Ontologies and Knowledge-based Systems Is there a flexible way to represent relations? How can knowledge bases be made to interoperate semantically? � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 1 1 / 12
Choosing Individuals and Relations How to represent: “Pen #7 is red.” � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 2 2 / 12
Choosing Individuals and Relations How to represent: “Pen #7 is red.” red ( pen 7 ). It’s easy to ask “What’s red?” Can’t ask “what is the color of pen 7 ?” � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 3 2 / 12
Choosing Individuals and Relations How to represent: “Pen #7 is red.” red ( pen 7 ). It’s easy to ask “What’s red?” Can’t ask “what is the color of pen 7 ?” color ( pen 7 , red ). It’s easy to ask “What’s red?” It’s easy to ask “What is the color of pen 7 ?” Can’t ask “What property of pen 7 has value red ?” � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 4 2 / 12
Choosing Individuals and Relations How to represent: “Pen #7 is red.” red ( pen 7 ). It’s easy to ask “What’s red?” Can’t ask “what is the color of pen 7 ?” color ( pen 7 , red ). It’s easy to ask “What’s red?” It’s easy to ask “What is the color of pen 7 ?” Can’t ask “What property of pen 7 has value red ?” prop ( pen 7 , color , red ). It’s easy to ask all these questions. � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 5 2 / 12
Choosing Individuals and Relations How to represent: “Pen #7 is red.” red ( pen 7 ). It’s easy to ask “What’s red?” Can’t ask “what is the color of pen 7 ?” color ( pen 7 , red ). It’s easy to ask “What’s red?” It’s easy to ask “What is the color of pen 7 ?” Can’t ask “What property of pen 7 has value red ?” prop ( pen 7 , color , red ). It’s easy to ask all these questions. prop ( Individual , Property , Value ) is the only relation needed: called individual-property-value representation or triple representation � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 6 2 / 12
Universality of prop To represent “a is a parcel” � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 7 3 / 12
Universality of prop To represent “a is a parcel” prop ( a , type , parcel ), where type is a special property prop ( a , parcel , true ), where parcel is a Boolean property � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 8 3 / 12
Reification To represent scheduled ( cs 422 , 2 , 1030 , cc 208) . “section 2 of course cs 422 is scheduled at 10:30 in room cc 208.” � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 9 4 / 12
Reification To represent scheduled ( cs 422 , 2 , 1030 , cc 208) . “section 2 of course cs 422 is scheduled at 10:30 in room cc 208.” Let b 123 name the booking: prop ( b 123 , course , cs 422) . prop ( b 123 , section , 2) . prop ( b 123 , time , 1030) . prop ( b 123 , room , cc 208) . We have reified the booking. Reify means: to make into an individual. What if we want to add the year? � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 10 4 / 12
Semantic Networks / Knowledge Graphs When you only have one relation, prop , it can be omitted without loss of information. Logic: prop ( Individual , Property , Value ) triple: � Individual , Property , Value � simple sentence: Individual Property Value . graphically: Prop Obj Val � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 11 5 / 12
An Example Semantic Network / Knowledge Graph building comp_sci lemon_laptop_10000 r107 building r117 ming lemon_computer room room model craig deliver_to brand owned_by logo comp_2347 lemon_disc packing color weight size cardboard_box light brown medium � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 12 6 / 12
Equivalent Logic Program prop ( comp 2347 , owned by , craig ) . prop ( comp 2347 , deliver to , ming ) . prop ( comp 2347 , model , lemon laptop 10000) . prop ( comp 2347 , brand , lemon computer ) . prop ( comp 2347 , logo , lemon disc ) . prop ( comp 2347 , color , brown ) . prop ( craig , room , r 107) . prop ( r 107 , building , comp sci ) . . . . � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 13 7 / 12
A Structured Semantic Network / Knowledge Graph room r117 ming cardboard_box building deliver_to packing computer comp_sci subClassOf building lemon_computer logo color r107 brown lemon_disc subClassOf lemon_laptop_10000 room size weight type medium craig light comp_2347 owned_by � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 14 8 / 12
Logic of Property p An arc c → v from a class c with a property p to value v means − every individual in the class has value v on property p : prop ( Obj , p , v ) ← prop ( Obj , type , c ) . Example: prop ( X , weight , light ) ← prop ( X , type , lemon laptop 10000) . prop ( X , packing , cardboard box ) ← prop ( X , type , computer ) . � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 15 9 / 12
Logic of Property Inheritance You can do inheritance through the subclass relationship: prop ( X , type , T ) ← prop ( S , subClassOf , T ) ∧ prop ( X , type , S ) . � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 16 10 / 12
Multiple Inheritance An individual is usually a member of more than one class. For example, the same person may be a wine expert, a teacher, a football coach,. . . . The individual can inherit the properties of all of the classes it is a member of: multiple inheritance. With default values,what is an individual inherits conflicting defaults from the different classes? multiple inheritance problem. � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 17 11 / 12
Choosing Primitive and Derived Properties Associate an property value with the most general class with that property value. Don’t associate contingent properties of a class with the class. For example, if all of current computers just happen to be brown. � D. Poole and A. Mackworth 2017 c Artificial Intelligence, Lecture 14.1, Page 18 12 / 12
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