1 Lectures on Conceptual Graphs Artificial Intelligence (CS 364) Khurshid Ahmad, Professor of Artificial Intelligence

2 K NOWLEDGE R EPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK Conceptual graphs form a knowledge representation language based on the one hand in linguistics, psychology and philosophy, and data structures and data processing techniques on the other Mapping of perception onto an abstract representation and reasoning system A conceptual graph consists of concept nodes and relation nodes The concept nodes represent entities, attributes, states, and events The relation nodes show how the concepts are interconnected

3 K NOWLEDGE R EPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK CATSITMATSTATLOC Percepts Rules for assembling Percepts Words Grammar Rules (“The cat sat on the mat”)

4 K NOWLEDGE R EPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK CATSITMATSTATLOC Procedures Type Definitions Emotions Episodes

5 K NOWLEDGE R EPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK CATSITMATSTATLOC Percepts Rules for assembling Percepts Words Grammar Rules Procedures Type DefinitionsEmotions Episodes

6 K NOWLEDGE R EPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK CATSITMATSTATLOC Percepts Rules for assembling Percepts Words Grammar Rules Procedures Type DefinitionsEmotions Episodes Conceptual Graph Semantic Net

7 Alternate Notation [cat] (stat) [sit] (loc) [mat] Square brackets denote concept nodes. Parentheses denote relation nodes. Graphs are easier to read. Linear notation take less space.

8 KNOWLEDGE REPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK – C ONCEPTUAL G RAPHS : Definition John Sowa, formerly of IBM, is one of the key proponents of conceptual graphs. Sowa’s project is to create ‘a system of logic for representing natural language semantics’. Given that there are ‘still many unsolved problems in semantics, the system of conceptual graphs must continue to evolve to accommodate new research’

9 KNOWLEDGE REPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK - Definition A graph-theoretic definition Conceptual Graphs are finite, connected, bipartite graphs The graphs are finite because any graph (in 'human brain' or 'computer storage') can only have a finite number of concepts and conceptual relations. The graphs are connected because two parts that are not connected would simply be called two conceptual graphs. The graphs are bipartite because there are two different kinds of nodes: concepts and conceptual relations, and every arc links a node of one kind to a node of another kind

10 KNOWLEDGE REPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK - Definition ‘Perception is the process of building a working model that represents and interprets sensory input’. Sensory input, through the modalities of sight, speech, hearing, touch, taste and smell can be reduced to light falling on the retina, vibration of ear drums, and so on. Sensory input can be further reduced to neurotransmitters (chemical or electrical). Percepts are fragments of images that fit together like pieces of a jigsaw puzzle

11 KNOWLEDGE REPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK - Definition The reception of sensory input, ‘a mosaic of percepts’, is converted into concepts: Concrete concepts – that have associated percepts Abstract concepts – that do not have any associated percepts

12 KNOWLEDGE REPRESENTATION: 1970 S S TRUCTURING THE S EMANTIC N ETWORK - Definition For Sowa, a sensory icon, say S, is matched in an ideal brain to a single percept P or to a collection of percepts, P i, which are combined to form a complete image: an interconnected set of percepts. Percepts are combined in the brain and their interconnections stored as a conceptual graph.

13 KNOWLEDGE REPRESENTATION: Semantic Nets and Conceptual Graphs Consider the sentence: “A cat sitting on a mat” This sentence can be interpreted at different levels: 1.There are concrete concepts: cat, mat and sitting which enable us to experience the external word and motor mechanism to react to it. 2.The words of our natural language, arranged in accordance with the grammar of the language, is one way of articulating and disseminating the experience.

14 A cat sitting on a mat 3.Each of the concepts in the sentence belongs to, or can be related to, a category or class: Animal>Cat; Furniture>Mat; Posture>Sit; Living Being>Animal; Household Objects>Furniture; Act>Posture Thus Cat – Sit – Mat Animal – Posture – Furniture Living Being – Act – Household Object A hierarchy of concept type defines the relationship between concepts at different levels of generality KNOWLEDGE REPRESENTATION: Semantic Nets and Conceptual Graphs Increasing Abstraction

15 KNOWLEDGE REPRESENTATION: Semantic Nets and Conceptual Graphs A cat sitting on a mat 4.The concepts cat-sit-mat are related to each other in that: a)It is a common observation that some animate objects do sit on certain concrete objects b)Even if we had never seen a cat sitting on a mat, we may derive the conceptual graph on the basis of observation (a) c)The order of the concrete concepts is important in that were we to say that mat-sit-cat, it would be difficult to match this stated percept with a conceptual graph in the ideal brain. Formation rules determine how each type of concept may be linked to conceptual relations.

16 KNOWLEDGE REPRESENTATION: Semantic Nets and Conceptual Graphs A cat sitting on a mat 5.The above sentence relates to an EPISODE or to some CONTEXT to which it is relevant. 6.Each episode may have some deeper mental associations, like emotions. 7.When we ask the question: what is the cat doing?, the answer is that the cat is sitting and that its current location is the mat. The cat’s STATe, its current ACTivity, its LOCation may each be related to a procedure of some type.

17 KNOWLEDGE REPRESENTATION: Definition – Semantic Nets? The collection of all the relationships that concepts have to other concepts, to percepts, to procedures and to motor mechanisms is called the semantic network.

18 KNOWLEDGE REPRESENTATION: Semantic Nets and Conceptual Graphs Each conceptual graph asserts a SINGLE proposition A semantic network is much larger including as it does a defining node for each type of concept, sublinks between the defining concepts, and links to perceptual and motor mechanisms, links to words and so on.

19 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS The concepts c 1 ……c n are linked by conceptual relations to form the conceptual graph U If a conceptual relation has n-arcs, then it is said to be n-adic, and its arcs are labelled 1, 2, …..n

20 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS Consider the sentence: Mary gave John the boring book authored by Tom & Jerry ① ② ③ Consider phrase ① as a conceptual graph: Person: Mary agentgive Person: Johnrecipient

21 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS The conceptual graph for phrase ② : bookboring And for phrase ③, we have: person: Tom bookauthor person: Jerry

22 boring book KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS The conceptual graph for phrase ② has only one arc and thus refers to a 1-ary or unary relation

23 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS The conceptual graph for phrase ① has two connected graphs each containing 2-arcs: Person: Mary agentgive and Person: Johnrecipientgive Both the graphs have two arcs each and are referred to as expressing a 2-ary or binary relation between the two concepts

24 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS The conceptual graph for phrase ③ has 3-arcs and is referred to as expressing 3-ary or ternary relation book Person: Tom author Person: Jerry

25 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS A sample of the inventory of conceptual relations Concept Relation Entity:*xEntity*yaccompaniment (ACCM) attribute (ATTR) characteristic (CHRC) content (CONT) part (PART) possession (POSS) support (SUPP)

26 KNOWLEDGE REPRESENTATION: CONCEPTUAL RELATIONS A sample of the inventory of conceptual relations Concept Relation Event(Act)Attributemanner (MANR) Event(Act)Entityresult (RSLT) source (SOUR) Event(Act)Entity (Animate)agent (AGNT) recipient (RCPT) Event(Act)Entity (Place)destination (DEST) path (PATH) Entity (Substance) material (MATR) FunctionDataargument (ARG) State*xState*ycausation (CAUS)

27 KNOWLEDGE REPRESENTATION: CONCEPT NODES? Recall that in the discussion of Collins and Quillian’s semantic networks, we have found that these networks were logically inadequate. This situation was not resolved in some of the subsequent formulations of semantic networks. Specifically, it was difficult in a typical semantic network notation to distinguish between nodes describing classes and subclasses classes and members

28 KNOWLEDGE REPRESENTATION: CONCEPT NODES? In the sentence: Tom is a cat, a feline mammal Tom is-a cat is-a feline is-a mammal individual species subclass class The relation ‘is_a’ is used to describe relationships between concepts that are mildly different.

29 KNOWLEDGE REPRESENTATION: CONCEPT NODES A good representation should allow us to distinguish between Individuals and species Species and classes Classes and subclasses Individuals may have properties that may not influence their belonging to a subclass: Tom is a brown tabby Should not influence the observation that: A tabby cat is a kind of cat

30 KNOWLEDGE REPRESENTATION: CONCEPT NODES In CG theory, ‘every concept is a unique individual of a particular type’. Concept nodes are ‘labelled’ with descriptors or names like ‘dog’, ‘cat’, ‘gravity’, etc. The labels refer to the class or type of individual represented by the node. Each concept node is used to refer to an individual concept or a generic concept. In CG theory we have a relation called NAME

31 KNOWLEDGE REPRESENTATION: CONCEPT NODES – SPECIFIC MARKERS CG allows nodes to be labelled simultaneously with the name of the individual the node represents and its type. The two are separated by a colon (‘:’) Tom, a cat, is brown Has a CG of: Cat: TomColourbrown

32 KNOWLEDGE REPRESENTATION: CONCEPT NODES – SPECIFIC MARKERS I have a neighbour with a black cat whose name I don’t know. Each concept node in a CG may be used to represent specific but unnamed individuals by a unique prescribed number: Cat: #999Colourblack I subsequently found out my neighbour’s children call the cat by different names: ‘Sylvester’, ‘Sugar Pie’ and ‘Squidgy Bod’

33 KNOWLEDGE REPRESENTATION: CONCEPT NODES – SPECIFIC MARKERS The CG for the neighbour’s cat is therefore: Name Sylvester Cat: #999Name Sugar Pie Name Squidgy Bod

34 KNOWLEDGE REPRESENTATION: CONCEPT NODES – GENERAL MARKERS General markers can also be used to refer to an unspecified individual. The CG: Cat Colour Brown Refers to an ‘unspecified cat’. Notationally, unspecified individuals are shown by the existence of an asterisk (‘*’) Cat:* Colour Brown

35 KNOWLEDGE REPRESENTATION: CANONICAL GRAPHS A conceptual graph is a combination of concept nodes and relation nodes where every arc of every conceptual relation is linked to a concept. This could lead sometimes to sensible statements like 'a bunny sitting on a mat' and at time will lead to nonsense like 'colourless green ideas sleep furiously' Sowa distinguishes the nonsensical graphs from those 'that represent real or possible situations in the external world' by declaring the later as canonical Certain conceptual graphs are canonical. New graphs may become canonical or be canonised by perception, formation rules, or through 'insight'

36 KNOWLEDGE REPRESENTATION: CANONICAL GRAPHS Formation rules: New conceptual graphs may be derived from other canonical graphs 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 rules of specialisation: they involve specialisation by selectional constraints. They are not rules of inference-- rather templates which are manipulated in order to incorporate new knowledge.

37 KNOWLEDGE REPRESENTATION: CANONICAL GRAPHS Consider the sentence: A girl is eating a pie fast GIRLMANRFASTAGNTEAT Girl: Sue OBJPIEAGNTEAT

38 KNOWLEDGE REPRESENTATION: JOINING CONCEPTUAL GRAPHS Consider the sentence: A girl is eating a pie fast The above graph shows a join operation between graphs GIRL: Sue MANRFASTAGNTEAT OBJ PIE AGNT

39 KNOWLEDGE REPRESENTATION: SIMPLYFING CONCEPTUAL GRAPHS Consider the sentence: A girl is eating a pie fast GIRL: Sue MANRFASTAGNTEAT OBJ PIE

40 KNOWLEDGE REPRESENTATION: GENERALISATION AND SPECIALISATION GIRLMANRFASTAGNTEAT Person: Sue OBJPIEAGNTEAT GIRL: Sue MANRAGNTEAT OBJ PIE FAST personAGNTEAT

41 KNOWLEDGE REPRESENTATION: ABSTRACTION & DEFINITION Verbs like believe, know, and feel take complete sentences as their objects: Consider the following sentences: Tony likes Alastair Cherie knows that Tony likes Alastair TONYLIKESALASTAIR TONYLIKESALASTAIR CHERIE KNOWS PROPOSITION

42 KNOWLEDGE REPRESENTATION: SCHEMA A schema for a bus that should not exceed 80km/h and should be limited to carry about 50 passengers: Bus:*x INST TRAVEL RATE SPEED 80km/h OBJ CONT AGNT DRIVE Passenger:{*} AGNT QTY DRIVER NUMBER  50

43 Exercise “A person is between a rock and a hard place”

44 Exercise Person Betw Rock PlaceAttr Hard

45 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. Consider the following statements: Mary is marrying a footballer Mary wants to marry a footballer Tom believes that Mary wants to marry a footballer ** Based on Sowa, John (1991). ‘Towards the expressive power of natural language’. In (Ed). John Sowa. Principles of Semantic Networks: Explorations in the Representation of Knowledge. San Mateo: Morgan Kaufmann Pub. Inc., pp

46 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS The statement ‘ Mary is marrying a footballer ’ has the following CG representation. PERSON: Mary PTNTFootballerAGNTMARRY The above CG can be treated as proposition and can act as a referent to another concept GRAPH, a nested graph: PERSON: Mary PTNTFootballerAGNTMARRY GRAPH:

47 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS The type label graph allows us to treat the nested graph as a literal, its meaning is irrelevant. The type GRAPH allows us to make further assertions about it. One assertion about a graph may suggest that the graph states a PROPOSITION. Another assertion could suggest that the graph, sometimes represented by a proposition, describes a SITUATION. PERSON: Mary PTNT FootballerAGNTMARRY GRAPH: PROPOSITION STMT

48 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS Another assertion could suggest that the graph, sometimes represented by a proposition, describes a SITUATION. PERSON: Mary PTNT FootballerAGNTMARRY GRAPH: PROPOSITION STMT SITUTATION STMT

49 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS 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.

50 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS The notion of nested propositions and situations becomes relevant when we describe the contexts of certain classes of verbs. Consider the sentence Tom believes that Mary wants to marry a footballer In the above statement, the concepts ‘BELIEVE’ and ‘WANT’ refer to states. These states have EXPeRiencers: Tom has the ‘experience’ of believing and Mary that of wanting. EXPR denotes the conceptual relationship of experiencing !

51 KNOWLEDGE REPRESENTATION: NESTED CONCEPTS The CG representation of the sentence Tom believes that Mary wants to marry a footballer is : PERSON: Tom PTNTEXPRBELIEVE PROPOSITION: PERSON: Mary PTNTEXPRWANT T PTNT FootballerAGNTMARRY SITUATION: The dashed line is a co-reference link.

52 KNOWLEDGE REPRESENTATION: MAPPING LANGUAGE TO CONCEPTUAL GRAPHS The basic principle in conceptual graphs is that the content words, words denoting entities, states, attributes, and events for example, map to concept nodes and function words, words that may inter- relate the concepts map to relation nodes. Content words, or lexical words, include nouns, verbs, adjectives and adverbs. Function words, or grammatical words, include prepositions and conjunctions, and certain classes of verbs.

53 KNOWLEDGE REPRESENTATION: MAPPING LANGUAGE TO CONCEPTUAL GRAPHS: Concept Nodes ‘Ordinary’ or common nouns, verbs, adjectives and adverbs map to type labels in concept nodes. Note that the concept nodes are shown by square brackets ‘[‘ & ‘]’ and relation nodes by parantheses ‘(‘ & ‘): this is Sowa’s linear notation ‘lady’  [LADY]; (to) ‘dance’  [Dance]; ‘happy’  [HAPPY] Proper Nouns map to the referent field of a concept whose type field specifies the type: Squidgy  [CAT: Squidgy]; 10 Downing Street  [BUILDING: 10 Downing Street] Determiners: The symbol with optional qualifiers is used in the referent fields for contextually defined references: ‘the cat’  [CAT: #]; ‘this’  [ Τ: #this] Plural nouns are represented by the plural referent {*} followed by an optional count: ‘eleven footballers’  [FOOTBALLER: 11}

54 KNOWLEDGE REPRESENTATION: MAPPING LANGUAGE TO CONCEPTUAL GRAPHS: Relation Nodes Modal auxiliaries, for instance can or must, map onto conceptual relations of POSSIBILITY (PSBL) and OBLIGATION (OBLG): The CG for ‘Tom can go’ is OBLG PERSON: Tom AGNTGO PROPOSITION The CG for ‘Tom must go’ is PSBL PERSON: Tom AGNTGO PROPOSITION

55 KNOWLEDGE REPRESENTATION: MAPPING LANGUAGE TO CONCEPTUAL GRAPHS: Relation Nodes Verb tense and aspect map to relation nodes like PAST or PROGressive (defined in terms of DURations, SUCCessor or Point-in-TIMe). The CG for ‘Tom went’ is: PSBL PERSON: Tom AGNTGO PROPOSITION The CG for ‘Tom could not go’ is PAST PERSON: Tom AGNTGO SITUATION PAST

56 KNOWLEDGE REPRESENTATION: Application of CG’s SIMULATION: Consider a CLIPS-template for a traffic light system (deftemplate trafficLight (slot name(type SYMBOL)) (slot currentColour(allowed-values red green)) (slot redTime(type FLOAT)) (slot greenTime(type FLOAT)) (slot whenChanged(type FLOAT)) (slot autoSwitch(allowed-valued on off))) The template can be instantiated by an assert statement which inserts values in slots. (assert (trafficLight (nameBlinky) (currentColourgreen) (redTime60) (greenTime60) (whenChanged 0) (autoSwitchon)))

57 KNOWLEDGE REPRESENTATION: Application of CG’s SIMULATION: The following is a procedural program for the traffic light system. Loop while autoSwitch; set currentColour to red; waitredTime; setcurrentColour to green; waitgreenTime; end loop; As a knowledge representation scheme this program does not explain why the system changes colour; the program does not keep a record of its colour changes and so on.

58 KNOWLEDGE REPRESENTATION: Application of CG’s SIMULATION: The following is a procedural representation for the traffic light system - a forward chaining production rule Ifthere is a trafficLight x, the currentColour of x is red, the redTime of x is r, the whenChanged of x is t, the autoSwitch is on, the currentTime is now, now  t + r, Thenmodify currentColour of x to green modify whenChanged of x to now The production rule is not easy to read and will not be able to represent processes where there is no natural time sequence.

59 KNOWLEDGE REPRESENTATION: Application of CG’s: A CG for a traffic light system If: TrafficLight: *x TurnsRedRedTimeAutoSwitch Time: *tDuration: *rState: on Then: ?t ?xTurnsGreen TimeSumTimes ?r