COWL contextualizing ontologies Fausto Giunchiglia October 22 2003

C-OWL: contextualizing ontologies Fausto Giunchiglia October 22, 2003 Paolo Bouquet, Fausto Giunchiglia, Frank van Harmelen, Luciano Serafini, and Heiner Stuckenschmidt

The Talk n n n Ontologies vs. Contexts A (restated) global semantics for OWL – Intuitions Three motivating examples A (new) local models semantics for OWL – Intuitions C-OWL: extending OWL with (context) mappings

Ontologies vs. Contexts n An Ontology is a model of some domain which is supposed to encode a view common to a set of different parties An ontology is built to be shared; n A Context is a model of some domain which is supposed to encode a view of a party A context is built to be kept local (where local implies not shared) n A context and an ontology of the same domain are likely to be very different (different goals, different approach, …)

Pro’s and Contra’s n Ontologies q Strengths n q Weaknesses n n n “easy” exchange of information consensus must be reached about their contents maintenance may become arbitrarily hard Contexts q Strengths n n q “easy” to define and to maintain can be constructed with no consensus with the other parties Weaknesses n Exchange of information by constructing explicit mappings among the elements of the contexts of the involved parties

Contextual Ontologies Contextual ontology = Ontology + Context mappings Key idea (in two steps): 1. 2. Share as much as possible (OWL import construct) Keep it local whenever sharing does not work (C-OWL context mappings) Notes: 1. 2. In many (most in the Web? ) cases sharing does not work and produces undesired results (semantic heterogeneity) Using context allows for incremental, piece-wise construction of the Semantic Web (bottom up vs. top down approach).

The Talk n n n Contexts vs. Ontologies A (restated) global semantics for OWL – Intuitions Three motivating examples A (new) local models semantics for OWL – Intuitions C-OWL: extending OWL with (context) mappings

A Global Semantics for OWL Index OWL Ontologies: <i, Oi> and their languages (e. g. , i: C, j: E, i: r. C) (Local language). A local concept (role, individual), Ci (Ri, Oi) is an element of C that appears in Oi either without indexes or with index equal to i. (Foreign language): … Anything (concept, role, individual) which is not local (OWL space). An OWL space is a family of ontologies {<i, Oi>} such that the language of every Oi contains all the other foreign languages

A Global Semantics for OWL (cont’ed) (OWL interpretation). An OWL interpretation for the OWL space {<i, Oi>} is a pair I = <∆I, (. )I>, such that I(i, C) ∆I for any i I and C Ci; q I(i, r) ∆I x ∆I for any i I and r Ri; q I(i, o) ∆I for any i I and o Oi; With ∆I domain of interpretation and (. )I interpretation function q Note: a global interpretation!

A Global Semantics for OWL (cont’ed) (OWL axiom and fact satisfiability). I satisfies a fact or an axiom ø of Oi according to the rules defined in [*] P. F. Patel-Schneider, P. Hayes, and I. Horrocks. Web Ontology Language (OWL) Abstract Syntax and Semantics. Technical report, W 3 C, February 2003. An OWL interpretation I satisfies an OWL space {<i, Oi>}, if I satisfies each axiom and fact of Oi, for any i

The Talk n n n Contexts vs. Ontologies A (restated) global semantics for OWL – Intuitions Three motivating examples A (new) local models semantics for OWL – Intuitions C-OWL: extending OWL with (context) mappings

Example 1: directionality Need to keep track of source and target ontology Example: n Construct O 2 by importing O 1 and adding it some new axiom n Want that axioms added to O 2 do not affect O 1 n O 1 contains axioms A B and C D n O 2 contains also axiom 1: B 1: C In new semantics, we want 1: A O 1. 1: D in O 2, but not in

Example 1 (cont’ed): directionality We want to avoid propagation of inconsistency Example: n O 1 contains axioms A B and C D n O 2 contains also axiom 1: B 1: C n We want to derive 1: A 1: D in O 2 but not in O 1 n … n O 2 contains also 1: A(a) and 1: not D(a) n O 2 is inconsistent In new semantics, we want to keep O 1 consistent

Example 2: local domains Need to give up hypothesis that of single global domain of interpretation Example: Car manufacturing ontology OWCM with domain of interpretation the totality of cars n individual constants Diesel and Petrol for Diesel engine and petrol engine n Axiom: a car has only one engine which is either Diesel or petrol Car ( 1) has. Engine. {Diesel, Petrol} Diesel Petrol Ferrari ontology, OFerrari describing Ferrari’s production n Imports OWCM standard n Axiom: engine of a Ferrari is either an F 23 or and F 34 i Ferrari (WCM: car ( 1) (WCM: has. Engine). {F 23, F 34 i} F 23 F 34 i In new semantics, we want to avoid (F 23)IFerrari = (Diesel)IWCM since Ferrari produces only petrol engines

Example 3: context mappings Need to state that two elements of two ontologies, though being extensionally different, are contextually related Example: n OFIAT describes cars from manufacturer point of view n OSale describes cars from car vendor point of view n OFIAT and OSale are largely independent and different n Two concepts of car defined in OFIAT and OSale, (i. e. Sale: Car and FIAT: Car) may be very different, still describing same real world object (different viewpoints) Not possible to state relation between two concepts with OWL syntax

The Talk n n n Contexts vs. Ontologies A (restated) global semantics for OWL – Intuitions Three motivating examples A (new) local models semantics for OWL – Intuitions C-OWL: extending OWL with (context) mappings

Exampe 1: Directionality n Consider all (local) ontologies as part of a OWL space n Split global interpretation into a family of local interpretations, one for each ontology n Allow for an ontology to be locally inconsistent (i. e. , not to have a local interpretation) n Technically: Associate inconsistent ontologies to a special “interpretation”, called a hole, that verifies any set of axioms

Example 2: Local Domains n Associate to each ontology a local domain n Local domains may overlap (two ontologies may refer to the same object) n Technically: An OWL interpretation with local domains for the OWL space {<i, Oi>} is a family I = {Ii}, where each Ii = <∆Ii, (. )Ii>, called the local interpretation of Oi, is either an interpretation of Li on ∆Ii, or a hole

The Talk n n n Contexts vs. Ontologies A (restated) global semantics for OWL – Intuitions Three motivating examples A (new) local models semantics for OWL – Intuitions C-OWL: extending OWL with (context) mappings

Example 3: adding context mappings to syntax (Bridge rules). A bridge rule from i to j is a statement of one of the four following forms, where x and y are concepts, or individuals, or roles of the languages Li and Lj (Context mapping). Given a OWL space {<i, Oi>} a mapping Mij from Oi to Oj is a set of bridge rules from Oi to Oj.

Context mappings (cont’ed) (Contextual ontology): It is a local ontology plus a set of bridge rules (context mappings). We sometimes write context meaning contextual ontology. (Context space). A context space is the pair 1. OWL space {<i, Oi>} (of local ontologies) 2. family {Mij} of (context) mappings from i to j, for any pair i, j (Interpretation for context spaces). It is the pair 1. I, where I is an OWL interpretation with holes and local domains and 2. rij, the domain relation from i to j, is a subset of ∆Ii x ∆Ii

Examples: Context mappings From example 3: Sale: Car and FIAT: car describe the same set of objects from two different viewpoints: (**) n Domain relation satisfying (**): rij(Car. ISale)= Car. IFIAT From example 2: (*) n Domain relation satisfying (*): r. WCM, Ferrari(Petrol)IWCM {F 23 IFerrari , F 34 i. IFerrari}

Context OWL (C-OWL) A contextual ontology is a pair: q q OWL ontology a set of context mappings where a mapping is a set of bridge rules with the same target ontology A context mapping is a 4 -tuple: q q A mapping identifier (URI) A source context containing an OWL ontology A target context containing an OWL ontology A set of bridge rules from the local language of the source ontology to the local language of the target ontology NOTE: mappings are objects (!!)

Conclusions n n Ontologies: share knowledge Contexts: keep knowledge local (not shared) Contextual ontologies: share as much as possible, keep local whenever necessary C-OWL (Context OWL): q OWL + q Local models semantics + q context mappings (limited, explicitly defined, visibility from outside)

Will C-OWL be of any use? n How often in the Web we will import ontologies and how often we will define context mappings (diversity as a defect, or diversity as a feature)? n Shouldn’t the Semantic Web be a Web of Semantic links (e. g. , context mappings)? Context mappings useful for: maintaining alignment, propagating info, (semantics driven) navigation, … n Shouldn’t discovering context mappings (e. g. , Semantic matching) be one of the core issues in building the Semantic Web?

Context mappings (cont’ed) (Satisfiability of bridge rules) A interpretation for a context space is a model for it if all the bridge rules are satisfied