Local Closed World Reasoning with OWL 2

Transcription

1 Local Closed World Reasoning with OWL 2 JIST 2011 Tutorial Jeff Z. Pan Department of Computing Science University of Aberdeen, UK Agenda 1. Brief introduction to Ontology and OWL 2 (10m) 2. Open vs. Closed World Assumption (15m) Motivation Some existing work 3. Negation as failure Box (NBox) (35m) Semantics Applications Relation to other approaches Demos 4. Hands-on Session (30m) 2 1

2 What is an Ontology A model of ( aspect of) the world Introduces vocabulary relevant to domain, e.g.: Anatomy Koala Specifies meaning (semantics) of terms Koala eat only part of Eucalypt eat partof only Plant Eucalypt is Plant Eucalypt 3 Components of Ontology Modelling elements: concepts (classes), roles (properties) individuals (objects) A TBox (Terminonagy Box) is a set of schema axioms (sentences), e.g.: i.e., a background theory for the vocabulary An ABox (Assertion Box) is a set of data axioms (ground facts), e.g.: gummy: Koala 4 2

3 Ontology Reasoning Infer implicit knowledge from explicit knowledge 5 Ontology Landscape Related DL-based standards (OWL, OWL2) are established Many DL reasoners available FaCT++, Pellet, HermiT, RacerPro, TrOWL The user community is growing fast Swoogle searches over 10,000 online ontologies Larger and larger ontologies SNOMED has 379,691 concepts More and more references to ontologies: 568 papers with SNOMED in title, 8,580 papers with SNOMED in text. (Google Scholar) more and more complicated ontologies FMA (Foundational Model of Anatomy, OWL DL) has 41,647 concepts and 123,564 axioms, 6 3

4 OWL 2 OWL 2 Full OWL 2 DL SROIQ Undecidable 2NExpTime- Complete OWL 1 DL SHOIN NExpTime- Complete OWL 2 RL OWL 2 EL EL++ PTime- Complete OWL 2 QL DL-Lite In AC 0 7 Agenda 1. Brief introduction to Ontology and OWL 2 (10m) 2. Open vs. Closed World Assumption (15m) Motivation Some existing work 3. Negation as failure Box (NBox) (35m) Semantics Applications Relation to other approaches Demos 4. Hands-on Session (30m) 8 4

5 Open vs. Closed World Assumptions OPEN WORLD ASSUMPTION Given an ontology O, a statement st can be true, or false, or unknown true: if every model of O satisfies st false: if every models of O does not satisfy st unknown: if models of O satisfy st Assuming ontologies only cover key aspects of the world can be built in different iterations CLOSED WORLD ASSUMPTION Given an ontology O, a statement st can be either true or false. true: if all models of O satisfy st false: otherwise ot satisfy st unknown: if interpretations of O satisfy st Assuming one has complete knowledge about the part of the world 9 Example: Open vs. Closed World Assumptions Under OWA Is Pepper Salad Spicy? UNKNOWN Under CWA Is Pepper Salad Spicy? No, because "Spicy={Curry Chicken, Spicy Grilled Shrimp}" Note Curry Chicken Spicy Salmon Fillet Spicy Grilled Shrimp Pepper Salad Spicy 10 5

6 Explicit CWA vs. Implicit CWA Is Spicy Grilled Shrimp the only Spicy? Spicy={Spicy Grilled Shrimp}? No, because background knowledge: "MinorSpicy" is Spicy CWA should support necessary reasoning Curry Chicken Salmon Fillet Spicy Grilled Shrimp Pepper Salad Note Minor Spicy Spicy Vege 11 Example: Open vs. Closed World Assumptions Can we close concept Vegetarian? Vegetarian={Yuting}? Maybe not Whether close a concept or not depends on applications Name Jeff Yuting Jek Yuan Vegetarian No Yes No 12 6

7 Local Closed World Assumption In general, it uses an OWA setting Assuming ontologies only cover key aspects of the world For certain parts, it allows CWA Assuming one has complete knowledge about the part of the world Implicit CWA should be allowed 13 DBox [Seylan et al., 2009] Accommodate a DB component in an ontology DBox is syntactically same as an ABox Consists of assertion axioms DBox fixes the extensions of DBox predicates Faithful encoding of database usually with unique name assumption (UNA) Does not allow implicit CWA 14 7

8 Epistemic Operators Used in e.g. MKNF (Minimal Knowledge and Negation as Failure) [Motik and Rosati, 2010] The K operator: things we know K Koala: the concept of all known Koala in the knowledge base The not operator: Negation as Failure not A is equivalent to (K A) Example madcow: not(carnivore) meaning madcow is not evidently (not known to be) a Carnivore MKNF increases the complexity of reasoning 15 Agenda 1. Brief introduction to Ontology and OWL 2 (10m) 2. Open vs. Closed World Assumption (15m) Motivation Some existing work 3. Negation as failure Box (NBox) (35m) Semantics Applications Relation to other approaches Demos 4. Hands-on Session (30m) 16 8

9 Negation as failure Box (NBox) [Ren et. al, 2010] Design goals 1. To allow inference w.r.t. the closed predicates (i.e. concepts and roles) also allows the closure of arbitrary predicate descriptions 2. To provide restricted forms of the K and not operators so that it does not increase the complexity of reasoning for OWL 2 DL 17 NBox: Syntax O=(TBox, ABox, NBox) TBox: schema axioms Every guest orders; Vegetarian orders Vege; Etc. ABox: data axioms Chicken is MinorSpicy; Shrimp is Spicy; Pepper is Vege; NBox: the set of closed predicates (concepts and roles) Closed concepts: Spicy, Vege Jeff Vegetarian Jek Guest Yuting Yuan order Shrimp Chicken Spicy Minor Spicy Salmon Vege Pepper 18 9

10 NBox: Semantics For concept B in NBox (T, A, N) = x: B iff (T, A) x:b E.g., Salmon is neither Vege, nor Spicy B is equivalent to not B B is equivalent to K B For role R in NBox (T, A, N) = (x,y): R iff (T, A) (x,y):r Jeff Vegetarian Jek Guest Yuting Yuan order Shrimp Chicken Spicy Minor Spicy Salmon Vege Pepper 19 NBox Reasoning Using classical reasoning to retrieve instance of predicates E.g., Pepper is Vege Guest Vegetarian order Using nominals to close predicates E.g., Vege = {Pepper Salad} Adding axioms back to ontology for incremental reasoning Yuting orders Pepper! Jeff Jek Yuting Yuan Shrimp Chicken Spicy Minor Spicy order Salmon Vege Pepper 20 10

11 Challenges for NBox Reasoning Challenge 1: Ontologies with nominals are harder to reason with Using approximate reasoning technologies [Ren et. al, 2010b] to reduce to a tractable DL Challenge 2: Incremental reasoning is usually difficult for expressive DLs EL supports tractable incremental reasoning services! 21 NBox and Epistemic Operators NBox supports epistemic operators in a restricted way: for concepts B in NBox, we have B is equivalent to not B B is equivalent to K B NBox does not increase the complexity of reasoning for OWL 2 DL 11

12 DBox vs. NBox DBOX does not support inference of closed predicates supports only atomic predicates NBOX supports inference of closed predicates supports predicate descriptions DBox can be reduced to NBox under unique name assumption by putting all DBox predicates into NBox and putting all DBox axioms into ABox 23 Grounded Circumscription [Sengupta et. al, 2011] vs. NBox GROUNDED CIRCUMSCRIPTION Positive information of predicates in M is complete Allow relative minimal models Equivalent to NBox when there is only one minimal model NBOX Positive information of predicates in NBox is complete Ontology K Closed predicates M = {Carnivore} Minimal Model I 24 12

13 Grounded Circumscription [Sengupta et. al, 2011] vs. NBox GROUNDED CIRCUMSCRIPTION Positive information of closed predicates is complete Allows relative minimal models If K is consistent, then (K,M) is consistent NBOX Positive information of closed predicates is complete Requires absolute minimal models Consistency checking helps detect false closed predicates Ontology K Closed predicates M = NBox = {Carnivore, Herbivore} Minimal Models No model exists (K,M) is consistent (K,NBox) is inconsistent 25 Integrity Constraints [Motik et. al, 2009] vs. NBox INTEGRITY CONSTRAINTS used to validate the ABox axioms do not contribute to reasoning ontology still uses OWA NBOX used to specify closed predicates contributes to reasoning ontology uses LCWA 26 13

14 Dynamic NBox Reasoning Useful e.g. in deployment lifecycle deployed components should be closed (in principle) undeployed components remain open O C in E C = {...} NBox C in NBox E REL D = {...} D in NBox E E _D E E _D X = {...} 27 Example Application of NBox Data source port type ONLY Some connection ONLY SQL data port type Query 1 data source Classifer data Merge data 1 Input Port SQL connection 1 class connection Connection Query 1 SQL data Which input port can be used here? Output Port 28 14

15 Example Application of NBox Data source port type ONLY Some connection ONLY SQL data port type Query 1 data source Classifer data Merge data 1 Input Port SQL connection 1 class connection Connection Query 1 SQL data Which input port can NOT be used here? Output Port 29 Example Application of NBox Data source port type ONLY Some connection ONLY SQL data port type Query 1 data source Occupied Merge data 1 Input Port SQL connection 1 class connection Connection Query 1 SQL data Which input port can NOT be used here? Output Port 30 15

16 Example Application of NBox Data source port type ONLY Some connection ONLY SQL data port type Restricted connection Occupied Merge data 1 Input Port SQL connection 1 class connection Connection Query 1 SQL data Which input port can NOT be used here? Output Port 31 Example Application of NBox CLOSED Data source port type Restricted connection Input Port Occupied Valid input port ONLY Some connection ONLY SQL connection 1 class connection Connection SQL data port type Query 1 SQL data Which input port can be used here? Output Port 32 16

17 TrOWL is a tractable OWL2 reasoning infrastructure developed at Aberdeen [ESWC2010] It supports many pluggable reasoners It works with OWL API, Protégé 4, Jena and Semantic Mediawiki Configuration through property files and feature modelling: Performance required Determine the best reasoner for a specific task Quality guaranteed transformations Faithful approximate reasoning Quill: OWL 2 DL -> OWL 2 QL (semantic approximation) [AAAI2007] REL: OWL 2 DL -> OWL 2 EL (syntactic approximation) [AAAI2010] Divide and conquer Modularisation [ISWC2009] Forgetting [ESWC2008,ISWC2009b] NBox reasoning Coming up soon: Stream Reasoning [CIKM2011], SPARQL NBox Demo Demo plan Load ontology Put input ports that can not be used (Test) into NBox Perform LCW reasoning with NBox Retrieve input ports that can be used (Input AND (NOT Test)) 34 17

18 Take Home Message You can use Local Closed World reasoning with the NBox approach in OWL 2 where do you want to go from here? 35 Agenda 1. Brief introduction to Ontology and OWL 2 (10m) 2. Open vs. Closed World Assumption (15m) Motivation Some existing work 3. Negation as failure Box (NBox) (35m) Semantics Applications Relation to other approaches Demos 4. Hands-on Session (30m) 36 18

19 NBox Reasoning with TrOWL Sample code available in the JIST 2011 USB key 37 NBox Support in TrOWL TrOWL supports NBox with 2 different approaches: Pre-closed predicates (atomic only) with an annotation property value close@en When loading ontology with RELReasoner, the closed predicates will be automatically added into the NBox Run-time specification of NBox with method RELReasoner.close(Set<OWLClassExpression> classes, Set<OWLObjectPropertyExpression> properties) Reasoner will include the predicates in classes and properties into the NBox Only the eu.trowl.owlapi3.rel.reasoner.dl.relreasoner class supports NBox Nominal support is needed for TrOWL NBox 38 19

20 Plan 0. Preparation 1. Load an ontology with TrOWL; 1.1 Get results for queries in the ontology; 2. Close certain predicates in run-time with NBox; 2.1 Get results for the same queries in the N-Ontology; 2.2 Compare the results with step 1.1; 3. Create a new ontology with same predicates preclosed; 3.1 Load the ontology with TrOWL; 3.2 Get results for the same queries in the pre-closed N- Ontology; 3.3 Compare the results with step 1.1 and 2.2; Preparation Install Eclipse if you haven t (Unzip the zip file and) Copy and paste the tutorial folder to your Eclipse workspace In Eclipse to create the project File->New->Java Project Enter JISTTutorial in Projectname Choose the Location Next->Libraries tab, check if the OWL-API and TrOWL JARs are properly included If not, remove the existing ones except the JRE, then Add External JARs -> navigate to the lib folder of the project, and add the two JARs inside. Finish Now you are ready to start the project

21 Example Ontology: Ordering Tbox: Every Guest ; Vegetarian Vege; Inverse Functionality Etc. Abox: Chicken is MinorSpicy; Shrimp is Spicy; Pepper is Vege; Individual Inequality Etc. NBox Closed concept: Spicy, Vege We do not explicitly close properties. Jeff Vegetarian Jek Guest Yuting Yuan order Shrimp Chicken Spicy Minor Spicy Salmon Vege Pepper Load Ontology with TrOWL 1.1 Query for instances of Unknown, no results found Guest Vegetarian order 1.1 Query for instances of Non-Vegetarian Unknown, no results found Only knows that Yuting is not a Non- Vegetarian. Jeff Jek Yuting Yuan Shrimp Chicken Spicy Minor Spicy Salmon Vege Pepper 42 21

22 2. Run-time Closure of Predicates Add Spicy and Vege into Nbox with the close method Perform reasoning Using classical reasoning to retrieve instance of predicates E.g., Pepper is Vege Using nominals to close predicates E.g., Vege = {Pepper} Adding axioms back to ontology for incremental reasoning Guest Vegetarian order Jeff Yuan Spicy Vege 2.1 Query for instances of {(Yuting, Pepper)} returned as answer Jek Yuting Shrimp Chicken Minor Spicy Salmon Pepper order Run-time Closure of Predicates cont. Inverse Functional Implicitly close Vegetarian UNA Making all other Guest different from Yuting Yuting is the only Vegetarian 2.1 Query for instances of Non- Vegetarian {Jeff, Yuan, Jek} Jeff Vegetarian Jek Guest Yuting order nvegetarian Yuan Shrimp Chicken Spicy Minor Spicy Salmon Vege Pepper order 44 22

23 2. Run-time Closure of Predicates cont. 2.2 Compare the results with step 1.1; relation and Non-Vegetarian now both have results. Vegetarian is implicitly closed. relation is also implicitly closed. Its domain Vegetarian and range Vege are both closed. The relation holds between its only subject and only object. Non-Vegetarian is not closed Create a new ontology with same predicates pre-closed Create a new ontology that clones all axioms from the original ontology Add annotation property with value close@en on Vege and Spicy into the new ontology Perform reasoning 3.1 load with TrOWL 3.3 querying 3.3 results are the same as the run-time closure

24 Local Closed World Reasoning with OWL 2 JIST 2011 Tutorial Thank you Questions? 24