Upper Ontology

DEFINITION SUB-DOMAINS CONTENT MANAGEMENT

CONCEPT DOMAIN - Upper Ontology

Description	The Upper Ontology domain encompasses five fundamental domains that establish the foundation for the modeling syntax and semantic. 1) The Predication Substrate defines basic constructs for relating ( Linkage) and classifying Elements from which ontological structures are grown. 2) The Reflexive Knowledge Graph defines the elementary constructs of Entity, Relation, their multi-level classification and mereological relationships. Its provides the foundation for open meta-modeling. 3) Packaging, as aspect of modularity, defines syntactic constructs used to group reusable entities ( Building Blocks) into modules called Containers. 4) Compositionality, another aspect of modularity, defines the syntactic constructs used to build Entitys that have an internal structure and boundaries. 5) The 4D Composite Knowledge Graph defines Bounded Individuals (entities that exists over space and time) how they are composed (aggregate mereology), qualified (properties) and connected, enabling effective representation of meaning.
External references	SysFEAT-TheoraticalFoundations-Introduction.pdf
Dictionary	SysFEAT Upper Ontology
Parent Domain	SysFEAT Foundation Ontology Map
Domain dependencies	Compositionality Packaging Predication Substrate Reflexive Knowledge Graph

DOMAIN HIERARCHY

DIAGRAM HIERARCHY

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  4D Composite Knowledge Graph
The purpose of the 4D Composite Knowledge Graph is to layer structured spatio-temporal concepts onto the Reflexive Knowledge Graph,
The 4D Composite Knowledge Graph integrates the capabilities of Reflexive Knowledge Graphs (entities, relationships,   Holonymy Relation and multi-level instance of Entity) with those of Compositionality (composite structures) resulting in the addition of the following key features:
1) Mereological   Aggregate Holonymy relationships, providing dynamic locality to composition.
2) Individual-Property distinction: a clear ontological separation between Bounded Individuals (entities that exist in space and time) and their properties ( Property). A dedicated Typology characterizes how individuals relate to and instantiate these properties.
3) Temporal Framing: the introduction of temporal connections ( Temporal Bounding) that define the temporal boundaries of Bounded Individuals, enabling the explicit modeling of state changes, events, and persistence over time.
- Bounded Individual
  Bounded Individuals are Individuals which have a life cycle, bounded by Temporal Boundings. Because of its composite nature, Bounded Individual is a sub-type of Bounded Aggregate.
  Bounded Individuals shall be made distinct from Class of Bounded Individual which they are instance of.
  Bounded Individuals are represented with light orange boxes (see the Meta-Model Legend).
  Examples:
  . The Eiffel tower (31st March 1889 - ...).
  . William Shakespeare in its Early Theatrical Career (1592-1600).
  . Confucius (685-758).
  . Mount Vesuvius eruption (Aug. 24-25, A.D. 79).
  . Oackland digital hospital after its renovation (2022 - ...)
  . The execution of the registration process at the Oackland digital hospital, by John Smith, on 17 March 2020.
- Class of Bounded Individual
  A Class of Bounded Individual is a Class of Individual which denotes Bounded Individuals that have a proper life cycle, bounded by Temporal Bounding Types.
  Class of Bounded Individual is the powertype of Bounded Individual. It means that all sub-types of Bounded Individual are instances of Class of Bounded Individual.
  Examples:
  - Car,
  - Application,
  - A Process Type ( Action Process Type) such as the registration process used at the Oackland digital hospital during the COVID-19 pandemic.
  Counterexamples:
  - Project is not a Class of Bounded Individual because its instances have a spatio-temporal extent. Project is a subtype of Bounded Individual.
  - Capability is not a Class of Bounded Individual. It is a Class of Property.
- Class of Class of Bounded Individual
  A Class of Class of Bounded Individual is a Class of Class of Individual which is the powertype of Class of Bounded Individual . It means that all sub-types of Class of Bounded Individual are instances of Class of Class of Bounded Individual.
- Class of Class of Individual
  A Class of Class of Individual is a that classifies Class of Individuals.
  Class of Class of Individual is the powertype of Class of Individual.
  Example:
  - Property Types such as Temperatures or colors.
- Class of Individual
  A Class of Individual is a First Order Class of Entitys that exist in space and time. It is the powertype of Individual.
  Class of Individuals are represented as dark orange boxes (see the Meta-Model Legend) .
  Examples:
  - Red;
  - 12 kg;
  - Top Secret (TS) confidentiality.
  - Birth,
  - Death,
- Class of Property
  A Class of Property is an abstract Class of Individual, which purpose is to qualify Bounded Individuals and their classes ( Class of Bounded Individual).
  Because instances of Class of Property are Propertys, they do not have proper instances: there are no instances of "red", but there are red Bounded Individuals.
  Example:
  - 10 degree celcius;
  - Ability to cook (a capability);
  - Red;
  - 12 kg;
  - Top Secret (TS) confidentiality.
  - 7/7 availability
- Individual
  Individuals are Entitys which represent things that exist over space and time.
  Individuals are represented as light orange boxes, while their classes are represented as dark orange boxes (see the Meta-Model Legend) .
  Examples:
  . The Eiffel tower completion (31st March 1889)
  . The Eiffel tower (31st March 1889 - ...).
  . William Shakespeare birth (1592)
  . William Shakespeare in its Early Theatrical Career (1592-1600).
  . Confucius (685-758).
  . Confucius death (758).
  . Mount Vesuvius eruption (Aug. 24-25, A.D. 79).
  . Oackland digital hospital after its renovation (2022 - ...)
  . The execution of the registration process at the Oackland digital hospital, by John Smith, on 17 March 2020.
- Individual State
  An Individual State is a temporal slice of a Bounded Individual.
  Examples:
  . The state of the Eiffel tower during the 1900 World Fair, with its improved elevators and electric illuminations (Apr 14, 1900 - Nov 12, 1900).
  . William Shakespeare in its early theatrical career (1592-1600).
  . Confucius in its early childhood.
  . The first Plinian phase of the Mount Vesuvius eruption (18 to 20 hour, Aug. 24 A.D. 79), that projected a column of volcanic debris and hot gases.
  . Oackland digital hospital after its renovation (2022 - ...).
- Property
  Property is the power instance of Class of Property. All its subtypes are instances of Class of Property such as:
  - 10 degree celcius;
  - Ability to cook (a capability);
  - Red;
  - 12 kg;
  - Top Secret (TS) confidentiality.
  - 7/7 availability
- Property Type
  A Property Type is a Class of Class of Individual Object that is used to classify Propertys.
  Example:
  - Temperature
  - Color
  - Weight
  - Confidentiality
  - Availability
- State Class
  A State Class is a class of the temporal slices of a Class of Bounded Individual. It is the powertype of Individual State.
  Examples:
  . The lifecyle phases of buildings such as a skycraper: construction phase, operation and maintenance phase, decommissioning phase.
  . The lifecycle phases of a person, such as childhood, adulthood, eldery stage.
  . The phases of a volcanic eruption: magma accumulation, plinian phase, eruptive phase, effusive phase, declining phase.
  . The lifecyle phases of a hospital such as construction phase, operation and maintenance phase, renovation and expansion phase, decommissioning phase.
- Temporal Bounding
  A Temporal Bounding is an Individual whose temporal extent is instantaneous, and whose spatial extent corresponds with the start or end of the Bounded Individuals for which it is the temporal border.
  Example:
  . The Eiffel tower completion (31st March 1889)
  . William Shakespeare birth (1564)
  . Confucius death (758).
  . Start of the first Plinian phase of the Mount Vesuvius eruption (18h, Aug. 24 A.D. 79)
  . Oakland hospital opening in 1994.
- Temporal Bounding Type
  A Temporal Bounding Type is Class of Individual that defines the type of temporal boundaries that delimitate Class of Bounded Individuals.
  It is a class of Temporal Bounding.
  Exemples:
  - Birth,
  - Death,
  - Start of the plinian phase of a volcanic eruption.
  - Hospital opening.
- Whole Life Class
  Whole Life Class is the power-type of Whole Life Individual.
  Examples:
  . A type of building such as a skycraper.
  . A type of person such as a philosopher.
  . A type of activity such as a volcanic eruption.
  . A type of facility such as a hospital.
  . A Process Type ( Action Process Type) such as the registration process used at the Oackland digital hospital during the COVID-19 pandemic.
- Whole Life Individual
  A Whole Life Individual is a Bounded Individual that is not the temporal slice of any other Bounded Individual.
  A Whole Life Individual includes its past and future.
  Examples:
  . The Eiffel tower (31st March 1889 - ...).
  . William Shakespeare (23 April 1564 - 23 April 1616).
  . Confucius (685-758).
  . Mount Vesuvius eruption (Aug. 24-25, A.D. 79).
  . Oackland digital hospital (1994 - ...).
  . The execution of the registration process at the Oackland digital hospital, by John Smith, on 17 March 2020.
Compositionality
The purpose of the Compositionality family of concepts is to provide syntactic mechanisms that support the construction of composite Building Blocks.
The Compositionality pattern handles situations where Building Blocks have an internal structure. Such Building Blocks are called Aggregate Blocks. They are made of internal nested Entitys called Aggregate Members. Aggregate Members contextualizes Building Blocks living outside the Aggregate Block structure (specialization in OMG - Kernel Modeling Language (KerML) is such an Aggregate Member).
Advanced Aggregate Block features are provided by Bounded Aggregates which hide their internal structure to the outside world by means of a formal boundary (see Ordering Connection).
- Aggregate Block
  An Aggregate Block is a Building Block which has an internal structure made of Aggregate Members which, through nesting ( Membership of -Aggregate Member-), contextualizes/aggregates ( Aggregation of -Building Block (Aggregate Member) - ) external Building Blocks within the Aggregate Block.
- Aggregate Entity Block
  An Aggregate Entity Block is a self-contained and independant Aggregate Block that is not an Ordering Connection.
  Examples:
  - Operating Eco-System;
  - Action Process Type;
  - Directive;
  - Agent Type.
- Bounded Aggregate
  A Bounded Aggregate is an Aggregate Entity Block which hides its internal structure to the outside world by means of formal Borders.
  The only way to access a Bounded Aggregate is through its formal Borders, which ensures the aggregate's internal consistency.
  The Borders of a Bounded Aggregate is determined by the Ordering Connections it can participate to.
  Within a Bounded Aggregate structure, Bounded Members can be linked together through Ordering Connectors.
  The nature of Ordering Connectors is given by their associated Ordering Connection.
  Examples:
  - Action Process Typees are bounded by their start and end events (see Behavioral Event).
  - Applications are bounded by their APIs borders ( API Service Point and API Request Point).
- Elementary Block
  An Elementary Block is a Building Block which doesn't have an internal structure.
- Ordering Connection
  An Ordering Connection is an Aggregate Block that defines possible connections between the Borders of two or more Bounded Aggregates.
  Examples:
  - Outcome Event.
  - Service Interface.
- Unbounded Aggregate
  An Unbounded Aggregate is an Aggregate Entity Block that does not have boundaries and, thereby, that cannot participate to Ordering Connections.
  Examples:
  - Operating Eco-System;
  - Directive.
Packaging
The Packaging domain defines the core elements of Building Block and Container which provide the basis for building modules.
Building Blocks are reusable units They have an independent existence. Thereby, they cannot be nested in other structures which would hide their existence (lexical scope). Because of their independent existence, they must be owned by an independent artifact which sole purpose is model management Containers . Containers are dedicated to model management:
. They own blocks to which they provide existence.
. They can provide namespace to blocks.
. They have dependencies on other Containers which blocks have relationships to blocks they packaged.
- Block Collection
  A Block Collection is a Mixed-Order Entity that is a set of Building Blocks.
  The grouping of Building Blocks can be achieved either by reference ( Reference Relation) or by nesting ( Nesting Relation), in which case the Block Collection serves as a Block Lexical Scope.
  Example:
  - Container Package as a Block Lexical Scope.
  - Asset Portfolio as a pure Block Collection.
- Block Lexical Scope
  A Block Lexical Scope is a Block Collection that is also a Lexical Scope for the Building Blocks it groups.
  A Block Lexical Scope defines the existence of its grouped Building Blocks through nesting.
- Building Block
  A Building Block is an autonomous Entity that contributes to the makeup of other Building Blocks.
  Building Blocks can be either reusable entities (packaged in Containers) or be local to the Aggregate Block that references them (see Block Lexical Scope and Hierarchical Member).
  Examples:
  - Functionality(ies), Business Process(es), Data Entity(ies), Tags, ARE Building Blocks.
  - Process Steps or Attributes of a data entity ARE NOT Building Blocks. They are members on an internal structure (see Aggregate Member).
- Container
  A Container is a collection of Building Blocks whose existence and meaning are defined by the Container.
  A Container is both:
  1. A Lexical Scope: the meaning and usage of a Building Block is only applicable within the context of the Container to which it belongs.
  2. A universe of discourse: the complete range of Building Blocks that are expressed, assumed, or implied in an architecture domain.
  Examples:
  - Container Package
  - Library
  - Enterprise
- Container Package
  A Container Package is a Container which sole purpose is model management.
  Examples: Library, Information Dictionary
  Conterexamples: Enterprises or Infrastructure Landscapes are Containers but are not Container Packages because they have functional purposes that go beyond model management.
Predication Substrate
The Predication Substrate defines the compositional system of Element, Class of Element, and local predicates ( Linkage) from which SysFEAT's ontological structures are grown. It provides the internal structure of predication - classification, specialization, powertyping, and Compositionality - as a single, universe-stratified, mechanically verified engine that every higher layer inherits.
Unlike predicate logic (where a predicate is not a term) and graph theory (where an edge is not a node), a Linkage is simultaneously the mechanism of relating an Element that can be classified, specialized, and related to other entities. This self-applicability is what allows the framework to provide a theory of Relation - not just relations, but the ability to classify relations, specialize them, and compose them, using the same machinery that applies to the Entitys they relate.
- Class of Element
  A Class of Element is an Element whose inhabitants are themselves Elements: a type one universe level above its members.
  Formally, ClassOfElement u = Element (lsuc u), so a class at level u is a type whose instances are Element u things.
  This universe gap is what separates a class from its members and prevents the self-reference paradoxes of naive set theory - while still allowing, through cross-level reasoning (metaInstanceOf), the class of all classes to be an instance of itself.
  A Class of Element is the Predication Substrate's answer to the question "what is a category of things?" - not a predicate that returns true or false, but a type that collects its instances as inhabitants.
- Element
  Element is the most primitive concept in the Predication Substrate: anything that can be the subject or object of predication.
  Formally, Element u = Set u - a type at universe level u. An Element makes no ontological commitment: it is neither an Entity nor a Relation, neither concrete nor abstract. It is simply something that can be talked about - classified, linked, composed. Every concept in SysFEAT is an Element at some universe level; what distinguishes concepts is the level at which they live and the Linkages they participate in.
- Linkage
  Linkage is the structural primitive of predication: a fibered, proof-relevant, compositional local predicate between a source Element and a target Element.
  A Linkage from S to T assigns to each source s :
  1) S a local type of evidence (localType s)
  2) and a projection (ref) that determines the target from the evidence.
  The reconstructed predicate s ⟨ L ⟩→ is then a dependent pair: a witness e : localType s together with a proof that ref e ≡ t.
  Linkage is simultaneously a generalized graph edge (with source, target, and composable edge data), a proof-relevant predicate (where two different edges between the same endpoints are distinguished), and an Element at a higher universe level (meaning it can itself be classified, specialized, and linked).
  This triple nature - edge, predicate, entity - is what resolves the polysemy that traditional frameworks impose between things-that-are and things-that-connect.
- Mixed-Order Element
  An Mixed-Order Element is an Element that can belong to multiple metamodeling order (mixed universes in Agda).
  Example:
  - Lexical Scope
  - Building Block
- Ordered Element
  An Ordered Element is an Element that can belong to only to a single metamodeling order (fixed universe in Agda).
  Example:
  - First Order Entity
  - Container Package
Reflexive Knowledge Graph
The Reflexive Knowledge Graph domain defines the top level constructs of Entitys, Relations, their multi-level classification and mereological relationships.
It forms the second layer of SysFEAT's graph architecture. In this domain, Relations are refied as first class Elements, allowing them to be further described and qualified.
Multi-level classification is implemented by PowerTyping, which enables open and flexible meta-modeling capabilities, This includes support for reflexive meta-modeling, for example allowing Meta-Class to be an instance of itself.
Powertyping also applies to relationships, including the Holonymy Relation relationship.
This design grounds the Reflexive Knowledge Graph in non-well-founded set theory, ensuring consistency in circular and self-referential structures (see associated external references).
The 4D Composite Knowledge Graph provides additional structuring of Entitys and Relations by implementing the Compositionality pattern which establishes the concepts of dynamic locality and connections.
-    Class of Entity
  A Class of Entity is a Class of Element that classifies Entitys. Being a subtype of Entity, it is also an instance of itself.
  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.
- Class of Mixed-Order 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 .
- Class of Ordered Entity
  Class of Ordered Entity is the Meta-Class (subtype of Class of Entity and instance of Meta-Class) of all power-type based Class of Entitys that follow a strict ordering of metalevels.
- Class Partition
- Entity
  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.
- Family of Class
- First Order Class
  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 Entity
  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 the powerinstance of First Order Class.
  First Order Entitys are the most common type of entities.
  The word "Individual" is sometimes used to designate particulars. In SysFEAT, the term Individual is reserved for particulars that have a spatio-temporal extent.
  Examples:
  . The set of numbers {1,2,3,4}.
  . The mathematical constant π (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).
- Lexical Scope
  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 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 Family of Class
  A Meta Family of Class is a Class of Classes of Element (its members are themselves Class of Elements), typically used to group or organize collections of Class of Elements that share some structural, relational, or definitional property.
  In contrast to families of sets, which are sets of sets, a family of classes operates at a higher ontological level-its elements may represent universes, types, or conceptual groupings rather than individual sets.
- Meta-Class
  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.
  In other word, Meta-Class is 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.
- Meta-Class Partition
- Mixed-Order Entity
  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.
  A Mixed-Order 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.
  It is the SysFEAT counterpart of MLT*'s orderless type, with two constitutive differences: transversality is carried by the universe polymorphism of the type system (rather than by a FOL axiomatization of integer levels), and cross-level classification goes through the controlled-reflexivity predicates (⊏ₘ, ∷ₘ), which makes it compatible with proof-kernel verification.
  Example:
  1) Aspects of Entitys, such as Lexical Scope.
  2) Building Blocks.
- Mixed-Order MetaClass
  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 powertyping, an allows some of the classes to be member of themselves.
- Ordered 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
- Ordered Meta-Class
  Ordered Class is the defined as the Meta-Class of all power-type based Class of Entitys that follow a strict ordering of metalevels.
- Power Class
  A Power Class of a class A—denoted as P*(A)—is the class whose members are every possible subclass of A, including A itself and the empty class.
- Second Order Class
  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 instancessuch as GreyWolf and Dodo), Occupation, and USArmyRank.
- Third Order Class
  Third Order Class is the meta-class that is the powertype of Second Order Class.
  Each instance of Third Order Class is a direct of indirect subtype of Second Order Class.