Artificial Intelligence

2. PROBLEM SOLVING

USING SEARCH AND

KNOWLEDGE

REPRESENTATION

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Search techniques

SSR(state space representations) concerns machine recognizable

representations, and search techniques concerns how to reach goal

state.

SSR Rules DT ANN

Search FC/BC Tree Traversal

Propagation

How reasoning

What knowledge

(classical AI)

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Search techniques

Search techniques:

◦ A systemic manner to find a sequence of operators that transforms from

initial state to goal state.

◦ breadth-first search (BFS), depth-first search (DFS), Branch&Bound(B&B)

◦ Hill-climbing search (HCS), best-first search (BestFS), A* search

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Search techniques

Problem with search:

◦ Combinatorial explosion

Branching factor (b): number of operators available at a state.

Depth (d): distance between initial and desired state (may be very

high).

size of search space = bd (in 10 step 8-puzzle ~ 210 ~ 410).

◦ Example: In 8-puzzle, b is 2 – 4 (Chess?)

Two approaches to solve combinatorial explosion.

◦ Goal decomposition

bd ⇒ n*bd/n

◦ Heuristic search

b´d where b´<< b

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Heuristic search

Heuristics

◦ Useful information or rule of thumbs that guide search through a problem

space

◦ May not be totally correct, but in general helpful to reach goal.

◦ Example:

Never apply an operator that leads to a state that has already been visited.

In navigator, prefer the way to reduce linear distance most to destination.

In 8-puzzle, prefer to move a tile into its desired position (Number of tiles in

position).

Heuristic search

◦ Search techniques using heuristic knowledge.

◦ Examples:

hill-climbing search (HC), best-first search (BestFS), A* search(A*)

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Search techniques

No extra knowledge

◦ BFS: Breadth First Search

◦ DFS: Depth First Search

Accumulated cost (g)

◦ B&B: Branch and Bound

Heuristic estimates (h')

◦ BestFS: Best First Search

◦ Simple HCS: Simple Hill Climbing Search

◦ Steepest Ascent Hill Climbing Search

Combined evaluation (g + h'):

◦ A*: bestFS using g+h’

Which one will be best?

◦ Answer: under what conditions! 6

A(10)

B(5) C(7)

D(20) E(4)

G(0)

F(0)

4 8

3 5

4

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Problem

For the following search space, find exploration

sequences for various search techniques - bfs, dfs,

b&b, bestfs, simple HCS, Steepest-ascent HCS, A*,

etc.

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Knowledge Representation

Knowledge

In real world, objects, concepts and relations exist.

→ if we know these, we have knowledge

◦ Ex. A particular person (me), a particular room (this room), number two

◦ Ex. The relationship of "greater than", Three is greater than two (a fact)

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<Example of a semantic network>

From Knowledge

To Knowledge Representations

Traditional knowledge representations

(to describe objects, concepts and relations)

◦ Natural language Hong Kil Dong, 7-327, two, greater than, Three is greater than

two. Hong Kil Dong is brave.

Ambiguity problem, hard to make machine recognizable.

◦ Mathematics: 3. 2, 4, >, 5.3 > 2 => can't handle all

◦ Logic: Hong_Kil_Dong, 7_329, two, greater( , ), greater(three, two)

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From Knowledge

To Knowledge Representations

Traditional knowledge representations

(to describe objects, concepts and relations)

◦ Pictures, drawings, symbols, etc.

Allocation of Mental Space

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From Knowledge

To Knowledge Representations

Computational representation

◦ Declarative representations (what):

file or database,

easy to represent objects, concepts, and relations (easy to add,

delete, modify data)

Relational DB

◦ Procedural representations (how):

usual program, sequence of actions,

hard to construct procedures (hard to program)

C++, Java, VB, PHP, JavaScript, etc.

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From Knowledge

To Knowledge Representations

Symbolic computational representations languages

◦ Maps objects, concepts, relations into symbols.

◦ All representation methods need representations and reasoning.

◦ Representation:

symbol represents objects, concepts, their properties, relationships.

◦ Reasoning:

representations must facilitate particular types of reasoning (called

symbolic computations).

◦ Examples:

logic(first order predicate logic), decision trees, semantic network, script,

frame, etc. (But, not ANN)

◦ Use AI languages for implementation

Lisp, Prolog, etc.

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Symbolic Computational Representation

In Lisp

(setq *rules* '(

(if (animal ?x) then (add (mortal ?x)))

(if (human ?x) then (add (animal ?x)))

)

)

(setq *facts* ‘((human TOM)))

(infer *facts* *rules*)

In Prolog

mortal(X) :- animal(X).

animal(X) :- human(X).

human(tom).

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Real world

language

math

logic

Symbolic comp.

Declarative : file & db Procedural : programs

Knowledge : represents objects concepts, relations using symbols Reasoning : add, access, del, modify knowledge Ex) Logic, SN, Frame, Script etc.

Comp

From Knowledge

To Knowledge Representations

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Knowledge representations:

◦ Decision trees.

Reasoning:

◦ following trees from the root until leaf.

Learning:

◦ Constructing decision trees.

KR, Reasoning & Learning in

Decision Trees

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KR, Reasoning & Learning in

Artificial Neural Network Knowledge representations:

◦ Neural network

Reasoning:

◦ Provide inputs then observe output layer

Learning:

◦ Construct and change networks (network structure and weights

on connections)

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KR, Reasoning & Learning in

Case Based Reasoning

Knowledge representations: Case-base

Reasoning: Find the most similar source problem and

solution, then transform the solution to the target

problem

Learning: remembering new cases.

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Analogy and CBR

CBR (Russel): intra-domain access,

less transformation,

Analogy (Gentner): inter-domain access

active transformation,

Derivational Analogy (Carbonnel):

how to store/map derivation

rela

tional

sim

ilarities

attribute similarities

literally similar

CBR analogy

similar appearance

target prob

sol

source prob

sol

access

transform

CBR

Analogy

sol

target prob

source prob

sol

access

mapping

deriva

tion

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Building a Knowledge Base?

Knowledge acquisition bottleneck:

◦ knowledge acquisition is known to be the bottleneck to building

knowledge base.

Machine learning:

◦ Solves knowledge acquisition bottleneck.

Business Rule Engine:

◦ Avoids knowledge acquisition bottleneck by separating

declarative codes (knowledge) from procedural codes

(programs).

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Summary

Search and Problem Solving

◦ Problem solving using search

◦ Heuristic search

Knowledge Representation

◦ Knowledge about world

◦ Traditional representation

◦ Computational representation

◦ Symbolic computational representation

Various knowledge representation for AI

◦ If/then Rules, DT, ANN, CBR

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