Standards Based Logical Twin Terminology

Below is an "inventory" of terminology I use to describe what I now refer to as "logical twin" or "logical digital twin" or "digital twin" of a financial report (a.k.a. financial report knowledge graph).  After I complete the full inventory, I will synthesize this into a practical and useful resource for general business reports.  The point of this exercise is to create a description of a knowledge-based system (a.k.a. knowledge graph, problem solving system) that is understandable to business professionals who desire to make use of such systems. This explanation will evolve and improve. Fundamentally, this is driven by systems thinking and systems engineering.

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The objective of the system is the effective exchange of information.  Important to the system is the elimination of “wild behavior” by accountants when report model of report being created can be modified.

• Description of report (specification of what is permitted); created by standards setter or regulator or anyone else specifying a report
• Machine readable form
• Machine readable form converted to human readable form
• Create report based on description (assisted by software utilizing machine readable description)
• Verify that report has been created per description (assisted by software utilizing machine readable description)
• Extract information from report per report description (assisted by software utilizing machine readable description)

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Logic is a formal system that defines the rules of correct reasoning.  Logic helps us understand the meaning of statements (a.k.a. declarative sentence) and to produce new meaningful statements. Logic is the glue that holds strings of statements together and pins down the unambiguous meaning of those statements. The elements of logic or building blocks of logic are describable. (formal language; mathematical logic; set theory; category theory; model theory; computability or recursion theory; proof theory; situation theory workflow)

A system is a group of interacting or interrelated elements that act according to a set of logical rules to form a unified whole.  A system is a set of parts (a.k.a. elements or atoms) that work together and that form a whole.  A system has boundaries.  A system can be natural, such as the solar system, or designed by humans, such as a bicycle. A system tends to have some deliberate, intentional aim; it has goal(s) and/or objective(s).  Systems evolve: genesis, custom, product, commodity.

A logical system, which has logical patterns of behavior which can be explained using logic, can be described using a logical theory.

A logical theory is a set of logical statements that explains the logical patterns of a logical system. A logical theory is an abstract conceptualization of specific important details of some area of knowledge. A logical theory tends to be a simplification of the important details of an area of knowledge with a focus on attaining specific goals or achieving specific objectives. The logical theory provides a way of thinking about an area of knowledge by means of the logic of deductive reasoning to derive logical consequences of the logical theory. (a.k.a. formal system; axiomatic system; logical axiom, declarative sentence, statement)

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 the aim of and knowledge in some area of knowledge.

Atomic design methodology is an approach to thinking about logical systems in a deliberate, hierarchical way. The building blocks of a logical system are atoms, molecules, organisms (a.k.a. assemblies; compound organisms; species).

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

• Logical conceptualization: A logical conceptualization has a set of models that are consistent with and permissible per that logical conceptualization.
• Model: A model has 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 declaration, 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, or fact.

Fundamentally, a logical conceptualization is a set of logical statements that form a logical theory.  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 theory 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. Once in machine-readable form, those logical statements can be interrogated using software applications. To the extent that this can be done effectively; software tools can assist professional accountants, financial analysts, and others working with those logical statements. A logical system is said to be consistent with a logical theory if there are no contradictions with respect to the logical statements made by the logical theory that describes the logical system. Consistent is defined as there being no logical contradictions or logical inconsistencies within the logical theory.

A logical theory can have high to low precision and high to low coverage with respect to describing a logical system. Precision (a.k.a. sound) is a measure of how precisely the information within a logical theory has been represented as contrast to reality of the logical system for the area of knowledge. Coverage is a measure of how completely information in a logical theory has been represented relative to the reality of the logical system for the area of knowledge.

When a logical system is consistent (a.k.a. valid) and it has high precision and high coverage the logical system can be considered a properly functioning logical system. When a system is working right, it creates a virtuous cycle. A logical system can be proven to be operating (a.k.a. properly functioning logical system; satisfies the goals/objectives; Book of Proof) per the logical theory that describes the logical system.

A system is in effect “blind” to things not covered by that systems rules. When coverage is not complete, blind spots can exist.

* The terms "precision" and "coverage" come from the book An Introduction to Ontology Engineering (PDF page 23), C. Maria Keet, PhD.

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A line of reasoning is an explanation of an approach to solving a problem or reaching a conclusion.

A line of reasoning has a problem solving method which could be forward chaining, backward chaining, sequential, or a hybrid which combines different reasoning approaches.

Logical reasoning is about arriving at a conclusion in a rigorous way.  There two broad categories of logical reasoning: deductive and non-deductive.  

Deductive reasoning provides a result that is guaranteed to be certain, therefore the result can be relied upon without doubt and humans need not be involved in a process because of the certainty of deductive reasoning.  Non-deductive reasoning, on the other hand, is not certain, meaning it could be correct but it could also be incorrect.  Non-deductive reasoning is based on probability.  Non-deductive reasoning is always fallible; there is always the possibility of error. And so non-deductive reasoning approaches must have a human in the loop to deal with that uncertainty.  There are three types of non-deductive reasoning: inductive, abductive, and analogy.

Semantics is study of linguistic meaning. (Formal semantics)

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Data is raw and unprocessed and tends to be understandable only in one context.  Information is data in context and has been processed and organized. Knowledge is refined and actionable information that has been processed, organized, and/or structured in some way making the information super-useful.  Insight and wisdom come from applying knowledge to some specific situation.

Knowledge is a form of familiarity with information from some specific area. Knowledge is often understood to be awareness of facts, having learned skills, or having gained experience using the things and the state of affairs (situations) within some area of knowledge.  An area of knowledge is a highly organized socially constructed aggregation of shared knowledge for a distinct subject matter.  An area of knowledge has a specialized insider vocabulary, underlying assumptions (axioms, theorems, constraints), and persistent open questions that have not necessarily been resolved (i.e. flexibility is necessary).  You can think about an area of knowledge as being characterized in a spectrum with two extremes:

• Kind area of knowledge: clear rules, lots of patterns, lots of rules, repetitive patterns, and unchanging tasks.
• Wicked area of knowledge: obscure data, few or no rules, constant change, and abstract ideas.

Sensemaking is the process of determining the deeper meaning or significance or essence of the collective experience for those within an area of knowledge. System stakeholders need to be in agreement as to an undisputed core knowledge of a system.  The Cynefin Framework provides a tool for understanding and categorizing knowledge.  Per the Cynefin Framework, knowledge can be categorized as being:

• Best practice (obvious)
• Good practice (only obvious if you have the right skills and experience)
• Emergent practice (tend to have to have more skills and experience, then can use principles to group alternatives)
• Novel practice (tends to be unique, but describable)

Knowledge of facts is distinct from opinion or guesswork by virtue of justification or proof.  Knowledge is objective.  Opinions and guesswork are subjective.  In our case we are talking about certain specific knowledge, the facts that make up that knowledge, being able to create a proof to show the knowledge graph system is complete, consistent, and precise;  and all of this logic being put into a form readable by a machine and reach a conclusion as to whether the information in the knowledge graph is functioning properly. Effectively, a machine can read that knowledge and mimic understanding of that knowledge represented in a knowledge graph and the information available to both a human reader and a machine reader would be the same and therefore the human and machine should reach the same conclusion.

Formally, knowledge graphs are part of graph theory and network theory. (a.k.a. semantic network; knowledge representation) Those explanations tend to be on the technical side.  I contend that a more approachable way to explain knowledge graphs is to use tools provided by the discipline of philosophy; specifically logic.  Why use logic?  Well, fundamentally knowledge graphs represent logic.  All these other explanations tend to focus on HOW to represent that logic rather than focusing on WHAT is being represented by a knowledge graph.  To explain knowledge graphs, you need more than just graph theory and network theory.  A knowledge graph is a designed (man made) logical system. The elements of logic play a roll in explaining knowledge graphs. Ontology-like things are part of knowledge graphs, so that information is necessary.  I want to use an atomic design methodology in the explanation of a knowledge graph.  I want to borrow some terms from situation theory to describe knowledge graphs; namely the notion of an "infon" and the notion of a "state of affairs".

A hypergraph is a special type of knowledge graph. A knowledge hypergraph is a collection of pairs of knowledge and can be used to document and explore information.

A neighborhood is other sets of facts that related to a fact.

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By "knowledge graph" I mean professional knowledge graph.  A professional knowledge graph is defined to be a strongly typed directed acyclic labeled property graph of semantic knowledge which includes a logical schema (a.k.a. data contract subgraph).  Professional knowledge graphs provided global content addressability.

A knowledge assembly is a set of knowledge graphs that, when processing, is seen as one unitary knowledge graph.

A knowledge graph system is a system driven by knowledge graphs.

A knowledge hive or "semantic hive" or a "hive plot" is a group that has a similar view and have similar "ontological commitment" or "knowledge commitment". Effectively, each "semantic hive" or "hive plot" is mutually exclusive: you belong to one semantic hive or another semantic hive, you cannot belong to both because that would be illogical.

A subgraph is a part of a knowledge graph (a.k.a. infon; induced subgraph; semantic subgraph).  A subgraph or infon is a unit of information.  This could be a hypercube, an assembly, a block of information.

Knowledge commitment is like ontological commitment which refers to the agreement to use a shared vocabulary, associations, and rules in a coherent and consistent manner within a specific context.

Classification is a broad concept that comprises the process of classifying, the set of groups resulting from classifying, and the assignment of elements to pre-established groups. Classification allows something to be described, allows for that description to be explained to others or to a software application, and allows for a description to be verified against that description.

Using a machine-understandable knowledge graph represented using a global standard technical syntax such as XBRL; it is possible to describe well understood and agreed upon quantitative and qualitative associations between financial facts or sets/assemblies of financial facts within a report, such as a financial report, more granular information in accounting working papers or audit schedules, or even non-financial information.  Such associations can have any degree of complexity or granularity, without sacrificing accuracy or nuance.

This information can then be reasoned on using a logic engine such as DATALOG which is an implementation of nearly a complete set of first order logic (i.e. some risky capabilities were removed from PROLOG to arrive at DATALOG in order to guarantee that catastrophic logical failures caused by logical paradoxes do not occur and therefore the knowledge graph processing is certain and reliable).

When two different logical systems communicate with one another, it is important that these systems share a common world view.  For safety and reliability the following world view alternatives should be shared by different logical systems exchanging information:

• Closed World Assumption  (used by relational databases) is preferred to the open world assumption which can have decidability issues;
• Negation as failure  (used by relational databases) should be explicitly stated;
• Unique name assumption  (used by relational databases) should be explicitly stated;
• Axiomatic (Zermelo–Fraenkel) set theory is preferred to naïve set theory.
• Dimensional fact model should be used.

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A logical twin or logical digital twin is effectively a professional knowledge graph. A logical twin is a deliberate innovation that is intended to be safe, practical, and consistently reliable.

A knowledge product is refined and actionable information that has been processed, organized, and/or structured in some way or put into practice in some way making the information super-useful.  The information is ready to use.  The knowledge is derived from expertise, research, lessons learned.  Knowledge products allow the user of the knowledge product to make informed decisions or better decisions.

• Data product: a reusable raw and unprocessed data asset, engineered to deliver a trusted dataset to a user for a specific purpose.
• Information product: organized, processed, and perhaps even interpreted data which provides context and meaning.
• Knowledge product: refined and actionable information that has been processed, organized, and/or structured in some way or put into practice in some way making the information super-useful.
• Decision product: tell a business professional what they need to do or actually execute an action making use of the information of the decision product.

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There tends to be three primary problem solving system implementation approaches: 

• Semantic web stack, 
• Graph database, 
• Logic programming.

All of this enables the possibility of creating Smart (Cognitive) Business Applications and Services. The law of irreducible complexity helps one understand that you cannot leave any of these parts out and expect the system to function correctly.  The law of conservation of complexity helps one understand that complexity cannot be removed from a system; but the complexity can be moved.

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The Law of Conservation of Complexity states that, "Every software application has an inherent amount of irreducible or essential complexity. The question is who will have to deal with that complexity: the application developer, the platform developer that the software runs on, or the software user."

Irreducible Complexity (a.k.a. essential complexity) is a term used to describe a characteristic of complex systems whereby the complex system needs all of its individual component systems in order to effectively function. (To effectively satisfy the aim of the system; meet the goals/objectives of the stakeholders of the system.)

Simple means that all accidental complexity that can be removed from a system, has been removed from the system; only essential complexity remains.

Simplistic means that essential complexity has been removed from a system in order to reduce overall system complexity and therefore the system cannot satisfy the aim or goals or objectives of the system.

Complexity can be broken down into two parts: essential complexity and accidental complexity.

A kludge is an engineering/computer science term that defines what is best described as a workaround or quick-and-dirty solution that contains excessive accidental complexity and is typically clumsy, inelegant, inefficient, difficult to extend and hard to maintain; but it gets the job done and includes all the necessary essential complexity. The nautical term for this is jury rig.  By contrast, elegance is beauty and gracefulness that shows unusual effectiveness and simplicity in a system that is free from accidental complexity.

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The Logical Theory Describing Financial Report (Terse), Financial Report Pieces, and Standard Business Report Model (SBRM) describe the logical statements which make up the logical theory that describes a financial report.  The Seattle Method is an approach to working with XBRL-based digital financial reports.

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A general-purpose financial report is a true and fair representation of information about an economic entity.  A financial report is not the actual economic entity, it merely conveys fairly high-fidelity information about an economic entity that is generally of very high-quality.  Consider the following use case of a general-purpose financial report:

Two economic entities, A and B, each have information about their financial position and financial performance. They must communicate their information to an investor who is making investment decisions which will make use of the combined information so as to draw some conclusions. All three parties (economic entity A, economic entity B, investor) are using a common set of basic logical principles (facts, statements, deductive reasoning, etc.), common financial reporting standard concepts and relations (i.e. US GAAP, UK GAAP, IFRS, IPSAS, etc.), and a common world view so they should be able to communicate this information fully, so that any inferences which, say, the investor draws from economic entity A's information should also be derivable by economic entity A itself using basic logical principles, common shared financial reporting standards (concepts and relations), and common world view; and vice versa; and similarly for the investor and economic entity B.

There is no natural way to represent an economic entity the way it “really is” in the real world; there are just certain purposeful and agreed upon selections of specific aspects of an economic entity, call them abstractions or models, that provide a useful enough simplification that satisfies specific goals we might have.  That is the nature of a general-purpose financial report, to represent information about an economic entity for a specific purpose. That representation is good enough to be useful. This is part of the universal technology of accountability.

Financial report knowledge graphs can be interrogated systematically and logically using machine-based processes.

Additional Resources:

• Distinguishing Between Good, Less Good, Bad, and Worse Ontology-like things
• Logical Theory Describing Financial Report (Terse)
• Financial Report Knowledge Graphs
• Method in Simple Terms (Video)
• Deductive and Inductive Arguments: What is the Difference? (Psychology Writing)
• Explaining Knowledge Graphs Logically
• Business Rules Manifesto
• Elements of Logic
• Logic Gates: The Building Blocks of Logical Circuits
• Logic Programming and Theories
• Deductive vs Inductive vs Abductive Reasoning
• Semantics of Contracts and Clauses
• Legal Documentation Hypergraph Specification
• Knowledge, Data, and LLMs
• Your Data Should be Beautiful
• Systems Theory: Method to my Madness
• Using logic programming for theory representation and scientific inference
• Puzzle Pieces for Digital Financial Reporting
• Modernizing the Global Audit Machine for the Future
• All About Knowledge
• Special Purpose Logical Spreadsheet for Accountants
• Multidimensional Data Literacy
• What is a Knowledge Graph? (Mike Dillinger)