Simple Explanation of Logical Systems and Logical Theory

Logic is a formal system that defines the rules of correct reasoning.  A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole.  A system can be natural, such as the solar system, or designed by humans.

A logical system, which has logical patterns of behavior, can be explained by a logical theory.  A logical theory is an abstract conceptualization of specific important details of some area of knowledge. The logical theory provides a way of thinking about an area of knowledge by means of deductive reasoning to derive logical consequences of the logical theory. (a.k.a. formal system)

A logical theory enables a community of stakeholders trying to achieve a specific goal or objective or a range of goals/objectives to agree on important logical statements used for capturing meaning or representing a shared understanding of and knowledge in some area of knowledge.

A logical theory forms a logical conceptualization and is made up of a set of logical models, structures, terms, associations, rules, and facts. In very simple terms,

  • Logical conceptualization: A logical conceptualization is a set of models that are consistent with and permissible per that logical conceptualization.
  • Model: A model is a set of structures that are consistent with and permissible interpretations of that model.
  • Structure: A structure is a set of logical statements which describe the structure.
  • Logical statement: A logical statement is a proposition, claim, assertion, belief, idea, or fact about or related to the area of knowledge to which the logical conceptualization relates.  There are five broad categories of logical statements:
    • Terms: Terms are logical statements that define ideas used by the logical conceptualization such as “assets”, “liabilities”, “equity”, and “balance sheet”.
    • Associations: Associations are logical statements that describe permissible interrelationships between the terms such as “assets is part-of the balance sheet” or “operating expenses is a type-of expense” or “assets = liabilities + equity” or “an asset is a ‘debit’ and is ‘as of’ a specific point in time and is always a monetary numeric value”.
    • Rules: Rules (a.k.a. assertions, restrictions, constraints) are logical statements that describe what tend to be convertible into IF…THEN…ELSE types of relationships such as “IF the economic entity is a not-for-profit THEN net assets = assets - liabilities; ELSE assets = liabilities + equity”.
    • Facts: Facts are logical statements about the numbers and words that are provided by an economic entity within a financial report.  For example, the financial report might state “assets for the consolidated legal entity Microsoft as of June 20, 2017 was $241,086,000,000 expressed in US dollars and rounded to the nearest millions of dollars.
  • Properties are logical statements about the important qualities and traits of a model, structure, term, association, rule, and fact.

Fundamentally, a logical conceptualization is a set of logical statements.  Those logical statements can be represented in human-readable form or they could be expressed in machine-readable form using a knowledge graph.  Once in machine-readable form, those logical statements can be interrogated using software applications.  To the extent that this can be performed effectively; software tools can assist professional accountants, financial analysts, and others working with those logical statements; augmenting their skills.

A logical system can be proven to be operating per the logical theory that describes the logical system.

(Image from Clipart Library)

The Standard Business Report Model (SBRM) provides a logical conceptualization of a business report. A financial report is a type of business report.  The Seattle Method provides a logical conceptualization of a financial report.  The Business Rules Manifesto provides important guiding principles.

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