AI – CS289 Knowledge Representation Conceptual Graphs 25 th September 2006 Dr Bogdan L. Vrusias

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Contents CG Arrow Rules Generalisation and Specialisation Nested Concepts CG Schemas Exercises

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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".

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Generalisation and Specialisation dog agentobject bone eat colour brown location porch animal: "Emma" colour brown Consider the following graphs: g1: g2:

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Generalisation and Specialisation location porch dog: "Emma" colour brown The restriction of g2 (based on g1) is: g3:

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Generalisation and Specialisation location porch dog: "Emma" colour brown The join of g1 and g3 is: g4: agentobject bone eat colour

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Generalisation and Specialisation location porch dog: "Emma" colour brown The simplification of g4 is: g5: agentobject bone eat

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Propositional Concepts Consider the example: "Tom believes that Jane likes pizza" experiencer believe person: "Tom" experiencer likes person: "Jane" object pizza proposition

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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: The CG for "Tom must go" is: agent go person: "Tom" PSBL proposition agent go person: "Tom" OBLG proposition

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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: agent go person: "Tom" PAST proposition

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Nested Concepts E.g.: "Tom believes that Mary wants to marry a footballer" person: "Tom" PTNTEXPRbelieve proposition person: "Mary" PTNTEXPRwant "Mary" PTNT FootballerAGNTmarry situation : co-reference link

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Plural Concepts Plural nouns are represented by the plural referent {*} followed by an optional For example the CG for "Birds singing in a sycamore tree" is: or for "Happy Birthday To You lasts 18 seconds" is:  ("for all" or "every") –E.g. "All living fish are wet" duration sec theme: "Happy Birthday To You" agent Bird: {*} sing in proposition Sycamore Tree attribute wet LivingFish: 

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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: ¬ [Situation: [Person: John] -> (Attr) -> [Fool] ] ¬ [Situation: [Person: John]->(Attr)->[Clever]->(Meas)->[Degree: #very] ] ]

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © CG Resources

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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 55km/h and should be limited to carry about 50 passengers: instrate speed:  55Km/h travelbus: *X objagent drive agent driver passenger:  50 cont

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © CG Schemas Example Consider the type definition graph for BUY shown below: Example from: ENTITYTRANSACTION MONEY GIVECUSTOMERGIVE SELLER OBJ INST PART AGNTSRCE RCPT AGNT

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © CG Schemas Example Consider the graph "Joe buying a necktie from Hal for $10": Person: JoeBUY Necktie $10Person: Hal OBJ INSTSRCE AGNT

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © CG Schemas Example The type expansion of the graph based on the concept type BUY is shown below: NECTIETRANSACTION $10 GIVECUSTOMER: JoeGIVE SELLER: Hal OBJ INST PART AGNTSRCE RCPT AGNT

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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] (Thme)->[Bike]->(Chrc)->[Color: Yellow]

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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] (Thme)->[Bike]->(Chrc)->[Color: Yellow] –A girl, Silde, is the agent of Ride, and the 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.

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © 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"

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Solutions "A person is singing a song" [Person] (Thme)->[Song] "John is singing" [Person: John]<-(Agnt)<-[Sing] "Bus number 9 is going to Copenhagen" [Bus: #9] (Dest)->[City: Copenhagen] "John was singing" (Past)->[Situation: [Person: John]<-(Agnt)<-[Sing] ]

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Solutions "Romeo marries Juliet" [Person: Romeo] (Benf)->[Person: Juliet] [Lover: Romeo] (Benf)->[Lover: Juliet] [Man: Romeo] (Benf)->[Woman: Juliet] but not [Monkey: Romeo] (Benf)->[Gorilla: Juliet]

AI – CS289 Knowledge Representation 25 th September 2006Bogdan L. Vrusias © Closing Questions??? Remarks??? Comments!!! Evaluation!