CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTSsanti/teaching/2013/CS... · Declarative Programming...

CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTS

11/6/2013 Santiago Ontañón [email protected] https://www.cs.drexel.edu/~santi/teaching/2013/CS380/intro.html

Summary so far: • What is AI?

•  Rational Agents

• Problem solving: •  Systematic search

•  Uninformed search: DFS, BFS, ID •  Informed search: heuristics, Best-FS, A*

•  Local Search: Hill Climbing, Simulated Annealing •  Adversarial Search: Minimax, alpha-beta, Monte Carlo Tree Search

• Next: knowledge representation + reasoning

Knowledge • Knowledge base:

Knowledge • Knowledge base:

•  A set of sentences in a formal language

• Knowledge-based agent:

• Declarative programming

Inference engine

Knowledge base

Domain independent

Domain specific

Declarative Programming •  Tell an agent WHAT to do, but not HOW.

• Encode all the necessary knowledge, and let the agent infer how to achieve the goals.

•  For example, instead of programming quick sort, we would tell an agent: •  Here’s a set of numbers. •  Now I want them sorted, which means that for every adjacent

numbers, a, b, they must satisfy a <= b. •  You (the agent) figure out how !

Wumpus World PEAS description

Performance measuregold +1000, death -1000-1 per step, -10 for using the arrow

EnvironmentSquares adjacent to wumpus are smellySquares adjacent to pit are breezyGlitter iff gold is in the same squareShooting kills wumpus if you are facing itShooting uses up the only arrowGrabbing picks up gold if in same squareReleasing drops the gold in same square

Breeze Breeze

Breeze

BreezeBreeze

Stench

Stench

BreezePIT

PIT

PIT

1 2 3 4

1

2

3

4

START

Gold

Stench

Actuators Left turn, Right turn,Forward, Grab, Release, Shoot

Sensors Breeze, Glitter, Smell

Chapter 7 5

Wumpus world characterization

Observable??

Chapter 7 6


Observable?? No—only local perception

Deterministic??

Chapter 7 7



Deterministic?? Yes—outcomes exactly specified

Episodic??

Chapter 7 8




Episodic?? No—sequential at the level of actions

Static??

Chapter 7 9





Static?? Yes—Wumpus and Pits do not move

Discrete??

Chapter 7 10






Discrete?? Yes

Single-agent??

Chapter 7 11






Discrete?? Yes

Single-agent?? Yes—Wumpus is essentially a natural feature

Chapter 7 12

Exploring a wumpus world

A

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Chapter 7 13


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Chapter 7 14


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Chapter 7 15


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Chapter 7 16


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WChapter 7 17


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Chapter 7 18


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Chapter 7 19


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Chapter 7 20

Other tight spots

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P?

P?P?

P?

Breeze in (1,2) and (2,1)⇒ no safe actions

Assuming pits uniformly distributed,(2,2) has pit w/ prob 0.86, vs. 0.31

A

S

Smell in (1,1)⇒ cannot move

Can use a strategy of coercion:shoot straight aheadwumpus was there ⇒ dead ⇒ safewumpus wasn’t there ⇒ safe

Chapter 7 21

Logic in general

Logics are formal languages for representing informationsuch that conclusions can be drawn

Syntax defines the sentences in the language

Semantics define the “meaning” of sentences;i.e., define truth of a sentence in a world

E.g., the language of arithmetic

x + 2 ≥ y is a sentence; x2 + y > is not a sentence

x + 2 ≥ y is true iff the number x + 2 is no less than the number y

x + 2 ≥ y is true in a world where x = 7, y = 1x + 2 ≥ y is false in a world where x = 0, y = 6

Chapter 7 22

Entailment

Entailment means that one thing follows from another:

KB |= α

Knowledge base KB entails sentence αif and only if

α is true in all worlds where KB is true

E.g., the KB containing “the Giants won” and “the Reds won”entails “Either the Giants won or the Reds won”

E.g., x + y = 4 entails 4 = x + y

Entailment is a relationship between sentences (i.e., syntax)that is based on semantics

Note: brains process syntax (of some sort)

Chapter 7 23

Models

Logicians typically think in terms of models, which are formallystructured worlds with respect to which truth can be evaluated

We say m is a model of a sentence α if α is true in m

M(α) is the set of all models of α

Then KB |= α if and only if M(KB) ⊆ M(α)

E.g. KB = Giants won and Reds wonα = Giants won M( )

M(KB)

x

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x x

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x xxx

xx x

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x x xx

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Chapter 7 24

Entailment in the wumpus world

Situation after detecting nothing in [1,1],moving right, breeze in [2,1]

Consider possible models for ?sassuming only pits

AA

B

??

?

3 Boolean choices ⇒ 8 possible models

Chapter 7 25

Wumpus models

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT PIT

PIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

1

2

BreezePIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

1

2

Breeze

PIT PIT

1 2 3

1

2

Breeze

Chapter 7 26

Wumpus models

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT

1 2 3

1

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Breeze

PIT PIT

PIT

1 2 3

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2

Breeze

PIT

PIT

1 2 3

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BreezePIT

1 2 3

1

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Breeze

PIT

PIT

1 2 3

1

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Breeze

PIT PIT

1 2 3

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Breeze

KB

KB = wumpus-world rules + observations

Chapter 7 27

Wumpus models

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT

1 2 3

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Breeze

PIT PIT

PIT

1 2 3

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Breeze

PIT

PIT

1 2 3

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BreezePIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

1

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Breeze

PIT PIT

1 2 3

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Breeze

KB1


α1 = “[1,2] is safe”, KB |= α1, proved by model checking

Chapter 7 28

Wumpus models

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT PIT

PIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

1

2

BreezePIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

1

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Breeze

PIT PIT

1 2 3

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Breeze

KB


Chapter 7 29

Wumpus models

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT

1 2 3

1

2

Breeze

PIT PIT

PIT

1 2 3

1

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Breeze

PIT

PIT

1 2 3

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2

BreezePIT

1 2 3

1

2

Breeze

PIT

PIT

1 2 3

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Breeze

PIT PIT

1 2 3

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Breeze

KB2


α2 = “[2,2] is safe”, KB ̸|= α2

Chapter 7 30

CS 380: ARTIFICIAL INTELLIGENCE LOGICAL AGENTSsanti/teaching/2013/CS... · Declarative Programming...

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