The Distributed Ontology, Model, and Speci cation Language DOL provides logic-independent structuring, linking, and modularity constructs. Its homogeneous OWL fragment, DOWL, we argue, can be seen as an ideal language for formalising ontology patterns in description logics. It naturally consumes earlier formalisms such as C-OWL or DDL, and extends these with various expressive means useful for the modelling of patterns. To substantiate this, we illustrate DOWL's expressive power with a number of examples, including ontology design patterns, networks of ontologies, and ontology combinations. The latter are used to formalise conceptual blending, based on DOWL features such as renaming, ltering, forgetting, interpretation, and colimit computation.
While the use of ontologies varies considerably, there are two recurring challenges: reusability and interoperability.
Reusability is an issue because the development of ontologies is typically done
manually by experts and, thus, an expensive process. Hence, it is desirable to be
able to reuse existing ontologies during the development of new ontologies. This
presupposes a framework that allows to build structured ontologies by identifying
modules and their relationships to each other. For example, it requires the ability
to combine two existing ontologies in a way that handles the namespaces of the
ontologies in an appropriate way. Further, the reuse of an existing ontology
often requires that the ontology is adapted for its new purpose. For example,
the adaption may require the extension of the ontology by new axioms, or the
extraction of a subset of the ontology, or the change of its semantics from open
world to closed world.
? This paper draws heavily on material from [
The interoperability challenge is closely related to the reusability challenge. Since the development of ontologies is not an exact science and is usually driven by project speci c requirements, two ontologies that have been developed independently will represent the same domain in di erent and, often, con icting ways. Thus, in a situation where two independently developed ontologies are supposed to be reused as modules of a larger ontology, the di erences between these ontologies will typically prevent them from working together properly. Overcoming this lack of interoperability may require an alignment or even an integration of these ontologies. This typically involves the identi cation of synonyms, homonyms, and the development of bridge axioms, which connect the two ontologies appropriately.
Addressing these two challenges, there is a diversity of notions providing design patterns for and interrelations among ontologies. The Distributed Ontology, Model and Speci cation Language (DOL) aims at providing a uni ed metalanguage for handling this diversity. In particular, DOL enjoys the following distinctive features: { structuring constructs for building ontologies from existing ontologies, like imports, union, forgetting, interpolation, ltering, and open-world versus closed-world semantics; { module extraction; { mappings between ontologies, like interpretation of theories, conservative extensions etc.; { alignments, interpretations, and networks of ontologies; { combination of networks.
DOL has been partially approved as a standard of the Object Management
Group (OMG), and its nalisation is planned for late 2016 [
DOL and its structuring language are designed as a multi-logic meta-language, already supporting all of the mainstream ontology languages in use today. In this paper, we outline the purely homogeneous DL-based OWL fragment of DOL, called DOWL. We illustrate that it provides substantial modelling support for the OWL user, and, moreover, encompasses and extends several well-known modelling approaches, namely in particular C-OWL and DDL, standard alignment techniques, as well as module extraction.
We illustrate some of these features here with two main use-cases that go beyond standard description logic or OWL modelling, namely (1) instantiable schematic ontology patterns, and (2) networks of ontologies and their combination, here applied to the computation of conceptual blends. We close with a discussion of reasoning and tool support, and an outline of future work. 2 2.1
Structured DOWL ontologies are generated by the following grammar, where O is a basic OWL ontology, is a signature (i.e. a set of entities: concepts, roles and individuals) and a signature morphism (i.e. a map between the entities of two ontologies): Onto ::= O | IRI | Onto and Onto | Onto then [ Anno ] Onto | Onto with | Onto reveal | Onto hide | Onto keep | Onto forget | Onto extract | Onto remove | Onto select O | Onto reject O | minimize Onto | maximize Onto | combine Network | { Onto } Anno ::= % def | % cons | % implied
A basic ontology O is written in some OWL serialisation, e.g. OWL Manchester syntax: Class : Woman EquivalentTo : Person and Female ObjectProperty : hasParent
As shown in this example, O can be an ontology fragment, which means that some of its entities are declared outside of O (e.g. in an imported ontology).
An IRI reference refers to an ontology existing on the Web, possibly abbreviated using pre xes, e.g.:
<http :// owl . cs . manchester . ac . uk / co-ode-files / ontologies / pizza .owl > or using pre xes: % prefix (
co-ode : <http :// owl . cs . manchester . ac . uk / co-ode-files / ontologies /> )% co-ode : pizza . owl
An extension of an ontology by new entities and axioms is written O1 then O2, where O2 is an ontology (fragment). An extension can optionally be marked as conservative (%cons after the \then"), stating that O2 does not introduce any new constraints in terms of the language of O1. In case that O2 does not introduce any new entities, the keyword %implied can be used instead of %cons; the extension then merely states intended logical consequences. The keyword %def stands for de nitional extensions, expressing that the interpretation of the new entities in O2 is uniquely determined by the axioms for a given interpretation of O1. The following OWL ontology is an example for the latter:1 Class Person
Class Female then % def
Class : Woman EquivalentTo : Person and Female Similar to extension is the union of two self-contained ontologies, written O1 and O2. Compared to extensions, O2 is restricted here, because it cannot be a fragment. On the other hand, O2 can be an arbitrary structured ontology, and not just a basic one, as for extensions.
A translation of an ontology to a di erent signature is written O with , where is a signature morphism. This is particularly useful when disambiguating homonyms that may accidentially get identi ed when uniting ontologies: FinancialOnto with Bank |- > FinancialBank and GeoOnto with Bank |- > RiverBank 1 Annotations such as %cons, %then and %def, introduce so called `proof obligations' on the meta-level. That is, what they claim to be the case may be true or false and therefore requires veri cation by proof (or sometimes su cient syntactic criteria).
DOL features four di erent forms of reduction of a large ontology to a smaller
signature. Assume that in some large medical ontology like SNOMED CT, we
are interested only in facts about hearts and heart attacks. Then we can write
one of:
SNOMED extract Heart , HeartAttack
SNOMED keep Heart , HeartAttack
SNOMED reveal Heart , HeartAttack
SNOMED select Heart , HeartAttack
With extract, we extract a SNOMED CT module2, which is a sub-ontology of
SNOMED CT capturing the same facts about hearts and heart as SNOMED
CT itself. The signature of the extracted module may be larger than just the
two speci ed entities (heart and heart attack). In extreme cases, we might get
the whole original ontology (which is of course not desirable, because then no
reduction has taken place). Using keep, we get a uniform interpolant, which
is not necessarily a sub-ontology, but rather an ontology that may involve new
axioms in order to capture the SNOMED CT facts about hearts and heart
attacks in an ontology featuring exactly the two speci ed entities, heart and
heart attack. However, such an ontology may be hard to compute, if it exists at
all. Then, we also can use reveal, which essentially keeps the whole of SNOMED
CT and provides some export interface consisting of heart and heart attack only.
This can be useful when interfacing SNOMED CT with other ontologies, e.g. in
an interpretation. Finally, the use of select simply removes all SNOMED CT
axioms that involve other symbols than heart and heart attack. While this can
be computed easily, it might leave the user with a poor ontology capturing only a
small fraction and only the basic facts of SNOMED CT's knowledge about hearts
and heart attacks. DOWL also adds language constructs to OWL to express
(non-monotonic) minimisation (resp. maximisation) of concepts, borrowing from
circumscription [
Class : Block Individual : B1 Types : Block
Individual : B2 Types : Block DifferentFrom : B1 then minimize {
Class : Abnormal
Individual : B1 Types : Abnormal } then
Class : OnTable Class : BlockNotAbnormal EquivalentTo :
Block and not Abnormal SubClassOf : OnTable then % implied
Individual : B2 Types : OnTable 2 DOL uses smallest depleting extractions.
-modules in the sense of [
Alternatively, we can maximise some entities. Using this, the example can be formulated in a more natural way, because now the concept of normal blocks is maximised: ontology Blocks_Alternative2 =
Class : Block Class : Normal Individual : B1 Types : Block , not Normal Individual : B2 Types : Block DifferentFrom : B1 %% B1 and B2 are different blocks %% B1 is abnormal Class : Ontable Class : NormalBlock
EquivalentTo : Block and Normal SubClassOf : Ontable %% Normally , a block is on the table maximize Normal vars Ontable BlockNotAbnormal then % implied
Individual : B2 Types : Ontable
%% B2 is on the table end 2.2
DOWL comprises a comprehensive meta-language layer to express di erent kinds of ontology alignments, following the main established semantics, as well as networks of alignments.
DOL represents the general alignment alignment A : O1 to O2 =
format introduced by the Alignment API s11 REL1 s12 ,
[ta8hr]ee aOosn1tionalnodFgiiegrse.spt1oecwbtiheveeraleyligOOn1e2dsa,ynsmdi1bOoaln2sd, afsori2er en:sd[:1na:s,RsuEmLinngs2nD,OMAIN ]
i = 1; : : : ; n, and si1 RELi si2 is a
correspondence which identi es a relation be- Fig. 1. Syntax of DOL Alignments
tween the ontology symbols, either using
a relation IRI or a symbol: > (subsumes), < (is subsumed), = (equivalent),
% (incompatible), 2 (instance) or 3 (has instance). The user can specify the
assumption about the universe where the relations in the correspondences are
interpreted using the assuming clause, with possible values SingleDomain (all
ontologies are interpreted over the same universe, which is also the default),
GlobalDomain (the domains of the ontologies are reconciled w.r.t. a global
domain of interpretation) and ContextualisedDomain (the domains are
connected via relations). DOWL's treatment of bridge axioms in the so-called
contextualised semantics closely mirrors the syntax and semantics of C-OWL [
We now illustrate how, using bridge ontologies, networks of alignments can
be transformed into networks of ontology interpretations (morphisms), making
them amenable to colimits. Let A be an alignment (using the notations above).
The formal relations between the contributing ontologies can be given as a
diagram in the shape of a W-alignment (see [
O1
O2
B
Bridge O1'
O2'
For OWL, this means that Class1 < Class2 is translated to O1:Class1 v O2:Class2, Class1 = Class2, to O1:Class1 O2:Class2 and so on. The signature morphisms 1 and 2 are signature inclusions.
Example 1. The foundational ontology (FO) repository Repository of Ontologies for MULtiple USes (ROMULUS)3 contains alignments between a number of foundational ontologies. We present here the alignment of the FOs DOLCE4 and BFO5 using DOL syntax. alignment DolceLite2BFO : <http :// www . loa-cnr . it / ontologies / DOLCE-Lite .owl > <http :// www . ifomis . org / bfo /1.1 > = endurant = IndependentContinuant , physical-endurant = MaterialEntity , physical-object = Object , perdurant = Occurrent , process = Process , quality = Quality , spatio-temporal-region = SpatiotemporalRegion , temporal-region = TemporalRegion , space-region = SpatialRegion to
The bridge ontology of this alignment will contain only equivalence axioms between the matched symbols.
Another alignment, between Dolce and GFO [
While alignments capture relations between ontologies, interpretations (or ontology morphisms) capture the notion that one ontology can be completely mapped into another one. For example, mereology can be mapped into Euclidean space by interpreting parthood as containment between regions in space. See section 4.3 for further examples. The network construct itself is an essential ingredient for the idea of combination, which in turn is the fundamental operation enabling a formalisation of conceptual blending.
Networks of OWL ontologies are introduced by the following grammar: NetworkDefn := network NAME = Network Network ::= NAME * [ excluding NAME * ] 3 See http://www.thezfiles.co.za/ROMULUS/home.html 4 See http://www.loa.istc.cnr.it/DOLCE.html 5 See http://www.ifomis.org/bfo/ Here, the NAMEs can name ontologies, alignments, interpretations or other networks. A network is speci ed as a list of network elements (ontologies, ontology mappings and sub-networks), followed by an optional list of excluded network elements.
DOL also provides means for combin- Combined Ontology (colimit)
ing a network of ontologies into a new
ontology, such that the symbols related in C
the network are identi ed. The syntax of
combinations is combine N where N is a Input 1 colimit morphisms Input 2
network. The semantics of such a
combination is given in terms of a colimit. O1 O2
We refrain from presenting the
categorytheoretic de nition here (which can be base morphisms
found in [
Fig. 2 shows the colimit of a diagram Fig. 2. Combined ontologies. consisting of two morphisms with a common source. The colimit identi es the symbols of O1 and O2 that have a common origin in the base ontology and keeps distinct the symbols that do not share in the base. We can now put together the alignments between DOLCE and BFO and respectively DOLCE and GFO into one network: network SpaceNetwork =
DolceLite2BFO , DolceLite2GFO
We then can combine DolceLite and BFO taking into account the semantic relations speci ed in the alignment DolceLite2BFO given above: ontology DOLCELiteAndBFO =
combine DolceLite , BFO , DolceLite2BFO The ontology combining the network of DolceLite2GFO will contain the axioms of DolceLite and BFO as well as the bridge axioms of the alignment between them. 3
Use Case 1: Ontology Design Patterns in DOWL
Ontology Design Patterns (ODP) are solutions for reoccurring ontology
modelling situations. [
Let us consider an example of a popular ODP: the rei cation of relations as events. Within Semantic Web research contexts, this strategy is often employed because both RDF and OWL do not support n-ary relationships directly.6 One use case is the representation of relationships that change over time.
We present below a simpli ed version of an ODP for temporally changing relationships.
Prefix : : <http :// ex . com / odp / basicEvent #> Ontology : <http :// ex . com / odp / basicEvent > Class : Occurrent Class : Continuant DisjointWith : Occurrent Class : Time ObjectProperty : has_agent Domain : Occurrent ObjectProperty : has_patient Domain : Occurrent ObjectProperty : has_start_time Range : Time ObjectProperty : has_end_time Range : Time Class : DomainPTN SubClassOf : Continuant Class : RangePTN SubClassOf : Continuant Class : ReifiedRelationPTN
SubClassOf : has_agent exactly 1 DomainPTN SubClassOf : has_patient exactly 1 RangePTN SubClassOf : has_start_time exactly 1 Time SubClassOf : has_end_time exactly 1 Time Range : Continuant Range : Continuant
This pattern involves a rei ed relationship (a class) and two additional classes (DomainPTN, RangePTN), which correspond to the domain and the range of the non-rei ed relationship. These three classes are basically schematic placeholders within the ODP. The ODP is instantiated by replacing them with `real' classes.
DOWL allows the reuse and modi cation of ODPs. For example, assuming we wanted to instantiate it for the `loves' relationship. The following DOWL code de nes the lovesOntology as an instantiation of the Basic-Event-ODP, where we have `love events', which involves two people: ontology lovesOntology = <http :// ex . com / odp / basicEvent > with
ReifiedRelationPTN |- > Love , DomainPTN |- > Person , RangePTN |- > Person
The resulting ontology contains all the axioms of the original ontology except that the generic pattern symbols have been replaced by Love and Person. Thus, the lovesOntology contains axioms like:
Class : Person SubClassOf : Continuant Class : Love SubClassOf : has_agent exactly 1 Person
SubClassOf : has_patient exactly 1 Person
The lovesOntology inherits the properties has_agent and has_patient from the ODP. DOWL also allows the replacement of these generic properties by more pertinent ones. E.g., we may de ne the lovesOntologyv2 as the ontology that is the result of replacing ontology lovesOntologyv2 = lovesOntology with has_agent |- > has_lover , has_patient |- > has_lovee
As one would expect, the lovesOntologyv2 contains the proper declarations of the object properties (with their domain and ranges) and the revised axioms: Class : Love
SubClassOf : has_lover exactly 1 Person SubClassOf : has_lovee exactly 1 Person 4.1
Use Case 2: Conceptual Blending in DOWL
Conceptual Blending is a theory for the
cognitive process behind creative thinking
and generation of novelty [
As mental spaces can be rich in information, the blends can take as many shapes as there are possible combinations. While humans can more or less automatically sort out the blends that make sense and are valuable, automatic blending needs guidance to avoid blends with con icting or useless information. 4.2
Conceptual blending has been formalised using an approach based on Goguen's
work on algebraic semiotics [
In [
As illustrated in Figure 3, the process of blending involves two input concepts
along some shared structure. The input concepts and the shared structure can all
be represented as OWL ontologies. Together with the ontology morphisms that
identify the shared structure, these ontologies form a DOWL network, which can
be combined (compare Figure 2 above). Because the combination usually yields
an ontology that contains too much information (often it is even inconsistent), it
usually needs to be weakened by removing axioms or by using more sophisticated
generalisation or debugging strategies [
Class : Dog SubClassOf : Mammal
SubClassOf : has_habitat some Home SubClassOf : has_body_shape some QuadrupleShape SubClassOf : has_part exactly 2 Hindlegs SubClassOf : has_part exactly 2 Forelegs
SubClassOf : covered_by some Hair Class : Owl SubClassOf : Bird
SubClassOf : has_habitat some Forest SubClassOf : has_shape some BirdShape SubClassOf : has_part exactly 2 Legs SubClassOf : has_part exactly 2 Wings SubClassOf : has_part exactly 1 Beak
SubClassOf : covered_by some Feathers
We now give an example of a conceptual blending network speci ed in DOWL, and blending the Dog-Owl. 4.3
ontology base =
ObjectProperty : has_habitat ObjectProperty : has_part Class : BackLimb Class : Animal
ObjectProperty : has_body_shape ObjectProperty : covered_by
Class : ForeLimb SubClassOf : has_part exactly 2 ForeLimb
SubClassOf : has_part exactly 2 BackLimb interpretation base2dog : base to Dog =
Animal |- > Dog , ForeLimb |- > Foreleg , interpretation base2owl : base to Owl =
Animal |- > Owl , ForeLimb |- > Wing , BackLimb |- > Leg
BackLimb |- > Hindleg ontology initialblend =
{ combine base , Dog , Owl , base2dog , base2owl } with Animal |- > Dowl ontology dowlblend = initialblend reject { Class : Dowl
SubClassOf : Bird SubClassOf : has_body_shape some QuadrupleShape SubClassOf : has_habitat some Home SubClassOf : covered_by some Feathers }
To demonstrate the idea, we illustrate how two animals, a dog and an owl, can be merged into a monster of sorts, a `dowl'. The input spaces are represented as simpli ed OWL ontologies in Figure 4. Naturally, the concepts are not fully represented, but the formalisations capture some of the important features of the animals. The base ontology contains information shared between the input spaces. Two interpretations map the base ontology onto the input spaces. See to the input spaces. The ontology initialblend consists of the disjoint union of all the features from the input spaces modulo the shared features from the base space. Thus, in initialblend the blended concept Dowl is an animal that has two forelimbs and two backlimbs, which is covered by hair and feathers, lives both in homes and in the forest and has both the shape of a bird and a quadruped. To achieve a reasonable concept, we de ne a second ontology, dowlblend, where we selectively weaken initialblend by rejecting certain axioms.
Class : Dowl SubClassOf : Mammal
SubClassOf : has_habitat some Forest SubClassOf : has_body_shape some BirdShape SubClassOf : has_part exactly 2 HindLeg SubClassOf : has_part exactly 2 Wing SubClassOf : covered_by some Hair
The resulting ontology contains a new concept: a birdlike mammal with hair living in the forest (see Figure 6). Note that the resulting concept combines aspects of the original concepts selectively, which is something that could not be done in OWL. Naturally, we could choose a number of di erent combinations. Here, evaluation of the blends is essential and needs to be connected not only to logical consistency, but to a consideration of rich background knowledge ontologies that can help ensure the quality of the blends. 5
The blending diagrams (or networks) can be analysed and computed by the
Heterogeneous Tool Set Hets, a proof management system. Hets is integrated
into Ontohub7, an ontology repository which allows users to manage and
collaboratively work on ontologies. DOL, DOWL, Hets, and Ontohub provide a
powerful set of tools making it easy to specify and computationally execute
conceptual blends, as discussed in [
Reasoning about DOWL ontologies and networks in many cases can be reduced to reasoning in OWL DL by using Hets for a) attening out the structuring constructs, which means computing an equivalent basic ontology for any structured ontology, and b) taking combinations (colimits) of networks, also resulting in a at OWL DL ontology. Concerning reasoning about the di erent forms of reduction, the easiest one is select and reject, which again can be attened out. For extract and remove, module extraction methods already provide at ontologies. For hide and reveal, the hiding can be uncovered (using colimits), also resulting in a at OWL DL ontology.
Future work concerns reasoning about DOWL ontologies that cannot be
attened. In the case of keep and forget, this is addressed in current research about
forgetting and uniform interpolation [
Acknowledgments. The project COINVENT acknowledges the nancial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under FET-Open Grant number: 611553.