Establishing a Bridge from Graph-based Modeling Languages to Ontology Languages

Establishing a Bridge from Graph-based Modeling Languages to Ontology Languages Tobias Walter Hannes Schwarz Yuan Ren (University of Aberdeen) 30.06.2010 TWOMDE 2010

Objectives
Introduction
Modeling of TGraphs and Schemas in OWL
Bridge
Cardinality Expressions
Quantified Expressions
Boolean Connectives
Path Descriptions
Advantages of the TGraph Approach and OWL
Conclusion

Introduction (TGraph Approach)
TGraph (Model)
Directed graphs, their edges and vertices are typed and attributed, and for each vertex the incident edges are ordered. In addition, the vertices and edges of the graph are ordered globally.
Example (M1 layer)
abstract syntax concrete syntax

Introduction (TGraph Approach)
Graph Schema (Metamodel)
Schemas define types of edges and vertices, associates them with attributes, and structures them in generalization hierarchies
grUML (Metamodeling Language)
Metamodeling language used for modeling schemas corresponds to a subset of UML class diagrams
Example (M2 layer)

Introduction (GReQL)
Graph Repository Query Language
declarative, expression-based query language for TGraphs
FWR expressions
from - declares variables
with - summarizes predicates which have to be fulfilled by the variables
report - determines the result structure of the query
Example
Constraint in GReQL:
from v:V with reMatch(v.name, ".*Action.*") report v as “Action “; forall n: V {ActivityNode} @ n.name <> ""

Description Logics
Description Logics (DLs) are logics designed to represent and reason on structured knowledge
The domain of interest is structured into ( TBox ):
concepts, which correspond to classes, and denote sets of individuals
roles, which correspond to associations, and denote binary relations on individuals
The knowledge is asserted through so-called assertions ( ABox )
Provide formal semantics
DLs provide the foundations for standard ontology languages, like OWL2
Knowledge Base TBox ABox Inference Engine Application

Each vertex class is represented as an OWL class
All vertex classes are subsumed by a super concept Vertex
Declaration ( Class (ActivityNode)) Declaration ( Class (Vertex)) SubClassOf (ActivityNode Vertex)

Each edge class is represented by an OWL class.
Two object properties which define the source ( from ) and target ( to ) vertices of an edge
An object property is declared as the chain of the two object properties
Declaration ( Class (HasNode)) Declaration ( ObjectProperty (fromHasNode)) ObjectPropertyDomain (fromHasNode HasNode) ObjectPropertyRange (fromHasNode ActivityDiagram) Declaration (ObjectProperty(toHasNode)) ObjectPropertyDomain (toHasNode HasNode) ObjectPropertyRange (toHasNode ActivityNode) Declaration ( ObjectProperty (HasNodeProperty)) SubObjectPropertyChain ( InverseObjectProperty (fromHasNode) toHasNode) HasNodeProperty)

All OWL classes representing edge classes and their object properties to and from are subsumed by one single object property topEdgeProperty ,
topEdgeProperty has a transitive super object property transitiveTopEdgeProperty
Declaration ( ObjectProperty (topEdgeProperty)) ObjectPropertyDomain (topEdgeProperty Vertex) ObjectPropertyRange (topEdgeProperty Vertex) SubObjectPropertyOf ( HasNodeProperty topEdgeProperty) Declaration ( ObjectProperty (transitiveTopEdgeProperty)) SubObjectPropertyO f(topEdgeProperty transitiveTopEdgeProperty) TransitiveObjectProperty (transitiveTopEdgeProperty)

Each attribute is transformed to a data property in OWL
Specialization relationships relating vertex classes and edge classes, respectively, are transformed to OWL subclass axioms
Declaration ( DataProperty (name)) DataPropertyDomain (name ActivityNode) DataPropertyRange (name xsd:string) SubClassOf(ObjectFlow ActivityEdge) SubClassOf(Action ActivityNode)

TGraphs themselves are transformed to a set of assertions.
.... Declaration (Individual(start)) Declaration (Individual(process)) Declaration (Individual(finish)) ClassAssertion (start Initial) ClassAssertion (process ControlFlow) ClassAssertion (finish Final) ObjectPropertyAssertion (controlFlowProperty start process) ObjectPropertyAssertion (controlFlowProperty process finish) ....

Cardinality Expressions
grUML
Cardinalities directly defined by annotating edge classes
OWL
Defined by class expressions ObjectMinCardinality , ObjectMaxCardinalit y, and ObjectExactCardinality
SubClassOf (ActivityNode ObjectExactCardinality (1 InverseObjectProperty (HasNodeProperty) ActivityDiagram))

Quantified Expressions
grUML+ GReQL
Universal quantification:
Existential quantification
OWL
ObjectAllValuesFrom class expression for universal quantification
ObjectSomeValuesFrom class expression for existential quantification
forall n: V { ActivityNode } @ n. name <> "" forall f: V {Final} @ exists a:V{ ActivityNode } @ a -->{ ActivityEdge } f SubClassOf (ActivityDiagram ObjectAllValuesFrom (HasNodeProperty ObjectIntersectionOf ( ObjectComplementOf ( DataHasValue ( name "")) ActivityNode ))) SubClassOf ( Final ObjectSomeValuesFrom ( InverseObjectProperty( ActivityEdgeProperty ) ActivityNode ))

Boolean Connectives
grUML + GReQL
operators and , or , not
OWL
ObjectIntersectionOf , ObjectUnionOf , ObjectComplementOf class expressions.
forall ad: V {ActivityDiagram} @ ( exists i:V{Initial} @ ad --> {HasNode} i) and ( exists f: V {Final} @ ad -->{HasNode} f) SubClassOf (ActivityDiagram ObjectIntersectionOf ( ObjectSomeValuesFrom (HasNodeProperty Initial) ObjectSomeValuesFrom (HasNodeProperty Final) ))

Path Descriptions (Simple Path Description)
grUML+ GReQL
--> (outgoing) , <-- (incoming), <-> (direction not important)
optionally an edge type restriction in curly braces.
forall v: V {Action} @ exists w: V @ v --> w forall w: V {ObjectNode} @ exists v: V @ w <--{ObjectFlow} v
OWL
ObjectSomeValuesFrom class expressions
topEdgeProperty or OWL class representing the edge type
SubClassOf (Action ObjectSomeValuesFrom (topEdgeProperty Vertex) ) SubClassOf (ObjectNode ObjectSomeValuesFrom (objectFlowProperty Vertex) ))

Path Descriptions (Goal- and Start-Restrictions)
grUML+ GReQL
Restriction of start and end vertices of a path description
Vertex class expression which restricts the start or end vertex is separated from the path description with a &
forall o: V {ObjectNode} @ exists v: V @ o --> &{Action, ObjectNode} v
OWL
Class expression to describe goal and start of edge
for example: ObjectUnionOf
SubClassOf (ObjectNode ObjectSomeValuesFrom (topEdgeProperty ObjectUnionOf (ObjectNode Action) ))

Path Descriptions (Sequential Path Description)
grUML+ GReQL
Simple concatenation of path descriptions
forall i: V {Initial} @ exists v: V @ i -->--> v
OWL
Nested ObjectSomeValuesFrom class expressions
SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)) )

Path Descriptions (Exponentiated Path Description)
grUML+ GReQL
Natural number to define exponents of path descriptions
forall i: V {Initial} @ exists v: V @ i -->^2 v
OWL
Nested ObjectSomeValuesFrom class expressions
SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)) )

Path Descriptions (Optional Path Description)
grUML+ GReQL
Marking a path as optional by surrounding it with brackets
forall o: V {ObjectNode} @ exists v: V @ o --> [-->] v
OWL
ObjectUnionOf expression to represent the optional path
SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)))

Path Descriptions (Alternative Path Description)
grUML+ GReQL
Marking a path as alternative by separating them with a pipe
forall o:V{ObjectNode} @ exists v:V @ o --> &{Action} | --> &{ObjectNode} v
OWL
ObjectUnionOf expression to represent alternative paths
SubClassOf (ObjectNode ObjectUnionOf ( ObjectSomeValuesFrom (topEdgeProperty Action) ObjectSomeValuesFrom (topEdgeProperty ObjectNode) ))

Path Descriptions (Iterated Path Description)
grUML+ GReQL
Use of Kleene operators * and + to define iterated path descriptions
forall i:V{Initial} @ exists f:V{Final} @ i -->+ f
OWL
Iterated path expressions realized by transitive object properties
SubClassOf (Initial ObjectSomeValuesFrom ( transitiveTopEdgeProperty ObjectSomeValuesFrom (transitiveTopEdgeProperty Vertex)))

Reasoning (1)
Reasoning on at least 2 layers (TBox/ABox)
Reasoning at schema layer
forall f:V{Final} @ exists v:V @ (f --> v) and not (f --> v) SubClassOf (Final ObjectIntersectionOf ( ObjectSomeValuesFrom (topEdgeProperty Vertex) ObjectComplementOf ( ObjectSomeValuesFrom (topEdgeProperty Vertex))))  Final is unsatisfiable

Reasoning (2)
Reasoning at instance- and schema layer
Declaration (Individual(initial)) Declaration (Individual(object1)) Declaration (Individual(final)) ClassAssertion (initial Initial) ClassAssertion (final Final) ObjectPropertyAssertion (objectFlowProperty initial object1) ObjectPropertyAssertion (objectFlowProperty object1 final) EquivalentClasses (ObjectNode ObjectUnionOf ( ObjectSomeValuesFrom (objectFlowProperty Vertex) ObjectSomeValuesFrom ( InverseObjectProperty (objectFlowProperty) Vertex)))  object1 has type ObjectNode

Explanations
Explanations of unsatisfiable classes
Explanations of inconsistent models/graphs
SubClassOf (Final ObjectIntersectionOf ( ObjectSomeValuesFrom (topEdgeProperty Vertex) ObjectComplementOf ( ObjectSomeValuesFrom (topEdgeProperty Vertex)))) Explanation from TwoUse Toolkit --------------------------------------- Unsatisfiability of Final: Explanation: Final equivalentTo not topEdgeProperty some Vertex and topEdgeProperty some Vertex SubClassOf (Initial ObjectSomeValuesFrom ( transitiveTopEdgeProperty ObjectSomeValuesFrom (transitiveTopEdgeProperty Vertex))) Explanation from TwoUse Toolkit --------------------------------------- CHECK CONSISTENCY Consistent: No Explanation: receiveOrder type Action Action subClassOf ActivityNode ActivityNode equivalentTo transitiveTopEdgeProperty some Final

Open World Assumption
Assumes incomplete information by default
Guidance and validation of incomplete models
Query for possible model element types types after Send Invoice Possible replacement of control nodes by one single object flow

Conclusion
Transformation bridge between Modelware and Ontoware
Intersection of modelware and ontoware
Standard modeling constructs
Path Descriptions
Differences
Reasoning technologies of OWL
Simplicity and Efficiency of TGraphs

Establishing a Bridge from Graph-based Modeling Languages to Ontology Languages

by Tobias Walter on Feb 06, 2011

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Establishing a Bridge from Graph-based Modeling Languages to Ontology Languages — Presentation Transcript