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:

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