Ontology Engineering Lab #3 – September 16, 2013

Review – RDF, RDF-S, and OWL  RDF provides rules to form well-formed statements  Three parts: subject, predicate and object  Commonly depicted as directed graphs having nodes and edges  Subject and Predicate must be a resource (an entity identified by a URI)  Object can be either a resource or a literal value  Predicates are binary only 2

Review – RDF, RDF-S, and OWL  This trio of languages provides a vocabulary for building machine processable ontologies  Class hierarchies (i.e. taxonomies) can be built by subsuming one named class under another (rdfs:subClassOf)  But we also can use restrictions on other relationships to create subclass and equivalent class relations to anonymous classes  Existential Restriction – members of the restricted class must be related via the property to at least one member of the object class  Universal Restriction – if a member of the restricted class is related via the property to an entity then that entity must be a member of the object class 3

Review – Necessary and Sufficient Conditions  “All acts of inhabitance are acts performed by persons.” is an expression of a necessary condition to be an act of inhabitance. Other ways to express this are:  If a1 is an act of inhabitance then a1 is performed by a person  If a1 is not an act performed by a person, then a1 is not an act of inhabitance  The class of act of inhabitance is a subclass of act performed by person  This is not, however, an expression of a sufficient condition for being an act of inhabitance  In order for S to be a sufficient condition of N it must be true that if S then N 4

Review – Equivalent Classes  Two classes are equivalent if and only if they have the same members  Example: Even Numbers and Numbers divisible by 2  If two classes are equivalent then membership in one is both a necessary and sufficient condition of the other  If n is an even number then n is divisible by 2  If n is divisible by 2 then n is an event number  In Protégé,  A Primitive Class is one that has only subclass restrictions (necessary condition)  A Defined Class is one that has equivalent class restriction (necessary and sufficient condition) 5

 The conditions of class membership can be expressed by providing a list of the individuals that are its members  e.g. A continent is one of Africa, Asia, Antarctica, Europe, North America, Oceania, South America  The technique can be used for subclass restrictions but seems best suited for equivalent class restrictions  The type of the individuals can be, but need not be, explicitly asserted (rdf:type). If not, it will be inferred by the reasoner Enumerated Classes 6

Set Operations on Classes 7  The intersection (and) operand can be used to express that a class is either a subclass of or equivalent to the class of individuals that are members of two or more classes  Example: Customer of the ACME Corporation is a person that has purchased a product from ACME Corporation  Example: A sister is a female sibling  The union (or) operand can be used to express that a class is either a subclass of or equivalent to the class of individuals that are members of any of two or more classes  Example: An agent is either a person or organization  Example: New York State misdemeanors are either Class A or Class B

Set Operations on Classes 8  The Complement (non-) operand can be used to express that class is a subclass of or equivalent to the class of individuals that are not members of one or more classes  Example: A Violation in NYS is any offence, other than a traffic infraction, for which a sentence to a term of imprisonment in excess of 15 days cannot be imposed  Example: Industrial diamonds are unsuitable for use as gemstones

Building a Taxonomy – Common Problems 9  A common occurrence in vocabularies and code lists is the formation of a term using operands such as “other” and “not otherwise specified”  Such terms change in meaning as new sibling terms are added to the list.  Use of the complement operand requires forethought and vigilance Mining and Quarrying Mining of Coal and Lignite Extraction of crude petroleum and natural gas Mining of metal ores Other mining and quarrying Mining support service activities Mining and Quarrying Mining of Coal and Lignite Extraction of crude petroleum and natural gas Mining of metal ores Other mining and quarrying Mining support service activities Quarrying of Stone, Sand or Clay *example excerpted from International Standard Industrial Classification of All Economic Activities, Rev.4

Closure Axioms 10  In New York State, a crime is a misdemeanor only if it carries a sentence of no more than 1 year  In New York State, a violation is a crime that carries a penalty of no more than 15 days  In Protégé we can represent this as a subclass axiom such as: New York State Criminal Act and carries_penalty_of some 'Less than 15 days'  While it may seem valid to infer that a violation is a subtype of misdemeanor, an OWL reasoner will not make such an inference because of the Open World Assumption

Closed World Assumption (CWA) 11  Some knowledge representations are part of a context in which it is assumed that any statement not asserted in the representation is false. This is known as the Closed World Assumption  Example: Any person not listed in a bank’s database as having an account does not have an account with that bank  Example: Every person not on the US No Fly List is able to use commercial air travel to and from the United States

Open World Assumption (OWA) 12  Knowledge representations in OWL make the Open World Assumption meaning that a statement that is not asserted cannot be inferred to be false.  Example: A taxonomy of all mammals does not exclude the possibility of discovering new ones  Example: A taxonomy of criminal acts does not exclude the possibility that an act will be deemed criminal at some future point.

Closure Axioms vs. the OWA 13  Does the statement: A Violation is a New York State Criminal Act and carries_penalty_of some 'Less than 15 days' imply that such an act does not carry a sentence of more that 1 year?  Not under the OWA which leaves undetermined whether a violation might not carry a second penalty of more than 1 year  To counteract the OWA we add a universal restriction (i.e. “only”) to say that the only restrictions on a class are those explicitly stated in set of existential restrictions (i.e. “some”)  Example: A Violation is a New York State Criminal Act and carries_penalty_of only ‘Less than 15 days’

Disjoint Axioms 14  Single inheritance (every class has only one parent class) in the asserted (as opposed to the inferred) class hierarchy of an ontology (taxonomy) is a desirable attribute.  If sibling classes (classes with the same parent) have members in common maintaining single inheritance becomes difficult  Adding disjoint axioms to a group of sibling classes is the explicit statement that the classes have no common members  Along with the complement operand, a disjoint axiom introduces the possibility of a contradiction

Coverage Axiom 15  In cases where a set of subclasses provides complete coverage of their parent class (i.e. every member of the parent class must be a member of one of the subclasses) we can add a coverage axiom to express this fact  A formulaic expression of a coverage axiom:  If A, B, and C are subclasses of Z and A, B, and C provide complete coverage of Z, then this can be expressed in the form that Z is a subclass of the union of A, B, and C.  Example: In New York State, a Felony is one of 5 types: Class A, Class B, Class C, Class D or Class E. So we can say that Felony is a subclass of the class (Class A, Class B, Class C, Class D, Class E)

Cardinality Restrictions 16  Minimum Cardinality – a restriction that asserts that members of the restricted class must have a specified number of members of the restricting class along the stated property  Example: A ZIP code must have part at least 5 digits  Maximum Cardinality – a restriction that asserts that members of the restricted class can have no more than a specified number of members of the restricting class along the stated property  Example: A ZIP code can have part no more than 9 digits

Cardinality Restrictions 17  Exact Cardinality - a restriction that asserts that members of the restricted class must have an exact number of members of the restricting class along the stated property  Example: A ZIP Plus 4 Code has part exactly 9 digits

A Shortcut for Disjoint Axioms 18  To make all subclasses disjoint one needs to write (n-1) + … (n-n) disjoint axioms where n is the number of subclasses.  Example: The five types of NYS felonies (Class A – Class E) there need to be 10 disjoint axioms  Class A is disjoint with Classes B, C, D, E  Class B is disjoint with Classes C, D, E  Class C is disjoint with Classes D, E  Class D is disjoint with Class E  To simplify this Protégé implements the owl:AllDisjointClasses class via the Make primitive siblings disjoint menu option (Ctrl + J)

A Shortcut for Disjoint Unions 19  For classes that are composed of the union of disjoint subclasses use the Protégé implementation of the owl:disjointUnionOf  Example: NYS Felony is either (Class A Felony or Class B Felony or Class C Felony or Class D Felony or Class E Felony) and all of these subclasses are disjoint

Exercise for 9/23 20  Create an.owl file that includes the content of the following assertions:  Every widget has a quality of size  Three disjoint subtypes of size are small, medium or large  Two subtypes of widget tasks are commercial widget tasks and industrial widget tasks  Commercial widget tasks use only small widgets  Industrial widgets are either medium or large and are used in industrial widget tasks  Medium sized widgets are made of at least 1 but not more than 3 small sized widgets