothing natural about a general purpose financial report (or business report), it is an invention of man.  A general purpose financial report is a high-fidelity, high-resolution, high-quality information exchange mechanism.

Logic is a set of principles that forms a framework for correct reasoning. Logic is a process of deducing new information correctly so that a chain of reasoning can be created.  Logic is a systematic way of thinking. Logic is about the correct methods that can be used to prove a statement is true or false.  Logic tells us exactly what is meant.  Logic allows systems to be proven.  Logic is a tool. Logic is a common language that can be agreed upon, understood by all parties, and which therefore enables precise communication.

Something is logical if it works according to or agreeing with the principles of logic.

A system is a cohesive set of interrelated and interdependent parts that form a whole.  A system can be either natural or man-made. Changing one part of a system usually affects other parts and the whole system with predictable patterns of behavior.

A logical system is a type of formal system.  To be crystal clear I mean a finite deductive first-order logic system. The point is to create a logical system that has high expressive capabilities but is also a provably safe and reliable system that is free from catastrophic failures and logical paradoxes (world view): axiomatic (Zermelo–Fraenkel) set theory; directed acyclic graphs; model theory; closed world assumption; negation as failure; unique name assumption; Horn logic. (a.k.a. logical theory, strong ontology; see the ontology spectrum)

There are many different ways to describe formal systems in human-understandable and machine-understandable terms.  ISO/IEC 11179-3:2013 describes this sort of information in global standard but technical terms.  It is my observation that each different approach to describing a formal system tends to have its own terminology for explaining what seems to be exactly the same thing, the explanations tend to not always be complete, and the explanations tend to be harder than necessary for a business professional to understand.

OMG's Ontology Definition Metamodel (ODM) tries to reconcile many different ways to represent logical systems.

This is my current best shot at explaining how to express the semantics of a logical system and map those semantics to the XBRL technical syntax in terms understandable to a business professional.

A logical system enables a community of stakeholders to agree on important common models, structures, and statements for capturing meaning or representing a shared understanding of and knowledge in some universe of discourse where specific flexibility/variability is necessary.  Because flexibility/variability is allowed in this sort of logical system, that flexibility/variability must be managed so that it can be controlled.  Models, structures, and statements allow for this necessary management and control.

The models, structures, and statements of a theory relevant to a particular universe of discourse generally allows for some certain specific system flexibility/variability and as such must be consciously unambiguously and completely as is necessary and practical in order to achieve a specific goal or objective or a range of goals/objectives.

A logical system can have high to low precision and high to low coveragePrecision is a measure of how precisely the information within a logical system has been represented as contrast to reality for the universe of discourse.   Coverage is a measure of how completely information in a logical system has been represented relative to the reality for a universe of discourse.

The level of precision and coverage expressively encoded within some logical system depends on the application or applications being created that leverage that logical system.

Further, a properly functioning logical system will have the following characteristics all of which should be demonstratable: 

Saying this in another way specifically for a financial report: (note that the term "statement" as is being used as defined by the components of a logical system, this is not the same as statement defined in terms of financial reporting)

All that is above relates to specifying the permissible semantics of a logical system.  The terms below tend to be related to the expression of those semantics in the form of some technical syntax:

Again, this is my current best attempt to represent this information.  Any feedback that improves this representation will gladly be considered.

Here is a comprehensive example of expressing the above semantics using the XBRL technical syntax.

Also, consider this.  If accountants do not bother to gain basic literacy in this information which inevitably will affect their lives; then they abdicate control over their future whether they like it or not. Check out this Ted Talk by Eli Pariser, Beware Online "Filter Bubbles".  Accountants need to pay attention. If you are stuggling to understand this information, I suggest reading this document.

Article originally appeared on XBRL-based structured digital financial reporting (http://xbrl.squarespace.com/).
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