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Learn about C-OWL, a framework that extends OWL by incorporating context mappings, allowing for local contexts and global semantics. Explore how sharing information and maintaining local viewpoints can improve ontological modeling. Discover strengths and weaknesses of both ontologies and contexts, and grasp the significance of incremental Semantic Web construction.
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C-OWL: contextualizing ontologies Fausto Giunchiglia October 22, 2003 Paolo Bouquet, Fausto Giunchiglia, Frank van Harmelen, Luciano Serafini, and Heiner Stuckenschmidt
The Talk • 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 • 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 beshared; • A Context is a model of some domain which is supposed to encode a view of a party A context is built to bekept local(where local implies not shared) • A context and an ontology of the same domain are likely to be very different (different goals, different approach, …)
Pro’s and Contra’s • Ontologies • Strengths • “easy” exchange of information • Weaknesses • consensus must be reached about their contents • maintenance may become arbitrarily hard • Contexts • Strengths • “easy” to define and to maintain • can be constructed with no consensus with the other parties • Weaknesses • 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): • Share as much as possible (OWL import construct) • Keep it local whenever sharing does not work (C-OWL context mappings) Notes: • 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 • 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 IndexOWL 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 CCi; • I(i, r)∆I x ∆I for any i I and rRi; • I(i, o) ∆I for any i I and oOi; With ∆I domain of interpretation and (.)I interpretation function 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, W3C, 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 • 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: • Construct O2 by importing O1 and adding it some new axiom • Want that axioms added to O2 do not affect O1 • O1 contains axioms A Band C D • O2 contains also axiom 1:B 1:C In new semantics, we want 1:A 1:Din O2, but not in O1.
Example 1 (cont’ed): directionality We want to avoid propagation of inconsistency Example: • O1 contains axioms A Band C D • O2 contains also axiom 1:B 1:C • We want to derive 1:A 1:Din O2 but not in O1 • … • O2 contains also 1:A(a) and 1: not D(a) • O2 is inconsistent In new semantics, we want to keep O1 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 • individual constants Diesel and Petrol for Diesel engine and petrol engine • Axiom: a car has only one engine which is either Diesel or petrol Car (1) hasEngine.{Diesel, Petrol} Diesel Petrol Ferrari ontology, OFerrari describing Ferrari’s production • Imports OWCM standard • Axiom: engine of a Ferrari is either an F23 or and F34i Ferrari (WCM:car (1) (WCM:hasEngine).{F23, F34i} F23F34i In new semantics, we want to avoid (F23)IFerrari = (Diesel)IWCMsince 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: • OFIATdescribes cars from manufacturer point of view • OSale describes cars from car vendor point of view • OFIAT and OSale are largely independent and different • 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 • 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 • Consider all (local) ontologies as part of a OWL space • Split global interpretation into a family of local interpretations, one for each ontology • Allow for an ontology to be locally inconsistent (i.e., not to have a local interpretation) • Technically: Associate inconsistent ontologies to a special “interpretation”, called a hole, that verifies any set of axioms
Example 2: Local Domains • Associate to each ontology a local domain • Local domains may overlap (two ontologies may refer to the same object) • 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 • 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 • OWL space {<i, Oi>} (of local ontologies) • family {Mij} of (context) mappings from i to j, for any pair i,j (Interpretation for context spaces). It is the pair • I, where I is an OWL interpretation with holes and local domains and • 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: (**) • Domain relation satisfying (**): rij(CarISale)= CarIFIAT From example 2: (*) • Domain relation satisfying (*): rWCM, Ferrari(Petrol)IWCM {F23IFerrari , F34iIFerrari}
Context OWL (C-OWL) A contextual ontology is a pair: • 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: • 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 • Ontologies: share knowledge • Contexts: keep knowledge local (not shared) • Contextual ontologies: share as much as possible, keep local whenever necessary • C-OWL (Context OWL): • OWL + • Local models semantics + • context mappings (limited, explicitly defined, visibility from outside)
Will C-OWL be of any use? • 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)? • 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, … • 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