Semantic Web for the Working Ontologist Dean Allemang Jim Hendler SNU IDB laboratory

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Working Ontology Contents 2 ■ Chapter 1 What is the Semantic Web? ■ Chapter 2 Semantic Modeling ■ Chapter 3 RDF-The Basis of the semantic Web ■ Chapter 4 Semantic Web Application Architecture ■ Chapter 5 RDF and Inferencing ■ Chapter 6 RDF Schema ■ Chapter 7 RDFS-Plus ■ Chapter 8 Using RDFS-Plus in the Wild ■ Chapter 9 Basic OWL ■ Chapter 10 Counting and Sets in OWL ■ Chapter 11 Using OWL in the Wild ■ Chapter 12 Good and Bad Modeling Practices ■ Chapter 13 OWL Levels and Logic

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Chapter 10 Counting and Sets in OWL ■ Unions and Intersections ■ Differentiating Multiple Individuals ■ Cardinality ■ Set Complement ■ Disjoint Sets ■ Prerequisites Revisited ■ Contradictions ■ Unsatisfiable Classes ■ Inferring Class Relationships ■ Reasoning with Individuals and with Classes ■ Summary 3

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ OWL provides a facility for defining new classes as unions & intersections of previously defined classes ■ Union Includes the members of all those classes combined ■ Intersection Includes the members that belong to every one of the classes 4

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ The intersection of two classes is a new class represented by naming that class (as shown above) or defining an anonymous class (as shown below) 5

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Natural language descriptions of restrictions often have a notion of intersection built-in e.g. “all planets orbiting the sun” ▶ -> the intersection of all things that orbit the sun & all planets e.g. “the set of major league baseball players” ▶ -> the intersection of the things that play on a major league team & baseball players 6

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ EXAMPLE: High-Priority Candidate Questions 7

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Closing the World Open World Assumption ▶ - makes counting difficult ▶ - makes the notion of set complement subtle There are ways in OWL to assert that certain parts of the world are closed 8 Rimbaud: I saw a James Dean movie last night. Rocky: Was it Giant? Rimbaud: No. Rocky: Was it East of Eden? Rimbaud: No. Rocky: James Dean only made three movies; it must have been Rebel Without a Cause. Rimbaud: Yes, it was.

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Enumerating Sets with owl:oneOf OWL allows us to enumerate the members of a class using a construct called owl:one of ▶ -> This means that the class SolarPlanet contains these eight individuals & no others 9

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Challenge 27 “In the dialogue with Rimbaud, Rocky used the fact that James Dean made only three movies to help determine what movie A has seen. How do we represent this in OWL?” 10

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Differentiating Individuals with owl:differentFrom We have to be explicit about the things & name things that are different from one another ▶ - because of the nonunique naming assumption ▶ -> This means that we can rely on the fact that ss:Earth & ss:Mars refer to different resources when making arguments by counting or by elimination 11

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unions and Intersections ■ Challenge 28 “Use OWL to model the dialogue between Rimbaud & Rocky so that OWL can draw the same inference that Rocky did-namely, that Rimbaud saw Rebel Without a Cause” 12

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Differentiating Multiple Individuals ■ owl:AllDifferent & owl:distinctMembers To simplify the specification of lists of items, all of which are different from one another The domain of owl:distinctMembers is owl:AllDifferent It is customary for the subject of an owl:distinctMembers triple to be a bnode 13

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Differentiating Multiple Individuals ■ owl:AllDifferent & owl:distinctMembers 14

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Cardinality ■ Cardinality restriction Allows us to express constraints on the # of individuals that can be related to a member of the restriction classes 15

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Cardinality ■ Challenge 29 “Model these facts in OWL so that Rimbaud’s conclusion follows from the OWL semantics” 16 Rimbaud: Do you own any James Dean movies? Rocky: They are the only ones I own. Rimbaud: Then I guess you don’t own very many movies! No more than three.

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Cardinality ■ Challenge 29 (cont’d) This triple can be inferred from the model because ▶ - all the values of the property ownsMovie for Rocky come from the class JamesDeanMovie ▶ - there are only three of them ▶ - they are all distinct 17

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Cardinality ■ Small Cardinality Limits minCardinality 1 ▶ -> indicates the set of individuals for which some for the specified property is required maxCardinality 1 ▶ -> specifies that a value is unique (but need not exist) minCardinality 0 ▶ -> describes a set of individuals for which the presence of a value for the onProperty is optional ▶ -> superfluous, but useful maxCardinality 0 ▶ -> indicate the set of individuals for which no value for the specified property is allowed 18

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Set Complement ■ The complement of a class is another class whose members are all things not in the complemented classes ■ Set complements can be easily misused (wrong) (right) 19

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Set Complement ■ Challenge 31 “Model this situation & conclusion in OWL” 20 Paul: Are you talking about James Dean? I love him! I have all his movies. Rimbaud: But, you aren’t obsessive, are you? I mean, You have other movies, too, don’t you? Rocky: I’m not obsessive! Paul: Of course, I have some movies that aren’t James Dean movies. Rocky: You must have at least four movies then!

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Set Complement ■ Challenge 31 (cont’d) 21

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Disjoint Sets ■ owl:disjointWith Two sets have no individual in common i.e. the sets are disjoint For any members of disjoint classes, we can infer that they are owl:differentFrom one another ▶ -> We can infer that ■ There is no owl:AllDisjoint 22

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Disjoint Sets ■ Challenge 32 “Model this situation & conclusion in OWL” 23 Paul: I am a big movie fan. Not only do I own all the James Dean movies, but I also have movies with Judy Garland, Tom Cruise, Dame Judi Dench, and Antonio Banderas! Rocky: You must own at least seven movies! Paul: How do you know that? Rocky: Because none of those people played in movies together!

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Disjoint Sets ■ Challenge 32 (cont’d) :Paul a :SevenMovieOwner 24

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Disjoint Sets ■ Challenge 32 (cont’d) 25

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Prerequisites Revisited ■ We’ll use prerequisites to determine a number of ways we can close the world ■ A reminder from Ch. 9 Something that has all its prerequisites satisfied is an EnabledQuestion 26

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Prerequisites Revisited ■ No Prerequisites How can we know that something has no prerequisites? ▶ -> Then we know that there are no triples of the form ▶ -> That is, WhatProblem has no prerequisites ▶ -> Therefore it satisfies the restriction ▶ -> hence 27

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Prerequisites Revisited ■ Counting Prerequisites Another way to determine that something has satisfied all of its prerequisites is to count how many of them are there are ▶ Suppose we know that something has exactly one prerequisite and also know its type ▶ -> So we know that all of the prerequisites are members of the class q:SelectedAnswer 28

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Prerequisites Revisited ■ Guarantees of Existence owl:allValuesFrom ▶ -> The membership of an individual A in an allValuesFrom restriction on property P does not guarantee that any triple of the form A P ? owl:someValuesFrom ▶ -> does guarantee that some value is given for the specified property owl:hasValue ▶ -> not only guarantee that there is such a triple, but also even specifies exactly what it is 29

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Contradictions ■ Challenge 33 “Model this situation & conclusion in OWL” 30 Rocky: You’re a Judy Garland fan? I have a couple of her movies, too! Rimbaud: Wait a minute! That can’t be right! You said that you own only James Dean movies, and now you say that you have a Judy Garland movie. They weren’t in any movie together!

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Contradictions ■ Challenge 33 (cont’d) The OWL semantics can tell us that there is a contradiction But it cannot tell us which assertion is wrong What does we mean by modeling? ▶ -> A model is a description of the world and can be mistaken If they are logically inconsistent, then we know that ▶ either our model is defective ▶ or our understanding of how it relates to the world is mistaken 31

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unsatisfiable Classes ■ A contradiction also arises when we define a class in an inconsistent way When we can prove that a class is empty, we say that the class itself is unsatisfiable ▶ -> There can be no individuals who are members of that class 32

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Unsatisfiable Classes ■ Propagation of Unsatisfiable Classes subclass ▶ -> A subclass of an unsatisfiable class is itself unsatisfiable someValuesFrom ▶ -> A restriction with owl:someValuesFrom an unsatisfiable class is itself unsatisfiable domain & range ▶ -> If a property has an unsatisfiable domain & range, then the property becomes basically unusable intersection of disjoints ▶ -> The owl:intersectionOf two disjoint classes is unsatisfiable 33

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Inferring Class Relationships ■ OWL allows us to draw a wide range of conclusions (inferences) about classes Intersection & subclass Union & subclass Complement & subclass Subclass propagation through restriction hasValue, someValuesFrom, & subClassOf Relative cardinality someValuesFrom & minCardinality 34

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Inferring Class Relationships ■ Overview of Entities in the Baseball Model 35

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Inferring Class Relationships 36 Class tree for the baseball ontology, as asserted Inferred structure of the Baseball model

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Reasoning with Individuals with Classes ■ Inferencing about individuals & inferencing about classes Very similar from an RDF perspective ▶ -> New triples are added based on the asserted triples Very different from a modeling perspective ▶ -> A-box reasoning vs. T-box reasoning ■ The utility of reasoning about classes is more subtle than that of reasoning about individuals It can take place in the absence of any data at all! Class reasoning determines the relationships between classes of individuals 37

Semantic Web for the Working OntologistDean Allemang, Jim Hendler Summary ■ We have introduced new notions of how to understand a model from RDF (data sharing & federation) to RDFS (inference) to the various levels of OWL (more comprehensive capabilities to infer new information) 38

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