Constructing domain ontologies is a demanding endeavour. The formalization of basic regularities of a domain requires not only familiarity with the domain but also understanding of the basic principles of logic and formal ontology. This is especially the case if ontology engineering is understood not as building (closed-world) models limited to the support of well-delineated reasoning use cases in restricted domains, but as providing interoperable and re-usable (open world) representations of the domain itself. This is a basic principle stressed not only by the defenders of so-called realist ontologies [1,2] but also by some (moderate) critics [3], which documents an increasing consensus on how to represent those areas of knowledge where people tend to agree on an observer-independent reality and benefit from standardised terms, such as in natural science and technology domains. An important tenet of these ontologies is collaborative ontology development and interoperability. Principles for this kind of ontology development have been formulated by the OBO Foundry consortium [4] and within the Good Ontology Design (GoodOD) guidelines [5]. Both propagate a concise foundational upper-level as a mainstay for interoperability, and there is also some evidence that foundational ontologiesdomain-independent top-level or domain-related upper-level ontologiesspeed up ontology development and improve quality [6]. This paper is intended to initiate a discussion on how foundational ontologies can help prevent typical errors in domain ontologies. This is also the reason why prototypical, partly made-up but easily understandable examples are used.
The work is based on BioTopLite (BTL2), an upper-level ontology [7], linked to BFO [8], using description logics [9] with OWL-DL expressiveness [10]. BTL2 has been designed with the intent to provide a rich set of constraining axioms to enforce the consistency of ontologies modelled thereunder. Although BTL2 is, in principle, domainindependent, its content is geared to the domains of health care and biomedical research. This explains, e.g., the provision of more fine-grained classes for chemical and biological entities (e.g. 'mono molecular entity', organism, cell, population) as well as the disjunctive class condition, created in order to deal with the ontological heterogeneity of key medical concepts like diseases, signs, and symptoms. Fig. 1 provides Protégé screenshots of the class and relation hierarchies, together with sample axioms. Classes, relations (object properties) and selected axioms in BioTopLite2 (BTL2) [7] In order to test and demonstrate how BTL2 axioms are useful for preventing ontology design errors, T-boxes with typical examples of bad modelling will be presented in order to challenge the underlying foundational ontology. Some of these examples are formulated very abstractly due to their high level of generality; others use terms from a specific domain but are still understandable for a broader public.
Each T-box is modelled as an extension of BTL2. The HermIT [11] reasoner was used to detect inconsistencies. The explanation of inconsistencies follows Protégé's OWL entailment explanation feature [12]. The examples are provided together with their results in the following section. The presentation of the original OWL expressions, the entailments and their justifications is done in the following order:
SRC -Axioms from ontology source (known satisfiable).
CHA -New axioms added that challenge the satisfiability of SRC. Cases in which an axiom is only transiently added, are marked by CHA-T. INF -Inference, in particular the detection of classes that are unsatisfiable w.r.t. the T-box constituted by SRC and CHA. EXP -Explanations of INF, with axioms collected from the explanation plug-in [12].
Reasoning examples under BTL2 are presented, in which deliberately erroneous axioms lead to an incoherent ontology, i.e., where one or more named classes turn out to be unsatisfiable, i.e. necessarily empty w.r.t. the T-box. This is expected to be detected by a DL classifier. In the following, a distinction is made between five error types, viz. (1) simple category errors, (2) value restrictions and transitive role errors, (3) complex domain/range constraint errors, (4) physical granularity errors, and ( 5) errors regarding unrealized realisables and non-referring information entities.
A category error occurs whenever a class is a taxonomic descendent of upper-level classes that are modelled as mutually exclusive (Disjoint Classes in OWL). Such errors typically occur when ontology mapping and alignment is guided by lexical criteria. For instance, when mapping content of the clinical ontology SNOMED CT [13] (namespace sct:) to the foundational ontology BTL2 (namespace btl2:) one might be tempted to equate sct:Process with btl2:process and place 'sct: The origin of such category errors may be manifold. A common cause is misleading class labelling. Ontology labels should be context-independent and self-explanatory, and they should avoid ambiguous terms [14]. A more severe problemlike herearises where the ontologies to be aligned fundamentally differ in upper level assumptions. In SNOMED CT, e.g., the subhierarchy 'sct:Qualifier Value (qualifier value)' is currently a badly organized reservoir for the most diverse terms, and the reason why hierarchies of pathological and physiological processes are placed therein remains unclear2 .
Value
Axiom like (2c) may fulfil their purpose in domain ontologies in which cells are the smallest objects, but as soon as smaller objects are allowed, the expression is inadequate assuming 'has part' being transitive. BTL2 obviates such a granularity restriction by stating that all material objects have subatomic particles as (transitive) parts.
Complex domain / range restrictions Domain / range restrictions are a suitable means to avoid ontology errors. However, in ontologies that use a small number of object properties like BTL2, this resource may be not expressive enough. For instance, if the relations 'btl2:is part of' and 'btl2:has part' are valid for material objects, immaterial objects, as well as for processes and information objects, formulating just domain / range restrictions at the level of these relations would still be compatible with an (unintended) model in which an object is part of a process or vice versa. This is why BTL2 encodes these restrictions using axioms like the one in (3f).
Realisable entities like functions and dispositions [16] depend on material entities and are realised in processes. However, the existence of realisables does not imply their realisation: The function of a screwdriver is to drive screws, and the disposition of a glass is to break under certain circumstances, but as there are screwdrivers that are never used and glasses that are never thrown to the floor. Because for all types of functions and dispositions there are instances that have never been realised, ontologies have to deal with unrealised realisables, which could be, e.g., expressed by (5a).
Unrealized_Function EquivalentTo btl2:function and not ('btl2:has realization' some owl:thing) (5a)
In order not to preclude the possibility that dispositions and functions happen to be never realised, ontologies under BTL2 should define them using the value restriction constructor: SRC btl2:function SubClassOf 'btl2:has realization' only btl2:process (5b) SRC Function_A EquivalentTo btl2:function and ('btl2:has realization' only Process_A)
Nevertheless, BTL2 does not reject a definition using an existential quantifier like in the following definition:
CHA Function_A EquivalentTo btl2:function and ('btl2:has realization' some Process_A)
Function_A would then exclude all unrealised function instances. Such a class (which might be considered anti-rigid [17] if assuming that realisable entities are always unrealised when they come into existence) is most likely not intended by the modeller. The detection of these errors requires checking consistency after transiently adding axiom (5e).
The explanation is given by the conjunction of axioms (5a), (
The axiomatization of non-referring information entities follows the same pattern. Information entities can be referring and non-referring [18]. A typical example is medical diagnosis [19]. BTL2 here uses the relation represents. This relation connects information entities with domain entity they correctly characterise. This allows to distinguish wrong diagnoses from correct diagnoses.
Cancer_Diagnosis EquivalentTo owl:Nothing
The explanation is given by the conjunction of axioms (5h), (5i), and (5k).
It was shown how a highly axiomatised foundational ontology like BioTopLite (BTL2) can incorporate constraints that reject bad modelling decisions that lead to unsatisfiable classes. A distinction was made between those cases in which the upper level axioms suffice for detecting such inconsistencies and those in which additional "challenges", i.e. transiently added axioms are necessary. Most of the former cases capitalise on disjoint class axioms present in the upper level ontology. This comes near to the so-called logical anti-patterns introduced by [20], all of which require disjoint class axioms in order to detect inconsistencies. In contrast to the work presented, anti-patterns are very abstract logical expressions and independent of foundational ontologies. OntoClean [17] was presented as a methodology for detecting improper subclass axioms based on philosophically inspired, domain-independent properties of classes, the metaproperties unity, identity and rigidity. Although DL reasoners do not support meta-level reasoning, it has to be investigated whether certain elements from OntoClean could also included in DL-based foundational ontologies, e.g. by reifying them in terms of additional top-level classes 3 .
Several limitations of this work have to be highlighted: The typology presented is certainly non-exhaustive. It is primarily motivated by the author's experience and not yet by the relevance of those types of problems in ontologies employed in real-world applications. It could further be related to existing work in ontology evaluation, e.g., the OQuaRE framework [21]. The proposed approach will probably fail if application ontologies bypass the partition of upper categories of the foundational ontology or introduce new object properties that are not subproperties of the existing ones. The BTL2 authors claim that their inventory of object properties is close to sufficient and recommend to introduce predicates required by the domain (e.g., in the biomedical domain: treats, prevents, diagnoses, interacts, binds) not as object properties but as subclasses of btl2:process. Important causes of bad ontology design cannot be prevented or remedied by a foundational ontology. This includes erroneous representation of individuals as classes or vice versa (a typical error would be an A-Box OWL expression like "SodiumAtom Type btl2:atom), bad naming and insufficient documentation, as well as constraints on a meta-class level like in OntoClean. Constraining axioms similar to the proposed ones can be added to domain ontologies, e.g. to assure mereotopological non-overlapping [22]. Although BTL2 was used as a testbed, the proposed approach would lend itself to other ontologies as well. Especially BFO would benefit from a stronger axiomatization, as the most popular version, which is the umbrella of most OBO ontologies lacks axioms beyond subclass and disjoint class axioms. This deficiency has been addressed by the 2.0 version, which is, however, not fully available in OWL due to its use of ternary relations. The fact that BTL2 uses the whole range of constructors allowed by OWL-DL has a negative impact on reasoning performance. This makes debugging of large ontologies intractable. This was the case when aligning SNOMED CT with BTL2 [23]. The solution was to use small modules created from random
signatures as described in [24]. As a solution a two-step approach was proposed: (i) at design time using the rich foundational ontology for debugging random modules of a (large) domain ontology under construction, and (ii) at runtime placing the final domain ontology under a light version of the same foundational ontology for enabling efficient reasoning.