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)
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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!
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
Possible framing axiom:
(on C B) & (put B table) (on C B)
Framing axiom?
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
Example
• Pickup (x)
• Precondition formula: ONTABLE (x) & HANDEMPTY & CLEAR (x)
• Delete list:{ONTABLE (x), HANDEMPTY, CLEAR (x)}
• Add formula:
HOLDING (x)
Cognitive Science José Luis Bermúdez / Cambridge University Press 2010
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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