Yuan Ren , Kees van Deemter and Jeff Z. Pan Department of Computing Science

1. Charting the Potential of Description Logic for the Generation of Referring ExpressionINLG2010, July, 2010 Yuan Ren, Kees van Deemter and Jeff Z. Pan Department of Computing Science University of Aberdeen, UK

2. Background Generation of Referring Expressions (GRE) algorithms identify a target referent: Express info known to be true of target false of all else But how does GRE model knowledge?

3. Knowledge Representation in classic GRE • Sets of <Attribute,Value> pairs, e.g. • <Type, Poodle> • <Colour, Grey> • These are atomic facts. Can’t say • All poodles are grey • Kees is Dutch or Belgian • If x is part of y and y is part of z then x is part of z

4. Modern KR can do all this (and more) • KL-One and semantic nets • Modern descendants: Conceptual Graphs and Description Logic • Represent complex knowledge • Perform efficient automatic deduction • Why not use modern KR for GRE? • This talk: Description Logic (DL) • DL/OWL is now the language of the semantic web

5. Advantages • A richer model of reference • New targets become identifiable • Re-use • existing algorithms • existing ontologies • deduction for proving uniqueness • Info represented succinctly, e.g. • a part of b, b part of c, c part of d, … • For all x,y,z: if x part of y and y part of z then x part of z

6. Remainder of this talk Introduction to DL Areces et al. on DL and GRE Extending the expressivity Extending the algorithm Caveat: few empirical claims This talk is about what’s possible in GRE

7. Description Logics? • A family of logic-based KR formalisms • Describe domain in terms of concepts (classes), roles (properties, relationships) and individuals • Smallest propositionally closed DL is ALC (equivalent to K(m)) • Concepts constructed using booleans u, t, :, plus restricted quantifiers 9, 8 • Only atomic roles E.g., Someone who has a child that is a Doctor: 9hasChild.Doctor • Characteristic of reasoning: Implementability • Decidability: OWL2-DL (SROIQ) • Tractability: OWL2-EL, OWL2-QL, OWL2-RL

8. DL Knowledge Base • A TBox is a set of “schema” axioms (sentences), e.g.: {Dog v Animal, Dog v Woman hasFather ◦ hasBrother v hasUncle, feed ◦ love v feed} • i.e., a background theory • An ABox is a set of “data” axioms (ground facts), e.g.: {d1:Dog, w1:Woman, (w1,d1):feed, (d1,c1):love } • An NBox is a set of “complete” concepts and properties e.g.: {Dog,Woman}

9. GRE example Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 • Uniquely identifying an object in context. • d1: the Dog that loves some Cat • w2: the Woman that feeds some Dog that loves no Cat

10. From the DL point of view Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 • ABox assertion axioms • w1:Woman w2:Woman • d1:Dog, d2:Dog • c1:Cat, c2:Cat • (w1,d1):feed (w2,d2):feed (w2,d1):feed • (d1,c1):love

11. DL for GRE: the story so far • Areces et al. reinterpret GRE as a problem of computing ALC formulas. • An algorithm to compute REs (if exists) for all objects: • Generate-Test strategy • Start from atomic concept names, then extend with (negative) existential quantifier.

12. DL for GRE example Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 Referring Expression as a DL formula

13. ABox Not Enough Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 d1: the Dog that loves some Cat w2: the Woman that feeds some Dog that loves no Cat • TBox required • Dog v Person • Dog v Cat • Cat v Person • T v Dog t Person t Cat • feed ◦ love v feed • NBox required • {Dog,Woman,Cat,love, feed}

14. Additional Quantifiers Both women feed dogs and cats Woman w1 w2 feed d1 c1 Both cats are beloved by dogs and are fed by women Cat love Dog Both dogs love cats and are fed by women c2 d2 • Additional quantifiers make them referrable • c1: The cat which is fed by at least 2 woman • w1: The woman feeding only those fed by at least 2 women • w2: The woman who feeds all the dogs

15. Representing Quantifiers in Ontologies We can use Nouns Reflexive relations Generalised quantifiers, e.g., “only”, “five”, “at least two” Example: English: “The woman who loves at least two dogs” Set theory + GQ: {y in Woman: ≥2 (Dog,{z: Love(y,z)})} Literally, this says: “Women y such that there are at least two Dogs in the set of things that are loved by y” But which quantifiers exactly?

16. Representing Quantifiers with Ontologies • Quantifiers of Type 1, e.g., n = 1: the existential quantifier; • Quantifiers of Type 7, e.g., n = 0: the only quantifier; • Quantifiers of Type 6, e.g., n = 0: the all quantifier;

17. Generating SROIQ-enabled REs • GROWL: a GRE algorithm using OWL-2 • Generate-and-test strategy • Using DL reasoning • Generating increasingly complex descriptions • Complexity measured by the structure of the expressions • 1 complexity of (negated) atomic concept is 1 • 2 complexity of conjunction (disjunction) is the maximal complexity of conjuncts (disjuncts) +1 • 4complexity of existential (universal) restriction is the complexity of filler + 1

18. Generating SROIQ-enabled REs • GROWL: a GRE algorithm using OWL-2 • Starting from the basic terms, such as • Names (e.g. Dog, feed) • Inverse of named property (such as feed-) • Negation of another basic term (such as Dog, feed, feed-) • For each existing description, create new description by • Extending with conjunction/disjunction • Extending with existential/universal restriction • Extending with cardinality restriction • Until no new non-empty description can be created

19. Generating SROIQ-enabled REs • Deciding whether a new description should be accepted • Accept if no existing description has same extension • But still non-empty • Using standard reasoning services • Concept subsumption checking • Concept satisfiability checking

20. Example Revisited Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 • Starting from basic terms • D={Woman, Dog, Cat, not Woman, not Dog, not Cat, etc.} • Ins(Woman) = {w1,w2}, Ins(Dog) = {d1,d2}, Ins(Cat) = {c1,c2}, Ins(Woman)={c1,c2,d1,d2}, etc… • Extending Woman with maximal Cardinality restriction • Using (feed-) to extend • Using 0 as a cardinality value • Ins(<=0(feed-).Woman) = {c1,d1}, should be accepted as a candidate description because its extension is not covered by any existing description • D becomes {Woman, Dog, Cat, not Woman, not Dog, not Cat, <=0(feed-). Woman, etc.} • Extending <=0(feed-).Woman with conjunction • Using Cat to extend • Ins(Cat u <=0(feed-).Woman) = {c1}, c1 identified! • Using Dog to extend • Ins(Dog u <=0(feed-).Woman) = {d1}, d1 identified!

21. Generating SROIQ-enabled REs • Deciding whether a new description should be accepted • The more complex the description is, the less individuals should it cover • But still non-empty • Using standard reasoning services • Concept subsumption checking • Concept satisfiability checking

22. Example Revisited Woman w1 w2 feed d1 c1 Cat love Dog c2 d2 w1: the woman that does not feed all cats; w2: the woman that feeds all cats; d1: the dog that is fed by all women; d2: the dog that is not fed by all women; c1: the cat that is fed by all women; c2: the cat that is not fed by all women

23. Summary • Our contributions: • Using DL reasoning to infer implicit knowledge(i.e., using non-atomic information) • Allowing GRE with incomplete knowledge • Extending the expressivity of GRE to OWL-2(i.e., using new quantifiers, such as ≥2) • Introducing NAF for a partially closed world • Open issues: • How useful are the newly generated REs? • How to choose the “best” RE?

24. Future extensions (KvD: are these all extensions?) • Identifiers can be used • Using proper names as a basic term: • Partially/completely closed domain? • Completely open world is also doable: • [KvD: How is that an example of open world? Isn’t this more like an example of incomplete knowledge? I think these two are comparable. A world is open iff all agents/observers have only incomplete knowledge about it] • Unique name assumption? [KvD: Is this a future extension?] • Individual can have multiple names • Inference can infer the uniqueness • Incorporating both terminology and assertions? [KvD: I don’t get this] • YES WE CAN!