There are an interesting collection of correspondences that emerge when the interpretive method of predication is applied to the simplest sets of patterns. The results find curious resonance with philosophical efforts at categorization found throughout history.
Here is the first set of pattern logic primitives which are the set of indeterminate entities, or what in ADEPT are labeled as the trickle subtypes of the Shadow Entities of Aether (SEH) rivulet type. These are called trickle diagrams and they show the pattern of channel inputs that result in the 12 trickle subtypes of SEH. The large blue circles are labeled with the trickles's name and abbreviation in ADEPT LION notation as well as the algebraic interpretation that is the result of applying the laws of pattern logic. The trickles are assigned the Greek letter alpha variable and the dependencies (smaller circles) are assigned the Greek letters beta or gamma as variables. An underscore "_" represents the lack of an occasion for channel input. The trickle names are meant to summarize the algebraic interpretations semantically.
Surely some may be looking for an application of these primitive patterns that is more contemporary than the categorical systems of Kant and Aristotle. When one looks at the meanings of the primitive occasions in the first consideration, they can also be understood as the building blocks of an ontological model.
Oxford Languages defines ontology as "a set of concepts and categories in a subject area or domain that shows their properties and the relations between them."
While most ontology work focuses on a specific "subject area or domain" there are also "top level ontologies" that seek to identify the common "properties and relations" across multiple domains.
Going even deeper however, what pattern logic is actually offering is a formalization of what it means to be a "concept", "category", "domain", "property" or "relation". In other words, pattern logic presents a way of retooling any ontological system into a coherent and complete logical model grounded in the meaning of patterns.
The Web Ontology Language (OWL) is probably the most widely used approach to constructing ontologies today.
The underlying syntax of OWL is an extension of the Resource Description Framework (RDF), which is a network graph consisting of subject-predicate-object "triples" that link two "resource" nodes through a "property" edge.
ADEPT LION models the structure of a graph separate from the ontological meaning of individuals, classes, attributes and relations, thus cleanly separating by consideration a line between structure and logic which RDF and OWL blurs.
From the bottom-up an ontology consists of pure concepts or conceptualizations of actual things.
From the top-down an ontology consists of the classes by which individuals are grouped.
From the inside-out an ontology consists of relations between concepts and classes or sometimes even between classes.
Attributes establish the outside-in "dressing up" of classes and concepts with "properties" or "attributes".