First Steps in Description Logic,

First Steps in Description Logic, Patrick Blackburn INRIA Lorraine, Nancy, France Description Logic Day LORIA 24 September 2003 First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 1

Goal of this talk First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 2

Goal of this talk Non-technical overview of some basic ideas of description logic (DL). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 2

Goal of this talk Non-technical overview of some basic ideas of description logic (DL). First-order logic: x(man(x) y(woman(y) Loves(x, y))) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 2

Goal of this talk Non-technical overview of some basic ideas of description logic (DL). First-order logic: x(man(x) y(woman(y) Loves(x, y))) Knowledge representation: obtaining computational solutions to the kinds of problems that humans handle well (such as natural language understanding) involves representing and manipulating knowledge. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 2

Goal of this talk Non-technical overview of some basic ideas of description logic (DL). First-order logic: x(man(x) y(woman(y) Loves(x, y))) Knowledge representation: obtaining computational solutions to the kinds of problems that humans handle well (such as natural language understanding) involves representing and manipulating knowledge. Inference: obtaining new knowledge from old (or extracting implicit knowledge from explicit knowledge). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 2

Where we re going First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

Where we re going A little history First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

Where we re going A little history A first look at ALC First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

Where we re going A little history A first look at ALC TBoxes (or terminologies) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

Where we re going A little history A first look at ALC TBoxes (or terminologies) ABoxes (or world descriptions) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

Where we re going A little history A first look at ALC TBoxes (or terminologies) ABoxes (or world descriptions) Pointers to the later talks First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 3

What are description logics? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 4

What are description logics? Formalisms that represent knowledge of some problem domain (the world ) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individual occuring in the domain (the world description). Baader and Nutt, 2003. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 4

What are description logics? Formalisms that represent knowledge of some problem domain (the world ) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individual occuring in the domain (the world description). Baader and Nutt, 2003. Have a model-theoretic semantics. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 4

What are description logics? Formalisms that represent knowledge of some problem domain (the world ) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individual occuring in the domain (the world description). Baader and Nutt, 2003. Have a model-theoretic semantics. Heavy emphasis on how various types of reasoning (or inference) is to be carried out, and how they can be carried out computationally. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 4

Where did description logic come from? Semantic network formalisms for describing concepts. Quillian, 1967. Frame-based knowledge representation formalism. Minsky, 1981 First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 5

Cognitive versus logical Often driven by a cognitive (rather than engineering) approach to AI. Felt that these formalisms captured important forms of reasoning in a natural way, avoiding the complexities of first-order logic. In particular, very good at capturing the idea of hierarchical inheritance of information. Tremendously influential. For example Schanks, using frame based representations, did some of the most influential work in the computational linguistics of the period. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 6

Problems with network formalisms Not clear how different network formalism were related. They might look very similar but behave very differently. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 7

Problems with network formalisms Not clear how different network formalism were related. They might look very similar but behave very differently. Not always clear what they meant. No tradition of giving a precise semantics (model-theoretic or otherwise) to these formalisms. Although typically performed inference soundly, they were often not complete. That is, they were often not strong enough to infer all the knowledge that a user might require. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 7

Then the cleanup began Noted that the core elements of frames-based system could be geiven a semantics by making use of first-order logic. Hayes, 1979. Usable systems with a well understood semantics could be built by taking advantage of this insight. The key system here was KL-ONE. Brachman and Leveque, 1985. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 8

Then the cleanup began Noted that the core elements of frames-based system could be geiven a semantics by making use of first-order logic. Hayes, 1979. Usable systems with a well understood semantics could be built by taking advantage of this insight. The key system here was KL-ONE. Brachman and Leveque, 1985. So we re back to (first-order) logic? No more handle on the (attractive) idea of simple formalisms with simple inference procedures? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 8

Fragments Key insight: although you could use the ideas of logic (a formal language, model theoretic interpretation, model theoretically defined notions of inference) to understand network and frame based forms of representation and reasoning, you typically didn t need to use all of classical logic. Usually you just needed some nice fragment. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 9

Modern DL An important part of the subsequent histroy of DL has been finding these useful fragments, and learning how to work with them computationally. Enormously succesful has located fragments undreamed of by the network pioneers and have put the intuition that some forms of representation and reasoning are easier than others on a firm mathematical basis. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 10

The description language ALC C, D A (atomic concept) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) C D (concept union) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) C D (concept union) C (concept negation) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) C D (concept union) C (concept negation) R.C (existential quantification) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

The description language ALC C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) C D (concept union) C (concept negation) R.C (existential quantification) R.C (value restriction) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 11

Atomic Concepts Person, Male, Female, LongHaired, PhDstudent, French, Dutch, German, Argentinian, English,... How do we interpret these atomic symbols? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 12

Atomic Concepts Person, Male, Female, LongHaired, PhDstudent, French, Dutch, German, Argentinian, English,... How do we interpret these atomic symbols? Suppose we interpret them in this room (that is, suppose we take the people in this room as our model, or world). Then each atomic concept denotes a subset of this model. In fact concept descriptions are always interpreted as subsets of models. Note link with first-order logic: there we have first-order atomic formulas with one free variable Person(x), Male(x), Female(x), LongHaired(x), and so on, interpreted in exactly the same way. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 12

Atomic Concepts Person, Male, Female, LongHaired, PhDstudent, French, Dutch, German, Argentinian, English,... How do we interpret these atomic symbols? Suppose we interpret them in this room (that is, suppose we take the people in this room as our model, or world). Then each atomic concept denotes a subset of this model. In fact concept descriptions are always interpreted as subsets of models. Note link with first-order logic: there we have first-order atomic formulas with one free variable Person(x), Male(x), Female(x), LongHaired(x), and so on, interpreted in exactly the same way. What about and? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 12

Concept conjunction How do we interpret this? Male LongHaired First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 13

Concept conjunction How do we interpret this? Male LongHaired In this room it denotes: the set of men with long hair. Once again: concepts are subsets of the model. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 13

Concept conjunction How do we interpret this? Male LongHaired In this room it denotes: the set of men with long hair. Once again: concepts are subsets of the model. Male(x) LongHaired(x) Once again: concept descriptions correspond to first-order formulas with one free variable. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 13

Concept union How do we interpret this? Female PhDstudent First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 14

Concept union How do we interpret this? Female PhDstudent In this room: as the set of individuals who are either female or who are PhD students. Again: concepts denote subsets of our model. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 14

Concept union How do we interpret this? Female PhDstudent In this room: as the set of individuals who are either female or who are PhD students. Again: concepts denote subsets of our model. Female(x) PhDstudent(x) Again: concept descriptions correspond to first-order formulas in one free variable. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 14

Concept negation How do we interpret this? likedescriptionlogic First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 15

Concept negation How do we interpret this? likedescriptionlogic In this room: as the set of individuals who do not like description logic (so again, a concept is a subset of our little world). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 15

Concept negation How do we interpret this? likedescriptionlogic In this room: as the set of individuals who do not like description logic (so again, a concept is a subset of our little world). likedescriptionlogic(x) Once more, the corresponding first-order formula has one free variable. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 15

Existential Quantification Friend.Female For the first time we see a role (namely Friend). How do we interpret this? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 16

Existential Quantification Friend.Female For the first time we see a role (namely Friend). How do we interpret this? In this room: as the set of individuals who have a friend who is a female. Once again, this really is a concept (it is a subset of our model) but it is a concept defined using a binary relation (namely, friendship) between individuals. y(friend(x, y) Female(y)) Again, a concept description corresponds to a first-order formula in once free variable (here, x) but we access a second individual using the bound variable y and the first-order quantifier. Also, note that this is a relativised (or guarded) form of first-order quantification. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 16

Role restriction Friend.Female Again the role Friend is being put to work. How do we interpret this? First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 17

Role restriction Friend.Female Again the role Friend is being put to work. How do we interpret this? In this room: as the set of individuals who only have females as friends Note: once again this really is a concept (it is a subset of our model) but it is a concept defined using a binary relation (friendship) between individuals. y(friend(x, y) Female(y)) Again, a concept description corresponds to a first-order formula in once free variable (the x) but we access a second individual using the bound variable y and the first-order quantifier. And again we have a relativised (or guarded) form of first-order quantification. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 17

To summarize A A(x) C D C(x) D(x) C D C(x) D(x) C C(x) R.C y(r(x, y) C(y)) R.C y(r(x, y) C(y)) Fact: Every ALC concept can be translated into a first-order formula containing at most one free variable that means exactly the same thing. That is, anything you can say about a model in ALC you can say in first-order logic. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 18

ALC is a genuine fragment of first-order logic First-order logic can define concepts that ALC cannot. For example, the first-order formula Likes(x, x) defines the concept of being a person who does not like himself/herself. No ALC concept description can do this. So ALC is expressively weaker than first-order logic. Is this a good thing or a bad thing? That depends what you want to do. Certainly some mathematical logicians and (and probably some formal semanticists) would say it s a bad thing: ALC can t describe the concepts they are interested in. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 19

ALC is a genuine fragment of first-order logic First-order logic can define concepts that ALC cannot. For example, the first-order formula Likes(x, x) defines the concept of being a person who does not like himself/herself. No ALC concept description can do this. So ALC is expressively weaker than first-order logic. Is this a good thing or a bad thing? That depends what you want to do. Certainly some mathematical logicians and (and probably some formal semanticists) would say it s a bad thing: ALC can t describe the concepts they are interested in. But nothing comes for nothing: ALC is decidable over arbitrary models whereas first-order logic is undecidable First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 19

Description logic trades expressivity off for computational efficiency For many applications first-order logic offers too much. We simply don t need the expressivity it offers. For many applications ALC (or some other DL) offers an attractive alternative: a simple variable free syntax that can describe the concepts you are interested in, which is decidable, and for which computatonal tools exists. The DL community has explored in detail the landscape of fragments of classical logic it has put the early intuitions of the network formalism community that some forms of reasoning require a lot less than full firstorder logic on a solid mathematical and computational basis. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 20

Weaker languages The description language AL: C, D A (atomic concept) (universal concept) (bottom concept) C D (concept conjuntion) A (atomic negation) R. (limited existential quantification) R.C (value restriction) (Note: no concept union) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 21

Stronger languages Richer syntax on roles. Transitive closure. Counting: Person ( 1 haschild ( 3 haschild haschild.female)) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 22

How do we use this language? Formalisms that represent knowledge of some problem domain (the world ) by first defining the relevant concepts of the domain (its terminology), and then using these concepts to specify properties of objects and individual occuring in the domain (the world description). Baader and Nutt, 2003. So we need to learn about terminologies and world descriptions. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 23

TBoxes (or terminologies) A TBox (or terminology) is essentially a collection of definitions of the concepts we find interesting/useful/important for our application. For example, here is a collection of terminological axioms about families. Woman Person Female Man Person Woman Mother Woman haschild.person Father Man haschild.person Parent Father Mother GrandMother Mother haschild.parent MotherWithoutDaughter Mother haschild. Woman MotherWithManyChildren Mother 3hasChild A model for this terminology is any structure which makes all these axioms true. Such models are the worlds we find interesting for our application. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 24

More is possible Axioms don t have to have the form C D. It is also possible to write axioms of the form C D (that is, to insist that C is a subconcept of D). For example we could insist that Autistic NeedsSpecialSchooling. It is also possible to insist that two roles are identical (R S) or to say that one role is a subrole of another (S R). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 25

Need for inference already It is easy to write down an impressive collection of axioms that allegedly defines the concepts we are interesting. But how can we be sure the axioms make sense? Perhaps our definitions imply don t make sense. It would be nice is we could compute when terminolgies were red consistent. Moreoever, if we define lots of concepts in our TBox, we will swiftly lose track of how they are inter-related. It would be nice if we had a way to compute the red concept hierarchy. Both tasks are inference tasks, and both tasks can be computed for ALC terminologies. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 26

ABoxes or World Descriptions TBoxes pin down the kinds of models we are interested. that is, they spell out the general concepts we find interesting. But we also want to talk about particular individuals, their properties, and the relations they enter into. This is the job of the ABox. Dutch(MAARTEN) French(PIERRE) Woman(YVONNE) Friend(JULES, VINCENT) In a particular application domain, the TBox tends to be relatively stable, but we may need to work with several ABoxes (one for each family, say). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 27

Be careful! Warning for PROLOG programmers: semantics, not a closed world semantics. ABoxes have an open world Warning for classical logicians: a unique name assumption is typically named (that is, no entity can have two names). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 28

What I haven t talked about (I) Inference I ve mentioned the topic, but that s it. No problem: the next two talks are devoted to this subject. What kinds on inference services are interesting/useful? (Carlos Areces) How is inference to be carried out? That is, what kind of mechanisms are used in DL to ensure efficient inference? (Carsten Lutz) First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 29

What I haven t talked about (II) Applications What kinds of applications can benefit from DL? (Amadeo Napoli, Alexander Koller and Kristina Striegnitz) Computation What kinds of computational tools are available, and how can they be adapted to particular applications? (Ralf Möller). First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 30

Where to find out more) The Description Logic Handbook Theory, Implementation and Applications edited by Baader, Calvanese, McGuinness, Nardi and Patel-Schneider Cambridge University Press, 2003. First Steps in Description Logic, DLD, LORIA, Nancy, 23 September 2003. 31