Chapter 6: Applying the PSSH

Chapter 6:Applying the PSSH

Cognitive Science José Luis Bermúdez / Cambridge University Press 2010

Overview

• Explain why ID3 and SHAKEY both count as illustrations of the heuristic search hypothesis

• Introduce frame problem

• Introduce background to the language of thought hypothesis (as an application of the PSSH)


ID3 and PSSH

• ID3 transforms one highly complex symbol structure (database) into another (a decision tree)

• The decision tree itself works by transforming symbol structures according to rules

• Rules are the IF. . . THEN . . . rules built into the decision tree


Heuristic search

• Problems are solved by generating and modifying symbol structures until a solution structure is reached

• Problem-spaces are generally too large to be searched exhaustively (brute force algorithms)

• Search must be selective heuristic search rules


ID3 as heuristic search

• ID3 is a tool for navigating through the search space of decision trees

• The algorithm that it uses sorts through possible decision trees using measures of information gain and entropy reduction


Basic concepts

Entropy – level of uncertainty (relative to a target attribute)

Information gain – reduction of entropy (relative to the target attribute)

The algorithm compares different classifying attributes in order to determine which has the highest information gain


SHAKEY and logic programming

Basic ideas

(1) states in state-spaces characterized by sets of predicate calculus formulas

(2) problems are conjectures to be proved

(3) problem-solving is finding proofs using proof-theoretic techniques and heuristic search techniques


Turn on the light switch

1. Goal wff =

STATUS (SWITCH1, ON)

2. STRIPS solution =

{goto2 (BOX1), climbonbox (BOX 1),

Climboffbox (BOX 1)

Pushto (BOX 1, SWITCH 1)

Climbonbox (BOX 1)

Turnonlight (SWITCH 1)

GO SHAKEY!


The frame problem

• Applying an operator to a state in a state-space problem will affect some relations between objects in the state but not others

• How is the system to keep track of which relations have changed and which not?

• Proofs would be very complicated if there were axioms for each operator specifying the relevant changes and non-changes


Possible framing axiom:

(on C B) & (put B table) (on C B)

Framing axiom?


SHAKEY and the frame problem

SHAKEY has a limited solution to the frame problem built into it

The F-rules in STRIPS have three components• Precondition formula• Delete list• Add formula

The Delete list makes explicit how the state description needs to be altered


Example

• Pickup (x)

• Precondition formula: ONTABLE (x) & HANDEMPTY & CLEAR (x)

• Delete list:{ONTABLE (x), HANDEMPTY, CLEAR (x)}

• Add formula:

HOLDING (x)


Limitations of SHAKEY

• SHAKEY’s explicit solution to the frame problem works only because the microworld is so restricted

• Each operator will only have a small number of effects on the state• These can be explicitly listed

• But this won’t scale up, when we introduce other agents and a more complex environment

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Chapter 6: Applying the PSSH