1. Ontology Engineering Lab #4 - September 23, 2013

2. Review – Closure Axiom  Open World Assumption – that an unstated assertion can not be inferred to be false  Defined classes (in Protégé, classes having necessary and sufficient conditions) with universal restrictions are not inferred to be superclasses of primitive classes (in Protégé, classes that have only necessary conditions) having existential restrictions 2

3. Review – Closure Axiom  Example:  Defined Class: A crime is a misdemeanor only if it carries a sentence of no more than 1 year  Primitive Class: A violation is a crime that carries a penalty of no more than 15 days  A reasoner will not infer that a violation is a misdemeanor because it is possible that a violation may have another penalty in excess of a year  Force the inference by adding a closure axiom on the primitive class  A closure axiom is an universal restriction that is an intersection of all the class’s existential restrictions  Example: A violation crime and carries_penalty_of only ‘Less than 15 days’ 3

4. Review – Class Axioms  Enumerations – naming the members of a class  Set theoretic operations – intersection, union and complement  Disjoint axiom – defines classes to have no instances in common  Cardinality restrictions – defines how many instances of the restricting class can be related to the restricted class 4

5. Object Properties  rdfs:subPropertyOf – used to declare one object property is a subproperty of another property  Example: has_proper_part is a subproperty of has_part  Example: is_sister_of is a subproperty of is_sibling_of  Object Property Chain subPropertyOf – used to declare that if x is related to y by property 1 and y is related to z by property 2, the x is related to z by the parent property  Example: if a is the mother of b and b is the spouse of c, then a is the mother-in-law of c  Example: if a is the agent in b and b is the cause of c, then a is the proximate cause of c 5

6. Object Properties  rdfs:domain – used to declare that subjects of property statements must belong to the class extension of the indicated class description.  Example: Events as the domain of the has_agent property  rdfs:range – used to declare that the values of this property must belong to the class extension of the class description or to data values in the specified data range.  Example: Qualities as the domain of the has_quality property 6

7. Object Properties  owl:equivalentProperty - used to state that two properties are synonymous, or in other words, that they relate the same individuals  Example: is brother of and is male sibling of  Example: between and amid  owl:inverseOf - used to define an inverse relation between properties. If properties P1 and P2 are inverses then for any individuals i1 and i2, if i1 is related to i2 via property P1, the i2 is related to i1 via property P2  Example: is parent of and is child of  Example: precedes and follows 7

8. Object Properties  Functional Object Property – used to state that for each individual x, there can be at most one distinct individual y such that x is connected by the property to y.  Example: If x designates y and x designates z then y = z  Example: if x has mother y and x has mother z then y = z  Inverse Functional Object Property – used to state that for each individual x, there can be at most one individual y such that y is connected by the property to x.  Example: if y is starting instant of x and z is the starting instant of x, then y = z  Example: if y is the mother of x and z is the mother of x then y = z 8

9. Object Property  Reflexive Property – used to state each individual is connected by the object property to itself.  Example: Every class is a subclass of itself  Irreflexive Property – used to state that no individual is connected by the object property to itself.  Example: No Person is their own ancestor.  Symmetric Property – used to state that if an individual x is connected by the property to an individual y, then y is also connected by the property to x.  Example: If x is the spouse of y, then y is the spouse of x 9

10. Object Property  Asymmetric Property – used to state that if an individual x is connected by the property to an individual y, then y cannot be connected by the property to x.  Example: If x precedes y, then y does not precede x  Example: If x is the parent of y, then y is not the parent of x  Transitive Property – used to state that if an individual x is connected by the property to an individual y that is connected by the property to an individual z, then x is also connected by the property to z.  Example: if x precedes y and y precedes z, then x precedes z  Example: if x is a subclass of y and y is a subclass of z, then x is a subclass of z 10

11. 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”}  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 11

12. 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 12

13. Exercise for Week 5  Widget manufacturing has 5 component processes:  Mixing of material  Shaping of material  Heating of material  Cooling of material  Product Packaging  The component processes always occur in this order except if the process fails in which case the component process after the failing one are not completed  Continued on next slide… 13

14. Exercise for Week 5  Every one of the component processes has at least these inputs and outputs  Mixing – inputs (portion of water, portion of minerals, portion of additives), output (portion of slurry)  Shaping – input (portion of slurry), output (widget form)  Heating – input (widget form), output (widget having temperature between 100 and 110 degrees Celsius*)  Cooling – input (widget having temperature less than 110 degrees Celsius), output (widget having temperature less than 30 degrees Celsius)  Packaging – input (widget, cardboard box), output (boxed widget) (*For the purposes of the exercise I suggest simply using a data property such as ‘has_temperature_value’ also I’m not looking for you to express the Celsius scale part) 14