FUNDAMENTALS OF ARTIFICIAL INTELLIGENCE KNOWLEDGE REPRESENTATION AND NETWORKED SCHEMES

Transcription

1 Riga Technical University Faculty of Computer Science and Information Technology Department of Systems Theory and Design FUNDAMENTALS OF ARTIFICIAL INTELLIGENCE Lecture 7 KNOWLEDGE REPRESENTATION AND NETWORKED SCHEMES Dr.habil.sc.ing., professor Janis Grundspenkis, Dr.sc.ing., lecturer Alla Anohina-Naumeca Department of Systems Theory and Design Faculty of Computer Science and Information Technology Riga Technical University {janis.grundspenkis, alla.anohina-naumeca}@rtu.lv Address: Meza street 1/4- {550, 545}, Riga, Latvia, LV-1048 Phone: (+371) 67089{581, 595}

2 Knowledge representation Knowledge representation is the method used to encode knowledge in an intelligent system s knowledge base. The object of knowledge representation is to express knowledge in computer-tractable form, such that it can be used to help intelligent system perform well. 2/44

3 Knowledge base A knowledge base is an integral part of any knowledge-based intelligent system. It maps objects and relationships of the real world to computational objects and relationships. Knowledge base Object 1 Object 2 Object 3 Relation 1 Relation 2 Object 1 Relation 1 Relation 2 Object 2 Domain Object 3 3/44

4 But what is knowledge? Knowledge is an abstract term that attempts to capture an individual s understanding of a given subject. In the world of intelligent systems the domain-specific knowledge is captured. Domain is a well-focused subject area. Cognitive psychologists have formed a number of theories to explain how humans solve problems. This work uncovered the types of knowledge humans commonly use, how they mentally organize this knowledge, and how they use it efficiently to solve a problem. 4/44

5 Types of knowledge (1) Declarative knowledge Concepts Facts Objects Describes what is known about a problem. This includes simple statements that are asserted to be either true or false. This also includes a list of statements that more fully describes some object or concept (object-attributevalue triplet). 5/44

6 Types of knowledge (2) Procedural knowledge Rules Strategies Agendas Procedures Describes how a problem is solved. This type of knowledge provides direction on how to do something. 6/44

7 Types of knowledge (3) Heuristic Knowledge Rules of Thumb Describes a rule-of-thumb that guides the reasoning process. Heuristic knowledge is often called shallow knowledge. It is empirical and represents the knowledge compiled by an expert through the experience of solving past problems. 7/44

8 Types of knowledge (4) Meta- Knowledge Knowledge about the other types of knowledge and how to use them Describes knowledge about knowledge. This type of knowledge is used to pick other knowledge that is best suited for solving a problem. Experts use this type of knowledge to enhance the efficiency of problem solving by directing their reasoning in the most promising area. 8/44

9 Types of knowledge (5) Structural Knowledge Rule sets Concept relationships Concept to object relationships Describes knowledge structures. This type of knowledge describes an expert s overall mental model of the problem. The expert s mental model of concepts, subconcepts, and objects is typical of this type of knowledge. 9/44

10 Knowledge representation (1) In general, a representation is a set of conventions about how to describe a class of things. A description makes use of the conventions of a representation to describe some particular thing. The function of any representation scheme is to capture essential features of a problem domain and make that information available to a problem solving procedure. 10/44

11 Knowledge representation (2) A representation consists of four fundamental parts: A lexical part that determines which symbols are allowed in the representation s vocabulary. A structural part that describes constraints on how the symbols can be arranged. A procedural part that specifies access procedures that enable to create descriptions, to modify them, and to answer questions using them. A semantic part that establishes a way of associating meaning with the description. 11/44

12 Knowledge representation schemes (1) There are 4 schemes of knowledge representation: Logical schemes Predicate calculus Procedural schemes IF..THEN.. rules Propositional calculus Networked schemes Semantic nets Structured schemes Scripts Conceptual graphs Frames 12/44

13 Knowledge representation schemes (2) Logical schemes represent knowledge, using mathematical or orthographic symbols, inference rules and are based on precisely defined syntax and semantics. In procedural schemes knowledge is represented as a set of instructions for problem-solving. That allows to modify a knowledge base easily and to separate a knowledge base from an inference mechanism. Networked schemes use a graph to represent knowledge. Nodes of a graph display objects or concepts in a domain, but arcs define relationships between objects, their attributes and values of attributes. Structured schemes extend networked representation by displaying each node in a graph as a complex data structure. 13/44

14 Semantic nets Author: Quillian, 1967 Idea: Concepts are a part of knowledge about world. People perceive concepts and reason with them. Concepts are related with relationships between them. Relationships between concepts form understanding of people. 14/44

15 Definition of semantic nets Semantic network is a knowledge representation schema that captures knowledge as a graph. The nodes denote objects or concepts, their properties and corresponding values. The arcs denote relationships between the nodes. Both nodes and arcs are generally labelled (arcs have weights). Symbols of semantic nets: - A concept - A relationship 15/44

16 Nodes of semantic nets Nodes of semantic nets can represent: Concepts Objects Events Features Time etc. 16/44

17 Relationships (1) Several kinds of relationships are used in semantic nets: 1. Class - Superclass or IS-a relationship Car Is- a Vehicle Class Superclass 2. Instance-class or Is an instance of relationship John s car Is an instance of Car Instance Class 17/44

18 Relationships (2) 3. Part-Whole or Part of relationship Door Part of Car Part Whole 4. Object-Attribute or Has relationship John s car Has Color Objects Attribute 18/44

19 Relationships (3) 5. Attribute-Value or Value relationship Color Value Red Attribute Value 6. Logical relationships (and, or, not) 7. Linguistic relationships (examples: likes, owns, travels ) 19/44

20 Inheritance (1) Inheritance is possible in semantic nets. Inheritance is a process by which the local information of a superclass node is assumed by a class node, a subclass node, and an instance node. Example: All vehicle have a brand name and a model. A car is a class of a superclass Vehicle. So Car inherits all features of Vehicle, that is, Brand and Model Vehicle has has Brand name Model Is a Car 20/44

21 Example of semantic nets John s car Is an instance of Has Has Car Is a Vehicle Brand name Reg.No. Value LA 657 Value BMW Has Model owner Has Value John Age 22 Value 850 works Bank Has Value Lateko 21/44

22 Conceptual graphs Author: Sowa, 1984 A conceptual graph is a finite, connected, bipartite graph. Two types of nodes are used in conceptual graphs: - A concept - A conceptual relationship 22/44

23 Arcs of conceptual graphs (1) In conceptual graphs the following arcs are allowed: Between a concept and a conceptual relationship Between a conceptual relationship and a concept 23/44

24 Arcs of conceptual graphs (2) The following arcs are not allowed in conceptual graphs: Between a concept and a concept Between a conceptual relationship and a conceptual relationship 24/44

25 Conceptual relationships (1) Every conceptual relation r has a relation type t and a nonnegative integer n called its valence. The number of arcs that belong to r is equal to its valence n. A conceptual relation of valence n is said to be n-adic, and its arcs are numbered from 1 to n. For every n-adic conceptual relation r, there is a sequence of n concept types t 1,...,t n, called the signature of r. A 0-adic conceptual relation has no arcs, and its signature is empty. All conceptual relations of the same relation type t have the same valence n and the same signature s. The term monadic is synonymous with 1-adic, dyadic with 2- adic, and triadic with 3-adic. 25/44

26 Conceptual relationships (2) 1-adic relation Must be one outgoing arc from a conceptual relationship 2-adic relation Must be one outgoing and one ingoing arc 3-adic relation Must be two ingoing arcs and one outgoing arc 26/44

27 Concepts (1) Concepts have the following form: Concept = Type + Referent, where Type is a type of a concept, cannot be empty; Referent = Quantifier + Designator, can be empty Type: Referent Type Teacher: Mary Referent 27/44

28 Concepts (2) Forms of cocnepts: 1. A node containing only a type of a concept Type Dog There is a dog, but it is not specified which one dog 2. Type + individual marker. s of persons, places or organizations can be displayed by an individual marker. Type Dog: Reksi Individual marker 28/44

29 Concepts (3) 3. Specific but unnamed individual. Identity of a object can be acquired from context performing inference Dog: #134 Cup: # 4. Several objects: - By listing them Guests: {John, Mary, Michael} agent Sing object Song - Using {*} Birds: {*} Several birds 29/44

30 Concepts (4) 5. Precise number of Person Moves on 6. Units of measurements sec 7. All by using or Fish: attribute wet All fish are wet 30/44

31 Concepts (5) 8. A conceptual graph can include a concept which is a conceptual graph by itself Example: Person: Tom experiencer believes proposition object Person: Jane agent likes pizza object 31/44

32 Concepts (6) 9. Different combinations Number: 18 There is a number 18 There are eighteen numbers 18 Number: 18 There are eighteen numbers and all of them are equal with 18 There are 5 numbers and all are equal with 18 32/44

33 Operations of conceptual graphs (1) Theory of conceptual graphs defines 4 operations: Copying Restricting Joining Simplifying Copying allows acquiring of a new conceptual graph G1 which is identical with the already existent conceptual graph G. 33/44

34 Operations of conceptual graphs (2) Restricting allows replacing of a concept node by its specialization. Two cases are possible: Type can be replaced by an individual marker Type can be replaced by its subtype Joining allows joining of two conceptual graphs if they have an identical concept node. Simplifying allows removing of one of two identical nodes of a conceptual relation together with all its arcs. 34/44

35 Operations of conceptual graphs (3) In order to apply the mentioned operations a type hierarchy must be defined: if s and t are types of concepts and t s, then t is subtype of s. Examples: Manager Employee Person Dog Animal John Man Person 35/44

36 Operations of conceptual graphs (4) Example: For example, we have two conceptual graphs G1 and G2 and a type hierarchy Dog Animal G1 Is a Animal Meat-eater color brown G2 location Dog: Reksi porch color brown 36/44

37 Operations of conceptual graphs (5) Example: Restricting operation can be applied to the graph G1 by replacing type Animal with its subtype Dog: Reksi. A new graph G3 is acquired as a result. G3 Is a Meat-eater Dog: Reksi color brown 37/44

38 Operations of conceptual graphs (6) Example: Now we can join graphs G2 un G3, because they have an identical concept node Dog:Reksi. A new graph G4 is acquired. Is a Meat-eater G4 location porch Dog:Reksi color brown color brown 38/44

39 Operations of conceptual graphs (7) Example: By simplifying the graph G4 a new graph G5 is acquired. Is a Meat-eater G5 location porch Dog:Reksi color brown 39/44

40 Inheritance in conceptual graphs By using restriction and joining operations of conceptual graphs it is possible to support inheritance. When a type is replaced by an individual marker an instance inherits features from a type. When a type is replaced by a subtype then the subtype inherits features from the type. Example: The type hierarchy Chimpanzee Primate is defined Type Primate Part of hand replaces Inheritance made by a subtype Subtype Chimpanzee Part of hand replaces Inheritance made by an instance An individual marker Chimpanzee: bonzo Part of hand 40/44

41 Logic and conceptual graphs (1) In conceptual graphs it is possible to represent logical operations AND, OR and NOT. 1. Negation is implemented using a propositional node and a unary conceptual relation NOT Example: A conceptual graph displaying a sentence The sun is not shining NOT proposition Shine agent Sun 41/44

42 Logic and conceptual graphs (2) 2. Conjunction is displayed by placing both conceptual graphs in the common propositional node. Example: A conceptual graph displaying a sentence The study course is interesting and difficult proposition Study course attribute Interesting Study course attribute Difficult 42/44

43 Logic and conceptual graphs (3) Disjunction is represented by negation and conjunction: 1. A graph G1 must be placed an a propositional node and its negation must be made 2. A graph G2 must be placed an a propositional node and its negation must be made 3. Both negations must be placed in a propositional node and its negation must be made proposition Example: proposition Person: John attribute silly Not proposition Person: John attribute smart Not Not 43/44

44 Example G1 Student: # John G2 Language: C# language mean Program agent Student: # G3 Company: # EuroSoft G4 Company: # agent Develop object Applications mean Language: C# language G5 Company: # place Work agent Student: # 44/44