I have explained logical systems in simple terms. Essentially, a logical system is a set of models described by structures that contain terms, associations, assertions (rules); all of which are used to describe facts. All of this is summarized in this video that explains logical systems.
Using that description of a logical system, I created a logical model of a financial report. That financial report logical model is the basis for the forthcoming OMG Standard Business Report Model (SBRM).
I have described two very basic logical systems using three different syntax and a fourth was described in another syntax by someone else: (SFAC6 in OWL/RDF/SHACL is coming soon)
I have tried to extrapolate those simple, easy to understand logical systems that are rather easy to wrap your head around to larger financial report representations, proving that the financial report logical systems are properly functioning and therefore showing what is necessary in order to (a) create properly functioning systems and (b) determine if such a logical system is in fact properly functioning.
Now, the XBRL, Prolog and OWL/RDF/SHACL representations can be called "formal" because there are formal specifications for those syntaxes. The Excel format can at best be called "informal" because there is no formal specification as to how to represent the information within Excel. Also, the Excel format is a bit of a work in progress; I don't have it exactly where I want it right now.
However, if you take the informal Excel representation, and then effectively convert that to one of the formal syntax, say XBRL, then you can say that the informal Excel representation is effectively representing the logic of the financial information represented within Excel.
Why is this important? If I can take complex information, represent that information in any of four different technical syntax, and then use the processing capabilities of different existing tools and get the same "answer" as to what the information is logically conveying; then that is pretty darn good proof that all of the pieces of the logical system is working effectively.
The details of what this complex system needs to be able to do and why is described in my document Special Theory of Machine-based Automated Communication of Semantic Information of Financial Statements. (This 15 minute video provides a good overview of that document.)
While I am using this for financial reporting, the applicability here goes beyond financial reporting to general business reporting and the exchange of any complex information really.
Think semantic spreadsheet!