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Applying Rigidity to Standardizing OBO Foundry Candidate Ontologies

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. Introduction. OBO Foundry Ontologies Basic Formal Ontology (BFO) as the upper ontology

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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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