AI CS 364 Knowledge Representation Conceptual Graphs

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AI – CS 364 Knowledge Representation CG Arrow Rules • An arc is said to belong to a relation but to be attached to a concept. • As we mentioned previously a conceptual graph is a bipartite. This simply means that: – there are no arcs between a concept and another concept, – there are no arcs between a relation and another relation. – all arcs either go from a concept to a relation or from a relation to a concept. • A conceptual graph may have concepts that are not linked to any relation, but analogically this is not possible for relations. • For a conceptual relation with n arcs, the first n-1 arcs have arrows that point toward the circle, and the n-th or last arc (if any!) points away. 19 th September 2006 Bogdan L. Vrusias © 2006 3

AI – CS 364 Knowledge Representation CG Arrow Rules • There is also special standard language associated with the direction of an arrow. This language can be divided into two groups: – When reading in the direction of the arrows, – When reading against the direction of the arrows. • For each group, it also matters whether we are reading an arrow that points towards or away from a relation. • When reading in the direction of the arrows: – If the arrow points towards the relation, we often say "has a". – If the arrow points away from the relation, we often say "which is". • When reading against the direction of the arrows: – If the arrow points away from the relation, we often say "is a". – If the arrow points towards the relation, we often say "of". 19 th September 2006 Bogdan L. Vrusias © 2006 4

AI – CS 364 Knowledge Representation Generalisation and Specialisation • New conceptual graphs may be derived from other canonical graphs either by generalising or specialising by the rules: – copy, restrict, join, and simplify • Formation rules are the (generative) grammar of conceptual structures. All deductions and computations on canonical graphs involve some combination of them. • Formation rules are not rules of inference; rather templates which are manipulated in order to incorporate new knowledge. 19 th September 2006 Bogdan L. Vrusias © 2006 5

AI – CS 364 Knowledge Representation Generalisation and Specialisation Consider the following graphs: agent eat object dog colour bone brown g 1: animal: "Emma" location porch g 2: colour 19 th September 2006 brown Bogdan L. Vrusias © 2006 6

AI – CS 364 Knowledge Representation Generalisation and Specialisation The restriction of g 2 (based on g 1) is: dog: "Emma" location porch g 3: colour 19 th September 2006 brown Bogdan L. Vrusias © 2006 7

AI – CS 364 Knowledge Representation Generalisation and Specialisation The join of g 1 and g 3 is: agent g 4: location dog: "Emma" colour 19 th September 2006 object eat colour bone porch brown Bogdan L. Vrusias © 2006 8

AI – CS 364 Knowledge Representation Generalisation and Specialisation The simplification of g 4 is: agent g 5: dog: "Emma" colour 19 th September 2006 eat location object bone porch brown Bogdan L. Vrusias © 2006 9

AI – CS 364 Knowledge Representation Propositional Concepts • Conceptual graphs may include a concept type, proposition, that takes a set of conceptual graphs as its referent. • This allows definitions that involve propositions. • Propositional concepts are indicated as a box that contains another conceptual graph. • The conceptual graphs nested inside a context are the referent of that concept. 19 th September 2006 Bogdan L. Vrusias © 2006 10

AI – CS 364 Knowledge Representation Propositional Concepts • Consider the example: "Tom believes that Jane likes pizza" person: "Tom" experiencer believe object proposition person: "Jane" experiencer pizza 19 th September 2006 Bogdan L. Vrusias © 2006 likes object 11

AI – CS 364 Knowledge Representation Propositional Concepts • Modal auxiliaries, for instance can or must, map onto conceptual relations of possibility (PSBL) and obligation (OBLG): • The CG for "Tom can go" is: PSBL proposition person: "Tom" agent go • The CG for "Tom must go" is: OBLG 19 th September 2006 proposition person: "Tom" Bogdan L. Vrusias © 2006 12

AI – CS 364 Knowledge Representation Propositional Concepts • Verb tense and aspect, map to relation nodes like past (PAST) or PROGressive (defined in terms of DURations, SUCCessor or Point-in. TIMe). • The CG for "Tom went" is: PAST 19 th September 2006 proposition person: "Tom" Bogdan L. Vrusias © 2006 agent go 13

AI – CS 364 Knowledge Representation Nested Concepts • A context is represented by a concept with one or more conceptual graphs inside the referent field. • A context can have attached conceptual relations, and they also have their own type label. The conceptual graphs nested inside a context are the referent of that concept. • There are three types of nested concepts: graph, proposition, and situation: – When a conceptual graph is a referent of a concept of the type GRAPH, it is merely being mentioned; – When a conceptual graph is a referent of concept of type PROPOSITION or SITUATION, it is being used to state a proposition or to describe a situation respectively. 19 th September 2006 Bogdan L. Vrusias © 2006 14

AI – CS 364 Knowledge Representation Nested Concepts • E. g. : "Tom believes that Mary wants to marry a footballer" person: "Tom" EXPR believe PTNT proposition person: "Mary" EXPR want PTNT situation "Mary" AGNT marry PTNT Footballer : co-reference link 19 th September 2006 Bogdan L. Vrusias © 2006 15

AI – CS 364 Knowledge Representation Plural Concepts • • Plural nouns are represented by the plural referent {*} followed by an optional count @. For example the CG for "Birds singing in a sycamore tree" is: proposition sing • in Bird: {*} agent Sycamore Tree or for "Happy Birthday To You lasts 18 seconds" is: theme: "Happy Birthday To You" duration Interval: @18 sec • ("for all" or "every") – E. g. "All living fish are wet" Living. Fish: 19 th September 2006 attribute wet Bogdan L. Vrusias © 2006 16

AI – CS 364 Knowledge Representation CG and Logic • ¬ (Negation "not"): E. g. "The sun is not shining" ¬ [Situation: [Sun: #] <- (Agnt) <- [Shine] ] • (Conjunction "and"): E. g. "There exists a woman who is both beautiful and dangerous" [Proposition: [Woman: *x] -> (Attr) -> [Beautiful] [Woman: *x] -> (Attr) -> [Dangerous] ] • (Disjunction "or"): E. g. "John is either a fool or very clever" ¬ [Situation: [Person: John] -> (Attr) -> [Fool] ] ¬ [Situation: [Person: John]->(Attr)->[Clever]->(Meas)->[Degree: #very] ] ] 19 th September 2006 Bogdan L. Vrusias © 2006 17

AI – CS 364 Knowledge Representation CG Resources • http: //www. huminf. aau. dk/cg/index. html • http: //www. cs. uah. edu/~delugach/CG/ • http: //users. bestweb. net/~sowa/ 19 th September 2006 Bogdan L. Vrusias © 2006 18

AI – CS 364 Knowledge Representation Building CG Schemas • • • The basic structure for representing background knowledge for human-like inference is called the schema. Schema is a pattern derived from past experience that is used for interpreting, planning, and imagining other experiences. A schema for a bus that should not exceed 55 km/h and should be limited to carry about 50 passengers: bus: *X inst travel obj cont speed: 55 Km/h agent passenger: {*}@ 50 drive agent 19 th September 2006 rate driver Bogdan L. Vrusias © 2006 19

AI – CS 364 Knowledge Representation CG Schemas Example • Consider the type definition graph for BUY shown below: ENTITY OBJ GIVE AGNT OBJ PART RCPT TRANSACTION AGNT SRCE INST MONEY SELLER OBJ AGNT CUSTOMER PART GIVE RCPT Example from: http: //pages. cpsc. ucalgary. ca/~kremer/courses/CG/ 19 th September 2006 Bogdan L. Vrusias © 2006 20

AI – CS 364 Knowledge Representation CG Schemas Example • Consider the graph "Joe buying a necktie from Hal for $10": Person: Joe AGNT BUY SRCE Necktie INST Person: Hal 19 th September 2006 OBJ Money: @ $10 Bogdan L. Vrusias © 2006 21

AI – CS 364 Knowledge Representation CG Schemas Example • The type expansion of the graph based on the concept type BUY is shown below: NECTIE OBJ GIVE AGNT 19 th September 2006 OBJ PART RCPT TRANSACTION AGNT SRCE CUSTOMER: Joe SELLER: Hal Bogdan L. Vrusias © 2006 INST MONEY: @ $10 PART OBJ AGNT GIVE RCPT 22

AI – CS 364 Knowledge Representation Exercises • Say in your own words what the following CGs means: – – [Person]<-(Agnt)<-[Run] [Person: Peter]->(Poss)->[Car]->(Attr)->[Blue] [Rhino: Otto]->(Chrc)->[Colour: Orange] [Girl: Silde]<-(Agnt)<-[Ride]->(Thme)->[Bike]->(Chrc)->[Color: Yellow] 19 th September 2006 Bogdan L. Vrusias © 2006 23

AI – CS 364 Knowledge Representation Solutions • [Person]<-(Agnt)<-[Run] – A Person is the agent of an Act, which is Run. – Running has an agent which is a Person. – A Person is Running. • [Person: Peter]->(Poss)->[Car]->(Attr)->[Blue] – Peter has a possession which is a car. This car has an attribute, which is blue. – Blue is an attribute of a Car, which is a possession of a Person, who is Peter. – Peter's car is blue. 19 th September 2006 Bogdan L. Vrusias © 2006 24

AI – CS 364 Knowledge Representation Solutions • [Rhino: Otto]->(Chrc)->[Colour: Orange] – Otto the Rhino has a characteristic which is a Colour, Orange. – The Colour Orange is a characteristic of a Rhino, Otto. • [Girl: Silde]<-(Agnt)<-[Ride]->(Thme)->[Bike]->(Chrc)->[Color: Yellow] – A girl, Silde, is the agent of Ride, and theme of Ride is a Bike, and the Bike has a Characteristic which is a Colour which is Yellow. – A girl, Silde, is riding a yellow bike. – Silde is riding a yellow bike. 19 th September 2006 Bogdan L. Vrusias © 2006 25

AI – CS 364 Knowledge Representation Exercises • Please create the conceptual graph of the following sentences: – – – "A person is singing a song" "John is singing" "Bus number 9 is going to Copenhagen" "John was singing" "Romeo marries Juliet" 19 th September 2006 Bogdan L. Vrusias © 2006 26

AI – CS 364 Knowledge Representation Solutions • "A person is singing a song" [Person]<-(Agnt)<-[Sing]->(Thme)->[Song] • "John is singing" [Person: John]<-(Agnt)<-[Sing] • "Bus number 9 is going to Copenhagen" [Bus: #9]<-(Agnt)<-[Go]->(Dest)->[City: Copenhagen] • "John was singing" (Past)->[Situation: [Person: John]<-(Agnt)<-[Sing] ] 19 th September 2006 Bogdan L. Vrusias © 2006 27

(Benf)->[Person: Juliet]" src="https://present5.com/presentation/de5ce32ea63ff3e115c019fd54278e3b/image-28.jpg" alt="AI – CS 364 Knowledge Representation Solutions • "Romeo marries Juliet" [Person: Romeo]<-(Agnt)<-[Marry]->(Benf)->[Person: Juliet]" /> AI – CS 364 Knowledge Representation Solutions • "Romeo marries Juliet" [Person: Romeo]<-(Agnt)<-[Marry]->(Benf)->[Person: Juliet] [Lover: Romeo]<-(Agnt)<-[Marry]->(Benf)->[Lover: Juliet] [Man: Romeo]<-(Agnt)<-[Marry]->(Benf)->[Woman: Juliet] but not [Monkey: Romeo]<-(Agnt)<-[Marry]->(Benf)->[Gorilla: Juliet] 19 th September 2006 Bogdan L. Vrusias © 2006 28