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

AI – CS289AI – CS289Knowledge RepresentationKnowledge Representation

Conceptual GraphsConceptual Graphs

25th September 2006

Dr Bogdan L. [email protected]

25th September 2006 Bogdan L. Vrusias © 2006 2


ContentsContents• CG Arrow Rules

• Generalisation and Specialisation

• Nested Concepts

• CG Schemas

• Exercises



CG Arrow RulesCG 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.



CG Arrow RulesCG 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".



Generalisation and SpecialisationGeneralisation 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.



Generalisation and SpecialisationGeneralisation and Specialisation

dog

agent object boneeat

colour brown

location porchanimal: "Emma"

colour brown

Consider the following graphs:

g1:

g2:




location porchdog: "Emma"

colour brown

The restriction of g2 (based on g1) is:

g3:





colour brown

The join of g1 and g3 is:

g4:


colour





colour brown

The simplification of g4 is:

g5:




Propositional ConceptsPropositional 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.



Propositional ConceptsPropositional Concepts• Consider the example: "Tom believes that Jane likes

pizza"

experiencer believeperson: "Tom"

experiencer likesperson: "Jane"

object

objectpizza

proposition



Propositional ConceptsPropositional 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 goperson: "Tom"PSBL

proposition

agent goperson: "Tom"OBLG

proposition



Propositional ConceptsPropositional 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 goperson: "Tom"PAST

proposition



Nested ConceptsNested 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.



Nested ConceptsNested Concepts• E.g.: "Tom believes that Mary wants to marry a footballer"

person: "Tom" PTNTEXPR believe

proposition

person: "Mary" PTNTEXPR want

"Mary" PTNT FootballerAGNT marry

situation

: co-reference link



Plural ConceptsPlural 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:

• or for "Happy Birthday To You lasts 18 seconds" is:

("for all" or "every")– E.g. "All living fish are wet"

duration interval: @18 sectheme: "Happy Birthday To You"

agent Bird: {*}sing inproposition

Sycamore Tree

attribute wetLivingFish:



CG and LogicCG 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] ] ]



CG ResourcesCG Resources• http://www.huminf.aau.dk/cg/index.html

• http://www.cs.uah.edu/~delugach/CG/

• http://users.bestweb.net/~sowa/



Building CG SchemasBuilding 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:

inst rate speed: 55Km/htravelbus: *X

obj agent

drive

agent driver

passenger: {*}@50

cont



CG Schemas ExampleCG Schemas Example• Consider the type definition graph for BUY shown below:

Example from: http://pages.cpsc.ucalgary.ca/~kremer/courses/CG/

ENTITY TRANSACTION MONEY

GIVECUSTOMERGIVE

SELLER

OBJ

OBJ OBJ

INST

PART PARTAGNT SRCE

RCPT

RCPT

AGNT

AGNT



CG Schemas ExampleCG Schemas Example• Consider the graph "Joe buying a necktie from Hal for $10":

Person: Joe BUY Necktie

Money: @ $10Person: Hal

OBJ

INSTSRCE

AGNT



CG Schemas ExampleCG Schemas Example• The type expansion of the graph based on the concept type BUY is shown

below:

NECTIE TRANSACTION MONEY: @ $10

GIVECUSTOMER: JoeGIVE

SELLER: Hal

OBJ

OBJ OBJ

INST

PART PARTAGNT SRCE

RCPT

RCPT

AGNT

AGNT



ExercisesExercises• 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]



SolutionsSolutions• [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.



SolutionsSolutions• [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 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.



ExercisesExercises• 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"



SolutionsSolutions• "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] ]



SolutionsSolutions• "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]



ClosingClosing

• Questions???

• Remarks???

• Comments!!!

• Evaluation!

Documents

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