Logical Theory

A logical theory is a coherent set of logical statements that expresses a shared conceptualization of a domain of understanding (a.k.a. area of knowledge) to which a community of stakeholders is committed. A theory specifies the elements of the domain of understanding, the connections among them, the conditions that must always hold, and the facts and properties that characterize that domain of understanding. The that theory can be used by an implementation (a.k.a. representation). This is consistent with the triangle of meaning.

Below is terminology which is a metatheory which provides part of what amounts to a "building code" for constructing a theory in a consistent manner. Currently, different technical frameworks use different terms and some frameworks don't have the capability to express certain things because they are incomplete.

The intention here is to explain many different technical oriented things using terminology which is approachable by someone with a liberal arts degree (i.e. you don't need a degree in computer science). This is one possible vocabulary, there are other possible vocabularies.  The point is, a clear vocabulary is useful:

  • Logical conceptualization: A logical conceptualization is the worldview of a domain expressed in logical form. It defines the set of permissible models; all models that are consistent with the assumptions, distinctions, and rules of the conceptualization. (I think this is the metamodel.)
  • Model: A model (a.k.a. assembly) is a permissible interpretation of the conceptualization. It consists of a set of structures that satisfy the constraints of the conceptualization and instantiate its elements, connections, and conditions.
  • Structure: A structure (a.k.a. organism, subassembly, compound element, complex element, composite element, artifact, module, shape) is a compound element composed of logical statements that describe how a portion of the domain is organized. Structures assemble elements and connections into meaningful configurations. A structure defines something. (Same as SHACL shape)
  • Logical statement: A logical statement is a declarative proposition about the domain of understanding; a claim, belief, idea, notion, or fact. Logical statements are the units of meaning of the conceptualization and there are five broad categories (a.k.a. molecules) of logical statements:
    • Element (a.k.a. term, report element, thing, entity, node): An element is a logical statement that defines an idea or notion used by the logical conceptualization. An element is a unit of thought. An element may be primitive and therefore not decomposable or an element can be compound and decomposable into a set of primitive elements.  An example of primitive elements might be "assets”, “liabilities”, and “equity”. An example of a compound element might be “balance sheet”. Elements tend to be nouns. (Same as SKOS concept.)
    • Connection: (a.k.a. associations, relations, interrelationships, edge, dependent objects): Connections are logical statements that describe permissible relations between elements.  Connections assemble elements into structures and structures into models. An example of a connection is the statement "assets is part of the balance sheet".  Connections tend to be verbs.  The  following are common types of connections: (Same as SHACL rule)
      • Categorization (is-a, type of, general-special, class-of)
      • Compositional (has-a, part of, has part, whole part, instant-inflow, instant-outflow)
      • Aggregational (summation, mathematical)
      • Navigational (parent-child but where ordering does not matter)
      • Presentational (parent-child where ordering matters)
      • Simile (elements that are similar but not identical)
      • Equivalent (elements that are exactly the same)
      • Disjointed (elements that are explicitly not part of)
    • Condition (a.k.a. assertions, restrictions, constraints, axioms, rules): A condition is a logical statement that always must be satisfied within any valid model. Conditions can be connected using logical connectors (e.g. AND, OR, NOT, NOR, IF) and make use of logical operators (e.g. +, =, /, *. <, >, ^). An example of a condition is "Assets = Liabilities + Equity". (Same as SHACL rule)
    • Fact: A fact is a logical statement representing a measurement or observation typically expressed with numbers and words. For example, a fact might be “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. aspects, axis, facet) can be used to distinguish and differentiate the context of facts. (Same as RDF binary relation instance)
    • Property (a.k.a. quality, trait, attribute):  A property is a logical statement describing the important characteristics of a model, structure, element, connection, condition, or fact. An example of a property is "assets is a debit". (Same as OWL object property)
The following world view is assumed. Unless otherwise stated a closed world assumption is assumed. Unless otherwise stated Horn-clause logic is assumed.  Unless otherwise stated negation as failure is assumed.

Type theory is a foundational framework in mathematics and computer science that classifies elements, connections, and conditions based on their properties and behavior.  Think of types as a formal way of classifying things.  The Curry-Howard correspondence is a fundamental concept in type theory that establishes a deep connection between logic and computation, stating that types correspond to logical statements (elements, connections, conditions, facts) correspond to proofs.

Type theory enables formal verification.  A simple metaphor to cooking is that: molecules are the ingredients, proofs are like recipes, types are like dishes. Imagine: A type is a dish you want to make. A set of declarative rules is a recipe for that dish. A proposition is the name of the dish. A proof is the recipe that shows how to make it. If you can produce a recipe (declarative rules), the dish exists (the proposition is true). If no recipe exists, the dish is impossible (the proposition is false).

Following Atomic Design Methodology design principles; elements, connections, conditions, and facts are molecules that are then used to construct organisms.

Atoms are used to create molecules using data per the physical technical format you are using. Organisms can be grouped by species.

With this approach, digital information organisms can be created. With digital information organisms, sets of digital information organisms, i.e. containers, such as a general purpose financial statement can be created. Given that a general purpose financial statement is a specialization of a general business report; these same ideas can be applied to general business reports.

There is a cost for having an imprecise vocabulary.  All the Seattle Method theories use this terminology; terminology from this logical theory. This terminology serves as an abstraction layer which helps reconcile multiple different explanations used by technical implementations into one common language.


A logical system is a formally governed arrangement of elements, structures, connections, conditions, and facts that together define how a domain is represented, interpreted, and reasoned about by humans and machines. It includes a conceptualization of the domain, a world view, a set of permissible models, a formal language for expressing statements, and rules for determining which statements follow from others.

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