Local Closed World Reasoning in the Semantic Web Yuan Ren, Jeff Z. Pan University of Aberdeen, UK NJU Departmental Seminar, June 2012 Local Closed World Reasoning in the Semantic Web

Agenda Intelligent Systems and Semantic Technologies (5m) Open World Assumption v.s. Closed World Assumption (10m) Description Logics and Ontologies (10m) Local Closed World Reasoning in the Semantic Web (20m) Outlook (5m) http://www.trowl.eu

Approaches to AI AI: science and engineering of making intelligent machines, especially intelligent computer systems John McCarthy “Smart applications” Large scale raw data Pattern, relation, knowledge Complex inductive transformation & manipulation Magic number? Explanation? Complex structure?

Approaches to AI “Smart Data”: knowledge makes data smarter Data reusing: explanation Data enrichment: Hidden knowledge Deductive inference Structural ontological data Large scale raw data Pattern, relation, knowledge Complex inductive transformation & manipulation Annotation “Smart Data”: knowledge makes data smarter

The Semantic Web Web contains enormous amount of data Difficult for human or software to digest The Semantic Web: improve the description, sharing, discovery and exploitation of knowledge and data Inter-lined datasets Structured data models Standard languages Knowledge representation & reasoning Web data The Semantic Web Data exchange Languages

Domain(supervisedBy) isA post-graduate The Semantic Web Identify data objects with URIs Connect data objects with relations Describe connections with knowledge bases foaf#j_z_pan Lubm#supervisedBy LUBM: Domain(supervisedBy) isA post-graduate dblp#yuan_ren

Domain(supervisedBy) isA post-graduate The Semantic Web Query with the SPAQL language: Who is supervised by Jeff? foaf#j_z_pan LUBM#supervisedBy LUBM: Domain(supervisedBy) isA post-graduate dblp#yuan_ren How are the knowledge bases interpreted?

Agenda Intelligent Systems and Semantic Technologies (5m) Open World Assumption v.s. Closed World Assumption (10m) Description Logics and Ontologies (10m) Local Closed World Reasoning in the Semantic Web (20m) Outlook (5m) http://www.trowl.eu

Possible Interpretations of Knowledge Base A knowledge base can have multiple interpretations. curryChicken: not VegetarianFood pepperSalad: not SpicyFood curryChicken: not VegetarianFood pepperSalad: SpicyFood curryChicken: SpicyFood pepperSalad: VegetarianFood curryChicken: VegetarianFood pepperSalad: not SpicyFood curryChicken: VegetarianFood pepperSalad: SpicyFood

The Two World Assumptions Open world assumption Closed world assumption Given an knowledge base KB, a statement st can be true, or false, or unknown true: if st can always be derived by KB false: if st can never be derived by KB unknown: if st can be derived by some interpretations of KB Assuming KBs only cover key aspects of the world Compatible with the open nature of the web Given a knowledge base KB, a statement st can be either true or false. true: if st can always be derived by KB false: otherwise Assuming one has complete knowledge about the part of the world

Example: OWA v.s. CWA Menu Under OWA Under CWA Is Pepper Salad SpicyFood? UNKNOWN Under CWA No, because "SpicyFood={Curry Chicken, Spicy Grilled Shrimp}" Menu Food Note Curry Chicken Spicy Salmon Fillet Spicy Grilled Shrimp Pepper Salad

Example: OWA v.s. CWA Who leads a Tenure that leads a non-Tenure? CWA: no one OWA: Full Prof. Tenure Full Prof. lead lead Associate Prof. lead not Assistant Prof. lead Post-Doc Full Prof. is the answer in ALL possible interpretations!

Example: Explicit vs. Implicit CWA Is Spicy Grilled Shrimp the only SpicyFood? SpicyFood={Spicy Grilled Shrimp}? No, because background knowledge: "MinorSpicyFood" is SpicyFood CWA should support necessary inference Menu Food Note Curry Chicken Minor Spicy Salmon Fillet Spicy Grilled Shrimp Spicy Pepper Salad Vege

Example: Open vs. Closed World Assumptions Can we close concept Vegetarian? Vegetarian={Yuting}? Maybe not… Whether close a concept or not depends on applications Guests Name Vegetarian Jeff No Yuting Yes Jek Yuan

Local Closed World Assumption In general, it uses an OWA setting Assuming knowledge bases 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

Agenda Intelligent Systems and Semantic Technologies (5m) Open World Assumption v.s. Closed World Assumption (10m) Description Logics and Ontologies (10m) Local Closed World Reasoning in the Semantic Web (20m) Outlook (5m) http://www.trowl.eu

What is an Ontology A model of (some aspect of) the world Introduces vocabulary relevant to domain, e.g.: Anatomy Koala Specifies meaning (semantics) of terms Koala eat only some part of Eucalypt Eucalypt is Plant only eat some Plant Eucalypt partof

Components of Ontology Modelling elements: concepts (classes) roles (properties/relations) 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

Ontology Reasoning Infer implicit knowledge from explicit knowledge

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: 731 papers with “SNOMED” in title, 12,400 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,

Agenda Intelligent Systems and Semantic Technologies (5m) Open World Assumption v.s. Closed World Assumption (10m) Description Logics and Ontologies (10m) Local Closed World Reasoning in the Semantic Web (20m) Outlook (5m) http://www.trowl.eu

SPARQL SPARQL 1.o supports “!bound” SPARQL 1.1 supports “NOT Exist” A person who is not known as a post-graduate Realised by testing for the absence of a pattern in a graph

Integrity Constraints Widely used in RDBs to check data integrity Assuming the RDB contains COMPLETE information Based on model checking IC in DL-based ontologies ICs are syntactically same as TBox axioms Checking whether facts derivable with KB+ICs can be derived with KB only. Can be realised by SPARQL query answering. KB ? madcow is either a Herbivore or a Carnivore Q1: ?x <- ?x:Animal Q2: ?x <- ?x:Herbivore Q3: ?x <- ?x:Carnivore

Why Is SPARQL Not Enough? Queries do not change the semantics of the ontology i.e. does not really CLOSE anything SPARQL: Who is not known as a post-graduate? Jeff CWA: Who is not a post-graduate? No one It’s unknown whether Jeff is a post-graduate foaf#j_z_pan LUBM#supervisedBy LUBM: Domain(supervisedBy) isA post-graduate dblp#yuan_ren

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

Grounded Circumscription Minimising the extensions of closed predicates. Using minimal models w.r.t. the closed predicates A minimal model interprets a closed predicates with only named individuals in the knowledge base Knowledge base K Closed predicates M = {Carnivore, Herbivore} Minimal Models Why can we close concepts without complete knowledge? We still don’t know the exact type of madcow

Epistemic Operator 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) madcow: not(Carnivore) meaning madcow is not evidently (not known to be) a Carnivore MKNF increases the complexity of reasoning

Negation as failure Box (NBox) [Ren et. al, 2010] Closing a set of predicates with their inferable instances To allow inference w.r.t. the closed predicates To provide restricted forms of the K and not operators without increasing complexity drastically

Reasoning with NBox Using classical reasoning to retrieve instance of predicates E.g., Pepper is VegeFood Using nominals to close predicates E.g., VegeFood = {Pepper Salad} Adding axioms back to ontology for incremental reasoning Yuting orders Pepper! Guest some some Vegetarian order Food Jeff Yuan SpicyFood VegeFood Jek Minor Spicy Food Pepper Yuting Shrimp Salmon Chicken order

Agenda Intelligent Systems and Semantic Technologies (5m) Open World Assumption v.s. Closed World Assumption (5m) Description Logics and Ontologies (10m) Local Closed World Reasoning in the Semantic Web (20m) Outlook (5m) http://www.trowl.eu

LCWR and Other Themes in Ontology Reasoning Reasoning optimisation Many LCWR solutions increase the complexity of ontology reasoning E.g. NBox requires nominal support Developing optimised algorithms for LCWR, e.g. approximations Non-standard reasoning services Incremental reasoning (with increasing ontology) E.g. NBox adds definitions of closed predicates Justification (that explains the entailment) The closure of certain part of the knowledge base should be regarded as part of the explanation Combined reasoning with other formalisms Ontology + rules Ontology + RDB + datalog

LCWR and Other Themes in Knowledge Representation A unified framework for different LCWR solutions No actual semantic closure: Integrity constraints <-> SPARQL query level CWA Actual semantic closure: DBox <-> Grounded Circumscription <-> Epistemic Operator <-> NBox Relation with other non-monotonic approaches LCWR and abduction LCWR and induction

LCWR and Other AI Approaches The separation of complete knowledge and open knowledge leads to interesting insights Generalisation v.s. overfitting Closing does not mean overfitting Closing a concept does not preventing adding new instances to this concept Static knowledge v.s. dynamic knowledge Closed knowledge can also be dynamic! Explicit knowledge v.s. implicit knowledge Explicit closure -> implicit closure Reasoning is needed!

Question? Thank you! y.ren@abdn.ac.uk