1. Knowledge Representation
COMP3710 Artificial Intelligence
Computing Science
Thompson Rivers University

2. Knowledge Representation
Course Outline
Part I – Introduction to Artificial Intelligence
Part II – Classical Artificial Intelligence, and Searching
Knowledge Representation
Searching
Search Methodoloties
Advanced Search
Genetic Algorithms (relatively new study area)
Knowledge Represenation and Automated Reasoning
Propositinoal and Predicate Logic
Inference and Resolution for Problem Solving
Rules and Expert Systems
Part III – Machine Learning
Part IV – Some Advanced Topics
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Knowledge Representation

3. Knowledge Representation
Unit Outcomes …
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Knowledge Representation

4. Knowledge Representation
Reference
Chapter 3. Knowledge Representation
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Knowledge Representation

5. Knowledge Representation
Unit Outline
Introduction
The Need for a Good Representation
Example: Semantic Nets
Inheritance
Example: Frames
Object-Oriented Programming
Search Spaces
Semantic Trees
Search Trees
Combinatorial Explosion
Problem Reduction
Goal Trees
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Knowledge Representation

6. The Need for a Good Representation
If, for a given problem, we have a means of checking a proposed solution, then we can solve the problem by testing all possible answers. – Marvin Minsky
How to make a system solve a problem?
A computer needs a formal representation (model) of a problem in order to solve it.
A representation must be:
Efficient – not wasteful in time or resources.
Useful – allows the computer to solve the problem.
Meaningful – really relates to the problem.
Any good idea?
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Knowledge Representation

7. Example: Semantic Nets
A semantic net is a graph with nodes, connected by edges.
The nodes represent objects or properties.
The edges represent relationships between the objects.
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Knowledge Representation

8. Knowledge Representation
Inheritance
Inheritance is the process by which a subclass inherits properties from a superclass.
Example:
Mammals give birth to live young.
Fido is a mammal.
Therefore fido gives birth to live young.
In some cases, as in the example above, inherited values may need to be overridden. (Fido may be a mammal, but if he’s male then he probably won’t give birth).
Can we expand semantic nets to include inheritance?
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Knowledge Representation

9. Knowledge Representation
Example: Frames
A sort of extension of semantic nets with inheritance
A frame system consists of a number of frames, connected by edges, like a semantic net.
Class frames describe classes.
Instance frames describe instances.
Each frame has a number of slots.
Each slot can be assigned a slot value.
How to implement?
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10. Object-Oriented Programming
Object oriented programming languages such as Java, C++.
Use ideas such as:
inheritance
multiple inheritance
overriding default values
procedures and demons
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11. Knowledge Representation
Search Spaces
[Q] Do we always need to use such representations (models) in the previous slides?
Representation is really problem-specific.
Many problems in AI can be represented as search spaces.
A search space is a representation of the set of all possible choices (or states) in a given problem, one or more of which are the goal to the problem.
A search space is a set of all possible states, where
a state (oac node) is a set of values of all instances, and
states are connected by paths that represent actions.
[Q] Then state spaces are ???
Trees and graphs
[Q] Are search spaces always limited?
Not really
Finite state machine (FSM)?
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12. Knowledge Representation
Search Trees
Trees are easier to handle than graphs.
Used to represent search spaces.
Root node (i.e., state) has no predecessor. Which node in the above tree?
Leaf nodes have no successors. Which nodes in the above tree?
Goal nodes (of which there may be more than one)
[Q] What is the problem then, when you know what the goal is?
How to go to Vancouver from Kamloops?
How about the 8-puzzle game?
The missionaries and cannibals problem?
The paths to goal nodes from the root node may represent solutions to a problem.
[Q] What do we have to do when we do not know what the goal is?
In some other problems, goal nodes are the solutions. (In this case, goals are not known. But we know what goals are like.)
n-Queens problem
Graph coloring problem
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13. Knowledge Representation
Search Trees
H, I, J, K, M, N and O are leaf nodes.
A is the root node.
L is the goal node.
There is only one complete path to L from A:
A, C, F, L
[Q] How to find the path from the root to the goal node?
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14. Search Trees – Missionaries & Cannibals
Three missionaries and three cannibals want to cross a river using one canoe.
Canoe can hold up to two people.
Can never be more cannibals than missionaries on either side of the river.
Aim: To get all safely across the river without any missionaries being eaten.
[Q] How to solve?
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15. Search Trees – Missionaries & Cannibals
The first step in solving the problem is to choose a suitable representation, i.e., a state (a set of values of all instances) of the problem.
Environment and variables in the problem. We will need to trace the number of cannibals, missionaries and canoes on each side of the river.
Start state is therefore:
(# of cannibals, # of missionaries, # of boats) at the both sides
(3,3,1) at the starting side; (0,0,0) at the ending side
In fact, since the system is closed, we only need to represent one side of the river, as we can deduce the other side.
We will represent the finishing side of the river, and omit the starting side.
[Q] So the start state and the goal state are ???
(0,0,0), and (3,3,1)
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16. Search Trees – Missionaries & Cannibals
State – (# of cannibals, # of missionaries, # of boats) at the ending side
Now we have to choose suitable operators that can be applied:
[Q] What are the possible states from (0, 0, 0)?
Possible states – (0, 1, 1), (0, 2, 1), (1, 0, 1), (1, 1, 1), (2, 0, 1)
[Q] Which ones are safe (i.e., valid)?
(1, 0, 1), (1, 1, 1), (2, 0, 1)
[Q] Can we build up a search tree through safe (i.e., valid) states? What are the possible valid states from (1, 0, 1), (1, 1, 1) and (2, 0, 1)?
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17. Search Trees – Missionaries & Cannibals
Cycles should be removed.
[Q] What does this mean?
The nodes which are visited already should not be visited again.
Nodes represent states, edges represent operators.
There are two shortest paths that lead to the goal.
[Q] What is a solution here?
[Q] How to find a solution?
Construct a search tree, and then
Run BFS or DFS
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18. Search Trees – Missionaries & Cannibals
[Q] We will represent the starting side of the river, and omit the finishing side. Can you find a solution?
[Q] How about 4 missionaries and 4 cannibals?
Representation of the problem?
Search tree?
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19. Search Trees – Combinatorial Explosion
Problems that involve assigning values to a set of variables can grow exponentially with the number of variables.
[Q] E.g., what is the total number of possible cases with
n variables and m values for each variable?
[Q] How about the n×n tile puzzle?
9! (n = 3), 16! (n = 4), 25! (n = 5), …
This is the problem of combinatorial explosion.
Some such problems can be extremely hard to solve (NP-Complete, NP-Hard), i.e., it takes a very long time to solve.
[Q] How to solve then?
Construct a search tree, and then run DFS
[Q] What do we have to do then?
Selecting the correct representation can help to reduce this, as can using heuristics (see chapter 4).
No initial construction of a search tree; constructing tree while an algorithm is learning
[Q] Can you devise a proper representation (i.e., state) for the 3×3 puzzle game? [Q] Can you draw a search tree for the 2×2 puzzle game?
Environment?
Variables?
Click and try me!

20. Search Trees – Problem Reduction
Another idea is to break a problem down into smaller sub-problems (or sub-goals).
Nodes in the tree represent sub-problems.
The root node represents the overall problem.
Some nodes have child nodes, meaning all their children must be solved.
E.g. to solve the Towers of Hanoi problem with 4 disks, you can first solve the same problem with 3 disks.
The solution is thus to get from the first diagram on the left, to the second, and then to apply the solution recursively.
[Q] Can you devise a proper representation (i.e., state) for the problem with 3 disks?
[Q] Can you draw a search tree?
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21. Knowledge Representation
Review
How to represent a problem?
Search tree
States? Goal states?
What is a solution?
How to solve the combinatorial explosion problem, i.e., how to search the goal state quickly?
One possible idea – Problem reduction
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