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Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies

This paper discusses the integration of OntoClean's notion of rigidity with the Basic Formal Ontology (BFO) to enhance the standardization process for OBO Foundry candidate ontologies. Although OBO Foundry ontologies include various ratified and candidate entries, there is no formal procedure for ratification. The authors propose that this integration can assist modelers in aligning their work with BFO principles, thereby reducing errors related to ontology modeling. Key concepts include taxonomic hierarchies, properties, and decision trees for improved modeling consistency.

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Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies

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  1. Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies Patrice Seyed and Stuart C. Shapiro Department of Computer Science Center for Cognitive Science University at Buffalo ICBO

  2. Introduction • OBO Foundry Ontologies • Basic Formal Ontology (BFO) as the upper ontology • OBO includes Ratified/Candidate ontologies • But no formal (logical) criteria for ratification • OntoClean • Approach for detecting when the taxonomic relation is being used improperly • Formal integration between OntoClean’s notion of Rigidity and BFO’s theory of types

  3. Hypothesis • BFO and OntoClean’s notion of Rigidity can be integrated. • This integration can serve as a basis for a system that will assist a modeler in alignment with BFO and result in fewer modeler mistakes. • Provides a modeler with: • Formal System • Decision Tree

  4. BFO • Restricted set of highly generalized classes • Independent Continuant: Concrete ``Things’’ • Dependent Continuant: Qualities, Functions, Roles • Occurrent: Processes • BFO Classes are types(universals) • Domain level classes are assigned as subclasses • Restricted set of relations • Disadvantage • Its not always clear how to perform the assignments

  5. OntoClean • Constraints on taxonomic hierarchies • Rigidity, Identity, Unity, Dependence • Requires a modeler to assign certain features to each property of an ontology • A property is: Rigidif it is essential to all instances Non-Rigidif non-essential to some instance Anti-Rigidif non-essential to all instances Constraint: An Anti-Rigid property has only Anti-Rigidsubproperties.

  6. Modeling Example Applying Rigidity • Modeling Example Is Compound and CompoundReactant : Rigid, Non-Rigid, or Anti-Rigid? Compound Reactant Compound CompoundReactant Compound

  7. Step One: Categorical Unit • BFO • Type (Universal) • What the general terms of science refer to • Person, Student Role, Porous Quality • OntoClean • Property (attributive) • Meaning of general terms • (being a) Person, (being a) Student, (being) Porous • Unify Property and Type under the unit of Class

  8. Formal Theory of Classes • subclass_of(A,B) =def"xt(member_of(x,A,t) → member_of(x,B,t)) • exists_at(x,t) • Under a certain ontological theory, object x is within its domain and x’s existence spans some time, t. • Everything in the domain exists at some time: ∀x∃t(exists_at(x,t)) • membership at a time does not presuppose that existence spans that time ¬∀xt(∃A member_of(x,A,t)) → exists_at(x,t))

  9. Formal Theory of Classes • Two Features of classes: Instantiated(A) =def ∃xt(member_of(x,A,t) ∧ exists_at(x,t)) Members_Exist(A) =def ∀xt(member_of(x,A,t) → exists_at(x,t))

  10. Integrating Rigidity with BFO theory of types • ``Essential’’ reformulated w.r.t. to time: • Rigid(A) =def"x($t(member_of(x,A,t)) → "t(exists at(x,t) → member_of(x,A,t))) • Non-Rigid(A) =def$x($t(member_of(x,A,t)) ∧ $t(exists at(x,t) → Ømember_of(x,A,t))) • Anti-Rigid is incompatible with BFO

  11. Integrating Rigidity with BFO theory of types • Additional constraints on Rigid, and also on types: • Instantiated • Members_Exist • "A(Type(A) → Rigid(A)∧Instantiated(A)∧ Members_Exist(A))

  12. Integrating Rigidity with BFO theory of types instance_of(x,A,t) =defmember_of(x,A,t) ∧ Type(A) isa(A,B) =def"xt(instance_of(x,A,t) → instance_of(x,B,t)) "AB(isa(A,B) → Type(A) ∧ Type(B)) ⊦"A(Non-Rigid(A) → "B(¬isa(A,B) ∧ ¬isa(B,A)))

  13. Integration with BFO theory of Types • We lose the Anti-Rigid constraint. • What have we gained? • Non-Rigid Classes are not Types!? ? Compound Compound Reactant isa isa Compound Reactant Compound

  14. Modeling Example Compound ??? molecule-2 molecule-3 molecule-4 molecule-1 isa Compound Reactant reactantRole-2 compound-2 molecule-2 compound-2 reactantRole-3 compound-3 molecule-3 compound-3 compound-4 molecule-4 compound-1 compound-1 molecule-1 reactantRole-1

  15. Modeling Example Compound Compound Reactant-Role Role_Of molecule-2 molecule-3 molecule-4 molecule-1 subclass_of Compound Reactant reactantRole-2 molecule-2 compound-2 compound-2 reactantRole-3 compound-3 molecule-3 compound-3 molecule-4 compound-4 compound-1 compound-1 molecule-1 reactantRole-1

  16. Modeling Example Compound Compound Reactant-Role Role_Of molecule-2 molecule-3 molecule-4 molecule-1 subclass_of Has_Role Compound Reactant reactantRole-2 compound-2 compound-2 reactantRole-3 compound-3 compound-3 compound-4 compound-1 compound-1 reactantRole-1

  17. Dependent Continuant compound-3 compound-1 reactantRole-2 compound-2 compound-4 reactantRole-3 reactantRole-1 isa isa Compound Compound Reactant-Role Role_Of molecule-2 molecule-3 molecule-4 molecule-1 Independent Continuant subclass_of Has_Role Compound Reactant reactantRole-2 compound-2 compound-2 reactantRole-3 compound-3 compound-3 compound-4 compound-1 compound-1 reactantRole-1

  18. Modeling Example Compound Role molecule-2 molecule-3 molecule-4 molecule-1 subclass_of ??? Compound Reactant ? compound-2 compound-2 ? compound-3 compound-3 compound-4 compound-1 compound-1 ?

  19. Decision Tree • Proactive Avoidance of Multiple Inheritance and enforces examination of Non-Rigid classes • Introduces a class, one at a time • Asks a modeler to supply an example member of the class • Yes/No Questions • Correspond Upper Level Divisions, BFO/Rigidity Integration, Type-Level relations • A gentle approach of linking to BFO classes, and a refactoring when Non-Rigid classes are identified

  20. Entity isa isa Independent Continuant Dependent Continuant isa isa Role_Of Compound Compound Reactant-Role subclass_of Has_Role Compound Reactant

  21. Integration Summary • Classcovers both OntoClean’s notion of property and BFO’s notion of type. • A class might or might not satisfy Instantiated, Members_Exist, Rigid, or Non-Rigid • the latter two capturing the intuitions of Rigidity within our formal theory • BFO’s notion of type is captured by a class that satisfies Instantiated, Members_Exist, and Rigid.

  22. Future Work • Rigidity and Canonical domains • Connection of Non-Rigidity and Other Type-Level Relations • Expert review of decision tree procedure • Evaluate “accessibility” of questions • Integrate other OntoClean Components

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