A Method for Evaluating and Standardizing Ontologies

1 Introduction

For my thesis work I am developing a method for evaluating and standardizing ontologies based on an integration of the Basic Formal Ontology (BFO) and OntoClean. BFO serves as the upper ontology for the domain ontologies of the Open Biomedical Ontologies (OBO) Foundry 1 . The OBO Foundry initiative is a collaborative effort for developing interoperable, science-based ontologies. OntoClean is an approach for the quality assurance of ontologies, and helps a modeler detect when the subsumption relation is used improperly.

Ontologies developed for OBO use include some that have been ratified, and others holding the status of "candidate". To maintain consistency between ontologies, it is important to establish formal principled criteria that a candidate ontology must meet for ratification. The formalisms that result from our integration will serve as criteria an OBO Foundry candidate ontology must satisfy in order to be ratified. The formalisms will also serve as a constraints within a prototype of an ontology editor that interactively asks a modeler questions that helps alleviate constraint violations.

The first step in the integration is the unification of the categorical units of OntoClean and BFO. OntoClean uses properties, which are the intension of general terms. BFO uses types, "generalizations about the structure, order, and regularity that exists in nature that experiments and observations make possible" [Spear, 2007, p.16]. We unify property and type under the categorical unit class, since each has a corresponding class. member of(x,A,t) means that the object x satisfies the definition of class A at t. exists at(x,t) means that under a certain ontological theory, object x is within its domain, and it's existence spans t.

OntoClean requires that a modeler characterize their properties with respect to the notions of Identity, Unity, and Rigidity. 2 Identity holds for properties for which there is a way to uniquely identify its instances. Unity holds for properties for which their instances are integral wholes. Rigidity is a notion that characterizes a property as either: Rigid, essential to all its instances; Non-Rigid, non-essential to some instance; or Anti-Rigid, non-essential to all instances. In what follows we describe the completed work on integrating the Rigidity ticular x is an instance of type A at time t. If a general term refers to a class, but also to what is a BFO type, then each of the members of the class instantiates the type. BFO considers instance of, not member of, the most basic relation for constructing ontologies.

1 http://www.obofoundry.org/

2 Dependence will be addressed within the scope of Rigidity in the dissertation.

Particulars that instantiate a type are in some sense a part of a whole; types exist in their corresponding particulars [Smith, 2003, p.6], so there is a dependency between a type and its particulars. (This may be more controversial for types that are artifactual, however.) With the member of(x,A,t) relation, there is no commitment about the nature of A. Classes may be members of a class, but only particulars are instances of a type.

isa(A,B) means that all instances of A are instances of B. It is the "backbone" BFO relation for scientific classification, i.e., building taxonomies. isa is provably reflexive, transitive, and anti-symmetric. disa(A,B) ('d' for "direct") means there is no other type "in between" A and B in the isa hierarchy. disa is provably irreflexive, intransitive, and asymmetric, and isa is its transitive closure. The root type of the BFO upper ontology is Entity and is directly subtyped by Continuant and Occurrent. Continuants (e.g., a heart) are continuous with respect to time, while occurrents (e.g., process of a heart beating) are bound with respect to time. If an occurrent instantiates a type, it instantiates that type for all time.

BFO's theory of types commits to the Disjointness Principle, that two types have no instances in common unless one is a subtype of the other. The Single Inheritance Principle follows, that no type has more than one direct supertype. From the definition of disa and the Disjointness Principle, it follows that two types which have an instance and a direct supertype in common are identical. Candidate types (i.e., classes proposed as types in an OBO Foundry candidate ontology) that violate either principle are not types.

2.1 Dependency

BFO is influenced by Aristotle's division of particulars into substances and accidents. BFO refers to these under the types IndependentContinuant and DependentContinuant, which disjointly fall under Continuant. An example of an independent is a specific chunk of wood. An example of a dependent is the texture of that chunk of wood. The depends on(x,y,t) relation means that the dependent x depends on the independent y at a time t. Relative to our example, the texture is given the status of a particular in BFO, but it only exists when the chunk of wood exists, and cannot migrate from one chunk to another.

There are other type-level relations besides isa which, instead of subsumption, describe relationship patterns between particulars of two types. Depends On(A,B) means that for every instance of A there is some instance of B where the former instance depends on the latter instance. For example, a function of mitochondria is to supply cellular energy.

3 Applying Rigidity and Disjointness to BFO-Compliant Domain Modeling

Our reformulation of Rigidity is useful as a modeling construct for BFO and OBO because a Non-Rigid candidate type is frequently a class whose members are independents and the class definition implicitly refers to dependents. In the context of an evaluation method, the notion of Rigid and Non-Rigid candidates is useful together with the Disjointness Principle.

Violations of the Disjointness Principle follow the pattern A is a subtype of B and C, where under closed world reasoning, B is not a subtype of C, and vice versa. One reason for the violation is that B and C are types, and one is a subtype of the other, but it has not been specified yet by the modeler. Another possibility is that one candidate, B, is a type, and the other, C, is Non-Rigid. Let's assume that A is the candidate Molecule and C is the candidate Reactant. We assume that Reactant has the informal definition "A starting material in a chemical reaction." In this case members of Reactant are molecules and the class definition implicitly refers to other particulars which BFO considers roles. Because reactant roles are only played by molecules, Depends On(Reactant,Molecule) is the appropriate representation for the relationship, instead of isa(Molecule,Reactant).

4 Conclusion and FutureWork

The notion of class covers both OntoClean's notion of property and BFO's notion of type. A class might or might not satisfy Instantiated, Exists, Rigid, or Non-Rigid, the latter two capturing the intuitions of Rigidity within our formal theory of classes. BFO's notion of type is captured by a class that satisfies Instantiated, Exists, and Rigid. A domain modeler who wants her ontology to be ratified for OBO use and thus BFO-compliant must show that the candidate types of her ontology are indeed types by these criteria.

In future work we will integrate OntoClean's other components (i.e., Unity and Identity) with BFO. We will also more closely tie the current work to the ontology modeling process. In doing so we will treat our formalisms as a foundation for developing a phased, question-asking method that assists a modeler in determining if a candidate type satisfies Instantiated, Exists, Rigid, or Non-Rigid. Ofttimes ontology literature is obfuscated by philosphical lingo. We take a more intuitive approach in our method by asking the modeler questions using examples they provide for what they want to classify. Ultimately, the method we develop will provide a modeler assistance in evaluating candidate types. For those candidate types that do not satisfy criteria needed to be a type, the method will assist the modeler in determining how the candidate type can be formulated in a manner that is consistent with BFO's theory.