Knowledge Representation

1. Knowledge Representation CPTR 314

2. The need of a Good Representation • The representation that is used to represent a problem is very important • The representation used can make the difference between an efficient algorithm and an algorithm that doesn’t work al all

3. Associationist Theories • Associationist theories define the meaning of an object in terms of a network of associations with other objects • For the associationist, when humans perceive and reason about an object, that perception is first mapped into a concept • This concept is part of our entire knowledge of the world and is connected through appropriate relationships to other concepts • These relationships form an understanding of the properties and behavior of objects such as snow • For example, through experience, we associate the concept snow with other concepts such as cold, white, snowman, slippery, and ice.

4. Semantic Nets • The semantic net is a commonly used representation in Artificial Intelligence and it is based on the associationist theories • A semantic net is a graph consisting of nodes that are connected by edges • The nodes represent objects, and the links between nodes represent relationships between those objects • The links are usually labeled to indicate the nature of the relationship

5. Psychological evidence • Collins and Quillan (1969) modeled human information storage and management using a semantic network • They found that there is evidence that there is an intrinsic a hierarchical representation of concepts

6. Semantic network developed by Collins and Quillian in their research on human information storage and response times (Harmon and King 1985)

7. Semantic Nets • In semantic nets the links are arrows, meaning that they have a direction • One limitation of semantic nets is the inability to represent negations

8. Semantic net representation of snow and ice

9. Semantic Nets • Note that in the previous semantic net we have represented some specific entities (Frosty) and some general as (Snowman) • We use object oriented concepts as instances, classes and inheritance to build semantic nets

10. Frames • Frame-based representation is a development of semantic nets and allows us to express the idea of inheritance • A Frame system consists of a set of frames, which are connected together by relations • Each frame has one or more slots which are assigned slot values

11. Frame Example

12. Part of a frame description of a hotel room. “Specialization” indicates a pointer to a superclass

13. Frame Relationships • Generalizations • “Is a” • Aggregations • One object being part of another object • Associations • Meaning in two directinons • Example: Fido “chases” Fang and Fang is being “chased” by Fido

14. Inheritance • We might extend our frame system with the following additional information • Dogs chase cats • Cats chase mice • We now do not need to state explicitly that Fido chases Fang or that Fang chases mice. • We could add the following Fact: • Mammals have four legs • This is not true for humans. But we can define a default value that it may be overridden.

15. Procedures • A procedure is a set of instructions associated with a frame that can be executed on request • Frames may have demon procedures • Run automatically whenever a particular value changes or when a particular event occurs

16. Search Spaces • A search space is a representation of the set of possible choices in a given problem, one or more of which are the solution to the problem • Because a search space consists of a set of states, connected by paths that represent actions, they are also known as state spaces • The arrows between states represent state transitions

17. State space of the 8-puzzle generated by “move blank” operations.

18. Semantic Tree • A semantic tree is semantic net with the restriction of being a tree instead of a graph • This means that it cannot contain cycles while semantic nets could

19. Example: Traveling Salesman • A salesman must visit each of a set of cities and then return home. The aim of the problem is to find the shortest path that lets the salesman visit each city. • This is an NP complete problem • If we fix the starting city there is (n-1)! Possibilities to find the shortest path

20. Traveling Salesman Example • We can write the tree and possible distances • We can search the tree using brute-force. • Not very productive for large n; it can take thousand of years to solve • We can search using a heuristics • Heuristics is a rule or piece of information that is used to make search more effective or more efficient • In this case we could use the nearest neighbor heuristics for an approximation

21. An instance of the traveling salesperson problem.

22. Search of the traveling salesperson problem. Each arc is marked with the total weight of all paths from the start node (A) to its endpoint.

23. An instance of the traveling salesperson problem with the nearest neighbor path in bold. Note that this path (A, E, D, B, C, A), at a cost of 550, is not the shortest path. The comparatively high cost of arc (C, A) defeated the heuristic.

24. Goal Trees • A goal tree (also called an and-or tree) is a form of semantic tree used to represent problems that can be broken down in this way • We say that the solution to the problem is the goal, and each individual step along the way is a sub-goal

25. And/or graph of the expression (q and r => p)

26. And/or graph of the expression (q or r => p)

27. And/or graph a grammar. Some of the nodes (np, art, etc.) have been written more than once to simplify drawing the graph.