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 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Introduction (TGraph Approach) ,[object Object],[object Object],[object Object],abstract syntax concrete syntax

Introduction (TGraph Approach) ,[object Object],[object Object],[object Object],[object Object],[object Object]

Introduction (GReQL) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],from v:V with reMatch(v.name, ".*Action.*") report v as “Action “; forall n: V {ActivityNode} @ n.name <> ""

Description Logics ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Knowledge Base TBox ABox Inference Engine Application

Modeling of TGraphs and Schemas in OWL ,[object Object],[object Object],Declaration ( Class (ActivityNode)) Declaration ( Class (Vertex)) SubClassOf (ActivityNode Vertex)

Modeling of TGraphs and Schemas in OWL ,[object Object],[object Object],[object Object],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)

Modeling of TGraphs and Schemas in OWL ,[object Object],[object Object],Declaration ( ObjectProperty (topEdgeProperty)) ObjectPropertyDomain (topEdgeProperty Vertex) ObjectPropertyRange (topEdgeProperty Vertex) SubObjectPropertyOf ( HasNodeProperty topEdgeProperty) Declaration ( ObjectProperty (transitiveTopEdgeProperty)) SubObjectPropertyO f(topEdgeProperty transitiveTopEdgeProperty) TransitiveObjectProperty (transitiveTopEdgeProperty)

Modeling of TGraphs and Schemas in OWL ,[object Object],[object Object],Declaration ( DataProperty (name)) DataPropertyDomain (name ActivityNode) DataPropertyRange (name xsd:string) SubClassOf(ObjectFlow ActivityEdge) SubClassOf(Action ActivityNode)

Modeling of TGraphs and Schemas in OWL ,[object Object],.... 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 ,[object Object],[object Object],[object Object],[object Object],SubClassOf (ActivityNode ObjectExactCardinality (1 InverseObjectProperty (HasNodeProperty) ActivityDiagram))

Quantified Expressions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],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 ,[object Object],[object Object],[object Object],[object Object],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) ,[object Object],[object Object],[object Object],forall v: V {Action} @ exists w: V @ v --> w forall w: V {ObjectNode} @ exists v: V @ w <--{ObjectFlow} v ,[object Object],[object Object],[object Object],SubClassOf (Action ObjectSomeValuesFrom (topEdgeProperty Vertex) ) SubClassOf (ObjectNode ObjectSomeValuesFrom (objectFlowProperty Vertex) ))

Path Descriptions (Goal- and Start-Restrictions) ,[object Object],[object Object],[object Object],forall o: V {ObjectNode} @ exists v: V @ o --> &{Action, ObjectNode} v ,[object Object],[object Object],[object Object],SubClassOf (ObjectNode ObjectSomeValuesFrom (topEdgeProperty ObjectUnionOf (ObjectNode Action) ))

Path Descriptions (Sequential Path Description) ,[object Object],[object Object],forall i: V {Initial} @ exists v: V @ i -->--> v ,[object Object],[object Object],SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)) )

Path Descriptions (Exponentiated Path Description) ,[object Object],[object Object],forall i: V {Initial} @ exists v: V @ i -->^2 v ,[object Object],[object Object],SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)) )

Path Descriptions (Optional Path Description) ,[object Object],[object Object],forall o: V {ObjectNode} @ exists v: V @ o --> [-->] v ,[object Object],[object Object],SubClassOf (Initial ObjectSomeValuesFrom (topEdgeProperty ObjectSomeValuesFrom (topEdgeProperty Vertex)))

Path Descriptions (Alternative Path Description) ,[object Object],[object Object],forall o:V{ObjectNode} @ exists v:V @ o --> &{Action} | --> &{ObjectNode} v ,[object Object],[object Object],SubClassOf (ObjectNode ObjectUnionOf ( ObjectSomeValuesFrom (topEdgeProperty Action) ObjectSomeValuesFrom (topEdgeProperty ObjectNode) ))

Path Descriptions (Iterated Path Description) ,[object Object],[object Object],forall i:V{Initial} @ exists f:V{Final} @ i -->+ f ,[object Object],[object Object],SubClassOf (Initial ObjectSomeValuesFrom ( transitiveTopEdgeProperty ObjectSomeValuesFrom (transitiveTopEdgeProperty Vertex)))

Reasoning (1) ,[object Object],[object Object],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) ,[object Object],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 ,[object Object],[object Object],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 ,[object Object],[object Object],Query for possible model element types types after Send Invoice Possible replacement of control nodes by one single object flow

Conclusion ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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

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