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 logical patterns and 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, properties, 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. (Wikidata Conceptualization)
  • Model: A model is a set (a.k.a. assembly) of logical structures that are consistent with and permissible interpretations of that model. (Wikidata Model)
  • Structure: A structure is a set (a.k.a. assembly, compound term) of logical statements which describe the structure. (Wikidata Structure; Atomic Design Methodology)
  • 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.  A logical statement is a piece of information.  A logical statement is declarative.  There are five broad categories of logical statements: (Statement on Wikidata; Wikidata Statement)
    • Terms: Terms are logical statements that define ideas used by the logical conceptualization such as “assets”, “liabilities”, “equity”, and “balance sheet”. Terms tend to be nouns. (Wikidata Term)
    • Associations: Associations (a.k.a. relations, predicate) 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”. Associations tend to be verbs. The primary categories of associations are "is-a" and "has-a". Others include "equivalent-to" and "disjointed-from". Financial reporting has specific associations such  as "instance-inflow" and "instance-outflow". (Wikidata Is-a; Wikidata Subclass of; Wikidata Has-Part; Wikidata Part-Of; Wikidata Relation); 
    • 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”. (Wikidata Rule)
    • 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. Dimensions (a.k.a. dimensional fact model, dimensional modeling) can be used to categorize and  differentiate the context of facts. (Wikidata Fact; Wikidata Instance Of) (Wikidata Dimension)
    • Properties (a type of predicate) are logical statements about the important qualities and traits of a model, structure, term, association, rule, and fact. (Wikidata Property)

A logical conceptualization represented by a logical theory can be complete or incomplete (e.g. missing important statements). A logical conceptualization can be consistent or inconsistent (e.g. statements contradict one another). A logical conceptualization can be precise or in error (e.g. statements are not consistent with reality). Rules can be used to guide processes.

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 within limits.

(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 Logical Theory Describing Financial Report provides a logical conceptualization of a financial report.  The Seattle Method uses the logical conceptualization of a financial report.  The Business Rules Manifesto provides important guiding principles.

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