An  Aspect of Entity is a class of Mixed-Order Entitys that is transversal to order levels, defined polymorphically over the universe hierarchy (for every level u).

It is a polymorphic subtype of Entity (declaration:  Aspect of Entity u ??? Entity v)

An  Aspect of Entity has no direct instances: it represents an aspect - a transversal characteristic  - that an ordered class acquires through the aspect relation (⊏ₐₑ) without giving up its level anchoring.

Example:

1) Lexical Scope.

2) Building Block.

3) Aggregate Member

A  Class of Entity is a Class of Element that classifies Entitys. Being a subtype of Entity, it is also an instance of itself.

The  Class of Entity class is equivalent to “at least first-order class.”

Note:

1)   SysFEAT is a higher-order ontology, so   Class of Entity may have instances that are also  Class of Entity (Class of Classes).

2)   SysFEAT is also a non-well-founded and allows for self-referencing   Class of Entity.

A  Class of Mixed-Order Entity is a Class of Entity which instances can belong to different meta-modeling order.

This includes Class of Entitys that are instances of themselves, such as Meta-Class.

A  Concept Category is a Class of Entity, typically used to group or organize collections of Class of Entitys that share some structural, relational, or definitional property.

Micro Operating Asset, Mezzo Operating Asset and Macro Operating Asset are categorization of Operating Assets.

A ClassOfEntity whose instances are groupings of concept-representing

    classes within a CategorizationFamily, and which are not themselves

    concept-representing classes.

An  Entity is a distinct, identifiable Element that has a proper existence (living or non living). It is accessible by some referencing mechanism and can have Relations to other  Entitys.

The  Entity class is the powerinstance of Class of Entity: all subtypes of  Entity are instances of Class of Entity.

 First Order Class is the Meta-Class of all subclasses of First Order Entity.

Each instance of  First Order Class is a Class of Entity, each of whose instances is necessarily a First Order Entity.

 First Order Classes are the most common type of classes.

Examples:

. Buildings
. Mountains

. Deliveries

. Organizations

. Persons

A  First Order Entity is a kind of Ordered Entity that is not itself a class (Class of Entity): it cannot have instances. The " First Order Entity" class is itself the powerinstance of First Order Class. 

The Individual term is sometimes used to designate  First Order Entity. In  SysFEAT, as in BORO and OpenCyc, the Individual term is reserved for  First Order Entitys that have a spatio-temporal extent.

 First Order Entitys are the most common type of entities.

Examples:

. The set of numbers {1,2,3,4}.

. The mathematical constant ? (pi).

. The English word "Tree" (as a specific string of characters in a specific language).

. The Eiffel tower (31st March 1889 - ...).

. Mount Vesuvius eruption (Aug. 24-25, A.D. 79).

 Fourth Order Class is the Ordered Meta-Class that is the powertype of  Third Order Class.

Each instance of  Fourth Order Class is a direct of indirect subtype of Third Order Class.

A  Lexical Scope is a kind of Mixed-Order Entity that defines the existence, visibility, and accessibility of the entities nested within it through a Nesting Relation.

Nested Entitys have no independent identity or validity outside the lexical or structural scope in which they are defined - they exist only within and for the duration of their parent construct.

Every Entity belongs to exactly one  Lexical Scope.

A  Lexical Scope carries no intrinsic semantic meaning; it serves purely as a syntactic mechanism for establishing scope through hierarchical containment.

Examples:

1) Composite structures (Aggregate Block) nesting their internal constituents (Aggregate Member).

2) Social structures nesting their roles and functions.

3) Computer functions nesting their local variables or inner functions.

4) Packages nesting their Building Blocks (packaging).

 Meta-Class (also called  Class of Classes of Entity) is the Class of Entity of all Class of Entitys each of whose instances is necessarily a Class of Entity.

 Meta-Class is equivalent to “at least second-order class.”

Being the powertype of Class of Entity, all sub-classes of Class of Entitys are instances of  Meta-Class.

Since  Meta-Class is itself a sub-type of Class of Entity,  Meta-Class is an instance of itself.

 Mixed-Order Entity is a class of Entitys that is transversal to order levels, defined polymorphically over the universe hierarchy (for every level u).

It is a polymorphic subtype of Entity (declaration: MixedOrderEntity u ⊏⋆ₑ Entity v) and a power instance of Class of Mixed-Order Entity (declaration: ∷ₚₑ), which means that its subtypes may classify entities belonging to any universe level, whereas an Ordered Entity and its subtypes are anchored to a fixed level.

Example:

1) Lexical Scope (an Aspect of Entity )

2) N-Plus Order Entity

An  N-Plus Order Entity is a Mixed-Order Entity which level of universe is u+n.

Class of Entity is an 1+n N-Plus Order Entity.

Meta-Class is an 2+n N-Plus Order Entity.

 Ordered Entity is a class whose sub-types are classifed by a Class of Ordered Entity: It is the power instance of Class of Ordered Entity.

Examples:

- First Order Entity

- First Order Class

- Second Order Class

 Mixed-Order MetaClass is the Meta-Class of Class of Mixed-Order Entity.

All its instance are Class of Entitys that can belong to multiple level of metamodeling, and allows some of the Meta-Classes to be member of themselves.

 Second Order Class is the Meta-Class of all subclasses of First Order Class.

Each instance of  Second Order Class is a class, each of whose instances is a First Order Class.

First Order Class is an instance of  Second Order Class since, by definition, all of its instances are First Order Classes.

Examples:

1) Car-Brand (with instances such as VolkswagenCar and HondaCar),

2) AnimalSpecies (with instances such as GreyWolf and Dodo),
3) USArmyRank.

 Third Order Class is the Ordered Meta-Class that is the powertype of  Second Order Class.

Each instance of  Third Order Class Class is a direct of indirect subtype of Second Order Class.