Context Representation and Reasoning with Formal Ontologies

1. Context Representation and Reasoning with Formal Ontologies Juan Gómez-Romero1,2, University Carlos III of Madrid (Spain) Fernando Bobillo2, University of Zaragoza (Spain) Miguel Delgado2, University of Granada (Spain) Activity Context Workshop, AAAI’11, August, 2011 (1) Applied Artificial Intelligence Group (2) Approximate Reasoning and A.I. Group

2. Modeling context knowledge with ontologies Context representation Represent context information with standard ontologies Context-based reasoning Reduce the knowledge search space according to current context Extensions to non-classical ontologies Representation of vague, imprecise and uncertain knowledge Representation of context knowledgeto reason what is significantandsummarizeavailable knowledge Context representation and reasoning with formal ontologies

3. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

4. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

5. 1. An unified view on context Definitions Schmidt, Beigl and Gellersen (1999): Mix of geo-spatial data, ambient sensor inputs, user profiles (preferences, intentions, history, etc.), and service descriptions Dey and Abowd (2001): Any information (either implicit or explicit) that can be used to characterize the situation of an entity Henricksen (2003): The context of a task is the set of circumstances surrounding it that are potentially of relevance to its completion Kandefer and Shapiro (2008): The structured set of variable, external constraints to some (natural or artificial) cognitive process that influences the behavior of that process in the agent(s) under consideration Gomez-Romero et al. (2011): Any information of interest to the application not directly obtained by the domain data acquisition sensors: common-sense, human feedback, external or a priori resources, etc. Context representation and reasoning with formal ontologies

6. 1. An unified view on context Characteristics • Set of constraints to a reasoning process Soft: Delimit relevant information Hard: Check consistency of world interpretation • Influence behavior of the agent Adapt system functioning to the environment Avoid information overload Augment or embellish system results Modify acquired data and acquisition procedures • Cognitive process Use of formal specifications vs. ad hoc specifications Context is “first-level” knowledge Context representation and reasoning with formal ontologies

7. 1. An unified view on context Nomadic Access to Healthcare Information • A physicist wants to prescribe a treatment for a patient • The HIS provide a report of the patient’s clinical history • Information overload: Include only information relevant to the patient’s state, the diagnosis, and clinical procedure that is being carried out • Patient is unconscious and has a hemorrhagic laceration • Allergies to procaine should be taken into account The example can be extended to other Semantic Web scenarios • Keyword-indexed documents • Query expansion, query restriction • Data visualization • http://ecolexicon.ugr.es/visual/index_en.html (Java required) Example case Context representation and reasoning with formal ontologies

8. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

9. 2. Ontologies for context representation Representation of the mereological aspects of a reality created from a common perspective and expressed in a formal language Representation formalism that promotes knowledge integration, sharing and reuse Based on Description Logics (DLs), a family of logics with well-defined semantics specially designed to represent structured knowledge DLs are classified in levels (and named) according to their expressivity, which determines the computational complexity of reasoning with the logic (in general DLs, NExptime-complete) The Semantic Web uses ontologies to represent metadata and offers several supporting tools, such as the standard OWL language Ontologies Context representation and reasoning with formal ontologies

10. 2. Ontologies for context representation Concepts (classes, types) • Set of objects with common features • FOL unary predicates Instances (individuals) • Objects belonging to a class • FOL constants Relations (properties, roles) • Binary associations between two instances or an instance and a data type value (integers, strings, etc.) • FOL binary predicates Axioms • Restrictions defining concept, instance and relation features • FOL formulas Elements Context representation and reasoning with formal ontologies

11. 2. Ontologies for context representation Elements Context vocabulary Context description Context representation and reasoning with formal ontologies

12. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

13. 3. Reasoning with context ontologies Automatic procedure to obtain implicit axioms from explicit axioms • modus ponens • A • A → B • B Tableaux algorithms • Reasoning algorithms for DLs • Implemented by inference engines (HermiT, RACER, Pellet) • Theoretical efficiency is high, but worst cases are not frequent Ontology reasoning Resolution(propositionallogic) Context representation and reasoning with formal ontologies

14. 3. Reasoning with context ontologies Concept axioms • Satisfiability / Consistency • A concept is satisfiable if it is not a contradiction to the remaining axioms • Subsumption • A (super-)concept includes a (sub-)concept • Equivalence • Two concepts include the same instances • Disjointness • Two concepts do not have any common instance Instance axioms • Satisfiability / Consistency • An instance assertion is satisfiable if it is not a contradiction to the remaining axioms • Instance checking • An instance belongs to a class Entailment • An axiom is a logical consequence of a set of axioms Standard reasoning tasks Context representation and reasoning with formal ontologies

15. 3. Reasoning with context ontologies Context representation and reasoning • Exploitation of ontologiesin context-aware ubiquitous computing • Interpreting the current user situation • Using contextual knowledge to improve the performance of the system Contextualization of ontologies • How external or additional knowledge influences the interpretation of an ontology: consistency, validity, partitioning • Non-monotonic models vs monotonic DLs • Extend the OWL language with non-monotonic features Ontology design patterns • Recipesto help ontology developers to capture aspects of the application domain and represent them with existing languages from a common and well-understood perspective • No specific pattern aimed to the representation of context knowledge, either for specific or general domains Dealing with context in ontologies Context representation and reasoning with formal ontologies

16. 3. Reasoning with context ontologies Proposal Meta-model: design pattern to create context-aware ontologies that avoid information overload. Significance ontologies to represent which information of the domain is relevant in a given context CDS (Context-Domain Significance) pattern formulated in the basic DL ALC Directly translatable into OWL (≈ SHOIN(D)) In several cases, fuzzy knowledge must be considered Extension of the pattern using fuzzy DLs CDS pattern Context representation and reasoning with formal ontologies

17. 3. Reasoning with context ontologies Base ontologies • Context ontology(KC): vocabulary to describe context situations. • Domain ontology(KD): ontology to represent domain-specific knowledge. New significance ontology:CDS ontology (KS) • Complex contexts (Ci): • Concepts created using terms of KC. • Complex domains (Dj): • Concepts created using terms of KD. • s-connection (si,jor Pi,j): • A concept linking a complex context Ci and a complex domain Dj • Denotes that Dj is significant in situation Ci CDS pattern Context representation and reasoning with formal ontologies

18. 3. Reasoning with context ontologies Context ontology Domain ontology Context representation and reasoning with formal ontologies

19. 3. Reasoning with context ontologies Reasoning with the CDS pattern • Domain knowledgeIsignificantin a scenarioE • Algorithm (implemented in the CDS API): • Retrieve the complex contexts Cn more general than E • Retrieve the s-connections Pn,m involving Cn • Retrieve the complex domains Dminvolved in Pn,m • Retrieve the concepts I of the domain more specific than Dm Complete and decidable Complexity is determined by CiandDj(ExpTime-complete for ALC) Context representation and reasoning with formal ontologies

20. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

21. 4. Extending ontologies to the fuzzy case Impreciseknowledge cannot be represented • E.g.: A patient is slightly unconscious Partial similarities between contexts cannot be represented • E.g.: Anaphylaxis is quite similar to sepsis Relevance relations cannot hold to a degree • E.g.: Blood-borne diseases are less relevant than drug intolerances Fuzzy extension of the crisp meta-model, i.e. a design pattern to create fuzzy context-aware ontologies that avoid information overload and allow vague knowledge to be managed Limitations of CDS to manage context knowledge Context representation and reasoning with formal ontologies

22. 4. Extending ontologies to the fuzzy case The significance ontology is a fuzzy ontology (fCDS) created with an adaptation of the crisp rules of the CDS pattern The fuzzy significance ontology is expressed with the fuzzy Description Logic fALC Fuzzy DLs extends DLs to the fuzzy case • – Concepts are fuzzy sets – Axioms hold to a degree (inclusion!) • – Roles are fuzzy relations – Interpretation has fuzzy semantics Reasoning can be performed with a fuzzy DL reasoner or by reducing the fuzzy ontology to an equivalent crisp DL ontology and using a crisp inference engine (Bobillo, Delgado & Gómez-Romero, 2009) Fuzzy CDS pattern Context representation and reasoning with formal ontologies

23. 4. Extending ontologies to the fuzzy case Context representation and reasoning with formal ontologies

24. 4. Extending ontologies to the fuzzy case Reasoning with the fuzzy CDS pattern • Domain knowledge I a-significantin a scenario E • Knowledge significant and degree of significance Complete and decidable Complexity is determined by Ci, Dj, and the glbs to be calculated aggregation: min t-norm a ⊗b greatest lower bound: glb = sup{a : K <t ≥ a>}

25. Outline • A unified view of context (?) • Ontologies for context representation • Reasoning with context ontologies • Extending ontologies to the fuzzy case • Conclusions and future work Context representation and reasoning with formal ontologies

26. 5. Conclusions and future work Advantages of using ontologies to manage context knowledge • Expressiveness • Formal representation and reasoning • Standard languages and tools • Appropriate to deal with information overload • Extensions are being studied Future research • Standard specification of common context dimensions: location, time, preferences, etc. • Privacyissues • Study the applicability of full-fledged reasoningin real-world applications • Relation with context acquisition and interpretationtechniques • Are fuzzy extensions necessary/convenient? Notice! Context representation and reasoning with formal ontologies

27. Thank you! Questions, comments? Context representation and reasoning with formal ontologies