Applying Rigidity to Standardizing
OBO Foundry Candidate Ontologies
A. Patrice Seyed and
Stuart C. Shapiro
Department of Computer Science
Center for Cognitive Science
University at Buffalo
ICBO
Introduction
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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
Hypothesis
1. BFO and OntoClean’s notion of Rigidity can
be integrated.
2. 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
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
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:
Rigid if it is essential to all instances
Non-Rigid if non-essential to some instance
Anti-Rigid if non-essential to all instances
Constraint: An Anti-Rigid property has only
Anti-Rigid subproperties.
Modeling Example Applying Rigidity
• Modeling Example
Is Compound and Compound Reactant :
Rigid, Non-Rigid, or Anti-Rigid?
Compound Reactant
Compound
Compound
Compound Reactant
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
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))
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))
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) → member_of(x,A,t)))
• Anti-Rigid is incompatible with BFO
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))
Integrating Rigidity with
BFO theory of types
instance_of(x,A,t) =def member_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)))
Integration with BFO theory of Types
• We lose the Anti-Rigid constraint.
• What have we gained?
– Non-Rigid Classes are not Types!?
Compound Reactant
isa
Compound
Compound
isa
Compound Reactant
?
Modeling Example
Compound
molecule-2
compound-2
???
reactantRole-2
compound-3
molecule-3
molecule-4
compound-4
reactantRole-1
molecule-1
compound-1
isa
Compound Reactant
molecule-2
compound-2
molecule-3
compound-3
molecule-4
molecule-1
compound-1
reactantRole-3
Modeling Example
Compound
molecule-2
compound-2
Compound Reactant-Role
Role_Of
reactantRole-2
compound-3
molecule-3
molecule-4
compound-4
reactantRole-1
molecule-1
compound-1
subclass_of
Compound Reactant
molecule-2
compound-2
molecule-3
compound-3
molecule-4
molecule-1
compound-1
reactantRole-3
Modeling Example
Compound Reactant-Role
Compound
molecule-2
compound-2
Role_Of
reactantRole-2
compound-3
molecule-3
molecule-4
compound-4
reactantRole-1
molecule-1
compound-1
subclass_of
Has_Role
Compound Reactant
compound-2
compound-1
compound-3
reactantRole-3
Independent Continuant
Dependent Continuant
compound-3
compound-1
compound-2
compound-4
reactantRole-1
isa
isa
Compound
molecule-2
compound-2
reactantRole-2 reactantRole-3
Compound Reactant-Role
Role_Of
reactantRole-2
compound-3
molecule-3
molecule-4
compound-4
reactantRole-1
molecule-1
compound-1
subclass_of
Has_Role
Compound Reactant
compound-2
compound-1
compound-3
reactantRole-3
Modeling Example
Compound
molecule-2
compound-2
Role
?
?
compound-3
molecule-3
molecule-4
compound-4
?
molecule-1
compound-1
subclass_of
Compound Reactant
compound-2
compound-1
compound-3
???
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
Entity
isa
isa
Independent Continuant
Dependent Continuant
isa
isa
Role_Of
Compound
Compound Reactant-Role
subclass_of
Has_Role
Compound Reactant
Integration Summary
• Class covers 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.
Future Work
• Rigidity and Canonical domains
• Connection of Non-Rigidity and Other TypeLevel Relations
• Expert review of decision tree procedure
– Evaluate “accessibility” of questions
• Integrate other OntoClean Components