Example 2: Objects and their parts

Functional complex: parts with different roles

A gufo:FunctionalComplex is what most ordinary objects are: a whole whose parts (components) each contribute something different. A car's engine and its wheels do not play the same role in the car, so :Car, :Engine and :Wheel are all functional complexes, and the part-whole link between them is (a sub-property of) gufo:isComponentOf:

:Car a owl:Class , gufo:Kind ;
    rdfs:subClassOf gufo:FunctionalComplex .

:Engine a owl:Class , gufo:Kind ;
    rdfs:subClassOf gufo:FunctionalComplex .

:isEngineOf a owl:ObjectProperty ;
    rdfs:subPropertyOf gufo:isComponentOf ;
    rdfs:domain :Engine ;
    rdfs:range :Car .

:Car001Engine a :Engine ;
    :isEngineOf :Car001 .

Declaring a domain-specific sub-property (:isEngineOf) rather than using gufo:isComponentOf directly is optional but recommended: it lets you constrain domain and range per part type (an engine is a component of a car; a wheel, of a car too, but through its own property) while every asserted fact remains, by subsumption, also an instance of the general gufo:isComponentOf relation.

Collection: parts with a uniform role

The fleet is different: every member -- every car in it -- plays the very same role ("being a member of the fleet"). That uniform structure is what gufo:Collection is for. Because CityWheels buys and retires cars over time, the fleet's membership is variable, so it is specifically a gufo:VariableCollection (the alternative, gufo:FixedCollection, is for collections like a hand of cards dealt in a game, where swapping a member yields a strictly different collection):

:Fleet a owl:Class , gufo:Kind ;
    rdfs:subClassOf gufo:VariableCollection .

:isFleetMemberOf a owl:ObjectProperty ;
    rdfs:subPropertyOf gufo:isCollectionMemberOf ;
    rdfs:domain :Car ;
    rdfs:range :Fleet .

:CityWheelsFleet a :Fleet .
:Car001 :isFleetMemberOf :CityWheelsFleet .

Collections can also have sub-collections, when a subset of the members forms a collection in its own right -- gufo:isSubCollectionOf (transitive) is for exactly this, distinct from membership:

:ElectricSubfleet a :Fleet ;
    gufo:isSubCollectionOf :CityWheelsFleet .

:Car001 :isFleetMemberOf :ElectricSubfleet .

Quantity: no roles at all, just stuff

Gasoline has neither distinct components nor uniform "members" -- it is not made of parts in the way a car or a fleet is. gufo:Quantity models exactly this: a maximally self-connected portion of stuff. Note the class name, :QuantityOfGasoline, not just :Gasoline: its instances are individual portions of the stuff (this tankful, that delivery), not the material itself -- the same naming convention the gUFO usage guide uses for AmountOfMarble.

"Maximally self-connected" is not decoration; it is what constrains everything below. Any two portions of gasoline in contact are, together, one quantity rather than two, because neither of them alone is maximal. So a quantity of gasoline can never have a smaller quantity of gasoline as a part. What it does have as parts are portions of the different stuffs it is a blend of: pump gasoline is a blend of a petroleum distillate and ethanol, and each of those is a maximally self-connected portion of its own stuff even while mixed into the whole. This is the standard UFO illustration -- a portion of wine has a portion of water and a portion of alcohol as sub-quantities -- and gUFO's own definition of gufo:isSubQuantityOf uses it verbatim: "the quantity of water in a wine glass is a sub-quantity of the wine in that glass".

:QuantityOfGasoline a owl:Class , gufo:Kind ;
    rdfs:subClassOf gufo:Quantity .

:QuantityOfEthanol a owl:Class , gufo:Kind ;
    rdfs:subClassOf gufo:Quantity ;
    owl:disjointWith :QuantityOfGasoline .

:isEthanolPortionOf a owl:ObjectProperty , owl:FunctionalProperty ;
    rdfs:subPropertyOf gufo:isSubQuantityOf ;
    rdfs:domain :QuantityOfEthanol ;
    rdfs:range :QuantityOfGasoline .      # part and whole are of *different* kinds

:Car002FuelTankContents a :QuantityOfGasoline .

:Car002EthanolPortion a :QuantityOfEthanol ;
    :isEthanolPortionOf :Car002FuelTankContents .

Four further constraints come with subQuantityOf, each stated in the ontology as far as OWL allows. The first three all fall out of the same two facts -- quantities are topologically connected, and they are maximal:

• Non-shareable. A sub-quantity is part of at most one whole: a portion of ethanol cannot be mixed into two distinct quantities at once, because it would have to be in contact with both. Hence :isEthanolPortionOf a owl:FunctionalProperty.
• Exactly one sub-quantity per kind. Not a fact about blending recipes -- a consequence of maximality. Any two portions of ethanol inside the same quantity of gasoline are in contact, hence one maximal portion, hence one quantity. So there is exactly one quantity of ethanol that is part of a given quantity of gasoline, just as there is exactly one quantity of alcohol in a given quantity of wine:

  :QuantityOfGasoline rdfs:subClassOf
      [ a owl:Restriction ;
          owl:onProperty [ owl:inverseOf :isEthanolPortionOf ] ;
          owl:qualifiedCardinality "1"^^xsd:nonNegativeInteger ;
          owl:onClass :QuantityOfEthanol ] .

  A reasoner puts this to work: assert two differently-named ethanol portions of the same gasoline and it infers that they are the same individual -- which is exactly what maximality claims.
• Irreflexive (and asymmetric). No quantity is a sub-quantity of itself -- water cannot be part of water. gUFO notes that this holds of every parthood property but leaves it undeclared, because asserting irreflexivity on a transitive (OWL 2 "non-simple") property would break DL decidability. The typed properties here are not transitive and have no transitive sub-properties, so they are simple and can carry owl:IrreflexiveProperty and owl:AsymmetricProperty safely. This example therefore recovers, at the domain level, a constraint gUFO cannot state globally.
• Essential, and the whole extensional. Sub-quantities are essential parts; gUFO says so explicitly and adds that gufo:standsInQualifiedParthood -- its pattern for parthood holding only for a time -- "is not applicable for sub-quantities". Correspondingly, quantities are extensional: change any part and you have a different whole (strong supplementation holds, unlike for gufo:isSubCollectionOf, which satisfies only the weaker axiom). Essentiality is a modal claim and beyond OWL; the cardinalities above are the part of it OWL can carry.

Transitivity is the one characteristic not declared on the typed properties. It belongs to gufo:isSubQuantityOf, which gUFO declares transitive (Guizzardi, 2005, p. 184) -- unlike gufo:isComponentOf and gufo:isCollectionMemberOf, which are not. Each typed property here relates one specific stuff to another, so it is not transitive on its own; its assertions feed the transitive super-property instead:

:isBenzenePortionOf a owl:ObjectProperty ;
    rdfs:subPropertyOf gufo:isSubQuantityOf ;
    rdfs:domain :QuantityOfBenzene ;
    rdfs:range :QuantityOfPetroleumDistillate .

:Car002BenzenePortion a :QuantityOfBenzene ;
    :isBenzenePortionOf :Car002DistillatePortion .
    # inferred: :Car002BenzenePortion gufo:isSubQuantityOf :Car002FuelTankContents
    # -- which is what one means by saying the fuel in the tank contains benzene.

All of this is where quantities part company with functional complexes, and it is easy to get backwards. Unbolt a wheel and put it back on and the car has regained the very same component -- components can come and go while the whole keeps its identity. A quantity cannot: gUFO's gufo:Quantity comment states that it "has a fixed constitution, and thus, removing or adding a sub-quantity would result in a different quantity".

Mixing and splitting: new quantities, not new parts

So what does one say about Tuesday's delivery being pumped into the depot tank, and about fuel later being pumped from the tank into a car? Because constitution is fixed, none of these events gives an existing quantity a new part or takes one away. Each yields a different quantity, and what survives is a historical link, not a parthood link. gufo:historicallyDependsOn is the property for it (the same one used for causal and historical dependence between events in example 5 -- its domain and range are the fully general gufo:ConcreteIndividual, not just gufo:Event):

:DepotSupplyBeforeTuesday a :QuantityOfGasoline .
:TuesdayDeliveryLot a :QuantityOfGasoline .

:DepotSupplyAfterTuesday a :QuantityOfGasoline ;
    gufo:historicallyDependsOn :DepotSupplyBeforeTuesday , :TuesdayDeliveryLot .

:Car002FuelTankContents gufo:historicallyDependsOn :DepotSupplyAfterTuesday .

Note what is not asserted: neither input is a sub-quantity of the mixture. They are of the same kind as it, and after mixing neither is a maximally self-connected portion any more. Nor did :DepotSupplyBeforeTuesday simply grow into :DepotSupplyAfterTuesday -- a quantity does not survive a change of constitution.

If the ontology needs to track "the tank's supply" as one thing that persists across deliveries, the answer is not to stretch gufo:isSubQuantityOf to cover it. The persisting thing is the tank (a gufo:FunctionalComplex), successively constituted by different quantities of gasoline -- see gufo:isConstitutedBy and the gufo:TemporaryConstitutionSituation pattern in the gUFO usage guide, which uses exactly this arrangement for the Venus de Milo and its quantities of marble.