Logical Theory

A logical theory is a coherent set of logical statements that expresses a shared conceptualization of a domain of understanding to which a community of stakeholders is committed. A theory specifies the elements of the domain, the connections among them, the conditions that must always hold, and the facts and properties that characterize that domain of understanding (a.k.a. area of knowledge).

  • 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, artifact, module) 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.
  • 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 may be privative 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.
    • Connection: (a.k.a. associations, relations, interrelationships, edge): 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:
      • 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".
    • 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.
    • 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".
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.

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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