Theory

Semantics is the meaning behind the words we use. A theory defines the semantics of some system we use within an area of knowledge. A theory achieves this definition process using the formal language of logic. The elements of logic are used to provide definitions in the form of logical statements that form the theory.

A theory provides a deliberate, explicit, formal controlled vocabulary of terms which represent the important things (i.e. nature and structure) in a system, the organization (i.e. "is-a", "general-special") of those things (i.e. primitive things and complex/compound things; concrete things and abstract things) within that specific system which includes the categorization or classification of things, a description of the schemas (i.e. "has-part", mereology) of complex/compound things, business rules of the system (i.e. assertions, restrictions, constraints, conditions) which always must be true, the process by which information flows within a that system, and inference rules which can be used to better understand and work within the system. Finally, a theory also includes instances that relate to real world things.

(theory = terms + organization + schemas + business rules + process rules + inference rules + instances)

A theory needs to consider a metamodeling architecture when defining instances of objects, models for instances, models for models (i.e. metamodels), and models for meta-models (i.e. meta-metamodels). For example, Microsoft creates a report and a model to explain to describe that report.  Apple also creates a report and a report model.  What assures that Microsoft and Apple use the same theory to create each of their reports? The answer is a meta-model that describes how to build instances and models which the SEC provides.  But the ESMA also collects reports from, say, Nestle and Volkswagen. What assures that reports and report models of the SEC and ESMA are the same? A meta-meta model that both the SEC and ESMA must follow which assures that the reports and report models of Microsoft, Apple, Nestle, and Volkswagen all follow the same theory.

The theory provides a way of thinking about the system.  It could take a number of theories to describe a system. A theory generally relates to an area of knowledge and has a specific purpose (i.e. goals and objectives) that are important to the stakeholders which have an interest in that theory.

A logic gate is a fundamental logical operation (i.e. AND, OR, NOT) on one or more inputs to produce a single output. A logic circuit is a set of two or more logic gates that are connected to implement more complex logic. A process (a.k.a. the input–process–output (IPO) model or pattern) describes how information flows through a system, activities which change inputs into outputs, and can be described within a theory.

Another name for a theory is an axiomatic system.  Theories are made up of logic statements called axioms.  An axiom is a statement or proposition which is regarded as being established, accepted, or self-evidently true.


An ontology is a tool which can be used to describe a theory. The W3C's RDF, RDFS, OWL and SHACL.

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