Practical, Simple Explanation of a Logical System (Draft 1)

First, I have tried and tried to find a simple, practical, and complete explanation of the high-level model of a logical system. Rather than find that, I have found 50+ incomprehensive descriptions, most of which are incomplete.  Second, at the logical level of a system, the logical model of that system should be exactly the same for any physical implementation.  Meaning, the high-level logical model of EAV, RDF, PROLOG, GQL, XBRL, or any other physical implementation should be exactly the same. Further, propositional logic and predicate calculus likewise should be able to be described at a high level.

Here is my attempt to provide a practical, simple explanation of a logical system which is approachable to liberal arts majors (i.e. nontechnical oriented, an explanation approachable to business professionals). Effectively, I see this as a "meta-meta-model" that every logical system falls within.

Simple, Practical Explanation of a Logical System

Logic is a formal set of principles that form a framework for correct reasoning and communications.  

A logical statement is a proposition, claim, assertion, belief, idea, or fact about or related to a logical system.  A logical statement is a piece of information.  A logical statement is declarative (e.g. not a question).

A logical system is a group of interacting or interrelated logical statements that act according to a set of logical patterns to form a unified whole or conceptualization.  

A logical theory is a logical system that formal, explicit, deliberate specification of the important specific details of an intended shared conceptualization between a set of stakeholders of a system for an area of knowledge to achieve some specific set of goals/objectives. 

  • Conceptualization: Set of declarative logical statements that describe what is permissible per a system. Conceptualizations describe/specify, enable creation/construction, enable review/verification, and enable extraction/analysis.
  • Model: Set of logical statements that form/describe structures that are consistent with and permissible interpretations of that model. Models provide flexibility.
  • Term: Logical statement that defines/describes an idea/thing which is used within the logical conceptualization and distinguishes one idea/thing from other ideas/things. Ideas/things tend to be nouns.
  • Structure: Set of logical statements and type of term which describe assemblies of terms, associations, and restrictions.  A structure is an assembly of terms, associations, restrictions that are consistent with and permissible per that structure (compound, decomposable). A structure is a compound idea/thing and can be decomposed. Structures provide the ability to identify, refer to, and work with sets of ideas/things.
  • Association: Logical statement that describes a permissible interrelationship between an idea/thing within a structure. Associations tend to be verbs.
    • Type: Logical statement that groups or classifies an idea/thing into a useful set. A type is an important category of association. (a.k.a. class, subclass, superclass, generalization, specialization, wider, narrower)
    • Part: Logical statement that indicates that an idea/thing is part of some other idea/thing (a.k.a. part-of, has-part). Category of association.
    • Property: Logical statement that describes the important qualities/traits of a model, structure, term, association, or restriction. Category of association.
  • Restriction: Logical statement that describes a rule, constraint, or assertion of a structure or model.  Restrictions tend to be convertible into IF…THEN…ELSE types of logical statements. Restrictions can be connected together by joining restrictions using logical connectors (e.g. AND, OR, NOT, NOR, XOR, NAND).
  • Fact: Logical statement about the numbers and words that are described by and instances of a model.  Facts are differentiated from other facts using aspects (a.k.a. dimensions) which provide explicit context.

A conceptualization can be complete or incomplete (e.g. missing important logical statements); can be consistent or inconsistent (e.g. logical statements contradict one another); can be precise or imprecise (e.g. logical statements are not consistent with reality). A properly functioning logical system is said to be verifiably complete, consistent, and precise.

A conceptualization can be adequate or inadequate meaning that the conceptualization tested and validated to yield reliability and accuracy consistent with the specified purpose of the conceptualization's stakeholders.

This is my take on the relationship between the high-level:

If you have any feedback that would improve this representation, please send me your feedback.

So the above represents the "meta-meta-model" of a logical system. 

The Logical Theory Describing Financial Report and Financial Report Pieces describe a "meta-model" of the logical conceptualization of a financial report.  

The PROOF and SUPER PROOF and AASB 1060 represent financial reporting scheme base models (prototypes). Each of these financial reporting scheme base models have "reference implementations" of financial report models.

XBRL-based financial reports submitted to the U.S. Securities and Exchange Commission (SEC) using US GAAP and IFRS and European Single Market Authority (ESMA) using IFRS all fit into the above report models, base financial reporting scheme models, financial report meta-model, and logical system meta-meta model.

Additional Information:

Inputs that drove the above representation include but are not limited to:

Comments

Post a Comment

Popular posts from this blog

Relational Knowledge Graph System (RKGS)

Image
Relational Knowledge Graph System (RKGS) is an interesting idea that combines the relational paradigm and the knowledge graph paradigm.  This documentation, Why RKGS , explains the idea. This gets even more interesting with the notion of "relational AI".  RelationalAI is described as follows by the company of the same name, Relational.ai : “RelationalAI is a cloud-based relational knowledge graph management system, with state of the art probabilistic processing and declarative reasoning at scale to make developing Data Applications a superpower for your business.” This notion of knowledge graphs represented in relational databases fits into my belief that knowledge graphs have two aspects: the expression SYNTAX and the logic of what is expressed or SEMANTICS. While the LOGIC of a knowledge graph is always the same regardless of technical syntax used to express that logic; there are many, many different technical syntaxes that can be used to represent a knowledge graph. There
Read more

Getting Started with Auditchain Luca

Image
The Innovator's Dilemma points out that disruptive innovations often look like toys that are doing everything wrong. Auditchain Luca , which is part of the Auditchain Suite , is a unique approach to creating a knowledge graph .  To experience using Auditchain Luca, have a look at the Getting Started with Auditchain Luca instructions. Be sure to grab the Excel and JSON import files used for this getting started exercise.   This getting started exercise uses one of several different approaches to getting information into a tool for constructing and viewing professional quality knowledge graphs .  Additional getting started guides will be made available over time. Auditchain Luca might not make sense to you if you don't understand the paradigm shift that is occurring and if you have not shifted your mental map. For the next step in your journey, consider trying creating a report using a financial reporting scheme template . If you are struggling to figure out how to register or
Read more

Evaluating the Quality of XBRL-based Financial Reports

Image
From the time public companies started submitting XBRL-based financial reports to the U.S. Securities and Exchange Commission, I have been looking at those reports, trying to understand the XBRL-based reports, and trying to figure out how to get them right.  That information was used to figure out how to create software applications that help professional accountants get these reports right. Here is information that summarizes my testing and results which I stopped doing March 31, 2019: Analysis of the high level accounting relationships in the 10-Ks of about 5,716 financial reports  (5,063 public companies, about 89.1% got all these high level accounting relationships consistent with expectation, 623 were inconsistent and manual confirmation revealed the inconsistency was an error) Documentation that helps you understand 26 different types of errors in XBRL-based reports High quality documentation of hundreds of errors in XBRL-based reports submitted by public companies to the SEC Doc
Read more