1. ONTOLOGY ENGINEERING Lab #3 – September 15, 2014 1

2. Closure Axioms 2  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

3. Closed World Assumption (CWA) 3  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

4. Open World Assumption (OWA) 4  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.

5. Closure Axioms vs. the OWA 5  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’

6. Disjoint Axioms 6  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

7. Coverage Axiom 7  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)

8. Cardinality Restrictions 8  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

9. Cardinality Restrictions 9  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

10. A Shortcut for Disjoint Axioms 10  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)

11. A Shortcut for Disjoint Unions 11  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

12. Data Property  owl:DatatypeProperty – used to assert that a resource is related to a literal (un-typed) or an XML Schema built-in datatype (typed) value  Example: Name Bearer has_text_value xsd:String  Example: Nominal_Population_Value one of {“Small”, “Mid-Size”, “Large”}  Example: Interstate has_part some (TrafficLane and has_lane_width value 12) NOTE: In this example “has_lane_width” is the datatype property and the keyword “value” is what I was missing during the lab presentation  Recall that in OWL no links can be made to properties, or to literals, so declaring population values as done in the 2nd example above prevents it from being linked to other data 12

13. Data Property  Can be made equivalent to, or synonymous with, other data properties  Example: has_text_value equivalent to has_string_value  Can be made a subproperty of some other data property  Example: nominal_population_value subproperty of has_text_value  Can have domains and ranges specified  Example: nominal_population_value has domain geopolitical area  Can be disjoint with other data properties  Example: area_value disjoint with length_value  Can be functional properties  Example: has_national_identifier_value is a functional property 13

14. Assignment 14  Import Basic Formal Ontology (using the BFO 2.0 Classes Only file) into your Roadway Ontology  Arrange the current classes from the Roadway Ontology as subclasses of BFO.  Express the fact that “… a roadway of a higher classification should not connect to a single roadway of a lower classification” from p.11. Ignore the exceptions  Read the Level of Measurement article on Wikipedia (http://en.wikipedia.org/wiki/Level_of_measurement)http://en.wikipedia.org/wiki/Level_of_measurement  Read Sections 4.8 and 7.0 of the OWL 2 Web Ontology Language Primer (2nd Edition) (http://www.w3.org/TR/2012/REC-owl2-primer-20121211/) on Datatype properties and Advanced Use of Datatypeshttp://www.w3.org/TR/2012/REC-owl2-primer-20121211/  Use datatype properties to express the Lane Width, Annual Average Daily Traffic (AADT Rural) and Access attributes for Interstates as listed in Table 3-5 on page 22.  Consider how you manage change of the values of these attributes over time