"In order to formalize a language, there must be a specification of the signs and symbols of the formal language, as well as a specification of the permissible manipulations of the symbols."

• Constant 
• Variable 
• Operations or Functions
• Predicates
• Logical Symbols
  • Connectors
    • Implication
    • Disjunction (or)
    • Conjunction (and)
    • Negation (not)
    • Logical equivalence (if and only if)
  • Qualifiers
    • There exists (existential)
    • For all (universal)
• Punctuation marks (left and right parentheses; comma)

I think I am trying to say the same sort of thing in my enhanced description of an ontology-like thing.  I pointed out the need for four things:

In my view, the signs, symbols, and formal language of a financial reporting scheme should be as high as possible.  Perhaps a sub-language is necessary to document the higher level language that you use; but I believe the stuff used in the “alphabet” should be used to define things like (I am thinking about the FRF for SMEs reporting scheme elements of a financial report which include things like: assets, liabilities, equity, revenues, expenses, gains, losses, net income, net cash flow, investments by owners, distributions to owners.)

You also need to define other logical terms such as:

• roll up (a + b + c + n = total)
• roll forward (beginning balance + changes = ending balance)
• adjustment (originally stated balance + adjustments = restated balance)
• set

Then, you also need to define permissable logical relations between terms (i.e. if you do not define what is permissable, then ANYTHING is essentially permissable).  These fundamental relations are permissable:

• assets = liabilities + equity (statement of financial position i.e. balance sheet)
• net income = income from operating activities + income from peripheral and incidental activities (statement of operations i.e. income statement)
• beginning equity + net income + investments by owners, distributions to owners = ending equity (statement of changes in equity)
• beginning cash and cash equivalents + net cash flow = ending cash and cash equivalents (statement of cash flow)
• net cash flow = net cash flow from operating activities + net cash flow from investing activities + net cash flow from financing activities

Because some additional terms were used in the definitions of the rules above, you also need to define those terms so that they can be used within the rules of permissable relations:

• cash and cash equivalents
• income from operating activities, note that income from operating activities = revenues – expenses
• income from peripheral and incidental activities, note that income from peripheral and incidental activities = gains – losses

And finally, for my needs, I want to go one level deeper in a few areas of those elements of a financial report and so I also define these terms which are either defined or implied per the FRF for SMEs conceptual framework:

• current assets
• current liabilities
• noncurrent assets (implied by definitions of “assets” and “current assets”)
• noncurrent liabilities (implied by definition of “liabilities” and “current liabilities”)
• equity in noncontrolling interest
• equity in controlling interest (implied by definition of “equity in noncontrolling interest and “equity”)

So that would be my definition of the high-level conceptual framework of the FRF for SMEs reporting scheme.  I have formally defined this financial reporting scheme using the language/syntax XBRL.  Here are those artifacts:

• Human readable version
• Terms (XBRL taxonomy schema which references labels to make the terms more approachable by humans and references to authoritative literature)
• Rules (XBRL formula)
• Facts (XBRL instance which pulls everything together; this is the same thing using Inline XBRL; this is what I wish the inline XBRL would look like; notice you can click on facts or report elements to get details; here are the raw fact tables; and here are the business rules in a separate summary)

Luca Pacioli documented the double-entry accounting model. That model is based on mathematics and mathematics is based on logic.  Don’t think of what I am trying to do as “document what the FASB or IASB or GASB or IPSASB had created” per some financial reporting scheme.

What I am doing is different.  It is my observation that the standard setters are leaving out important information out which makes the standards “open to interpretation” where they really should NOT be open to interpretation.  Essentially, the documentation the standards setters are creating in books have gaps.  They do not have the precision and coverage as is described in C. Maria Keet’s book An Introduction to Ontology Engineering. Precision is a measure of how precisely you do or can represent the information of a domain within an ontology-like thing as contrast to reality.   Coverage is a measure of how well you do or can represent a domain of information within an ontology-like thing.

Or, saying this another way, I am using (a) the conceptual framework defined plus (b) empirical evidence that exists and (c) professional judgement to create an interpretation, a best practice interpretation, that is “precise” and has full “coverage” and proving that model mathematically and logically. 

For what financial accounting need to deliver to business, we must have a system that is provably sound and clear.  The institution of accountancy is built on the framework and theory created by logic and mathematics of double-entry accounting first developed by a Florence bank in 1211 AD and documented by mathematician and Franciscan friar Luca Pacioli in 1494 AD.

Introducing politics or philosophy or religion into the logic and mathematics of how an accounting system operates is not appropriate.  This is not to say that it is wrong to use politics to decide what goes into some financial reporting scheme.  What goes into some financial reporting scheme should be driven by what the users of that financial reporting scheme was created for; its fundamental purpose.

HOWEVER, politicians, regulators, standards setters, and others cannot simply mess with the logic and mathematics of financial reporting.  Those rules are above their pay grade.  Those rules are driven by nature and can be observed and documented but the rules of math and logic cannot simply be changed on a whim.

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Financial reporting comparability: toward an XBRL ontology of the FASB/IFRS conceptual framework