College aantekeningen
Aantekeningen Human Cognition deeltentamen 2
- Instelling
- Universiteit Van Amsterdam (UvA)
Aantekeningen deeltentamen 2
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Voorbeeld 3 van de 19 pagina's
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Voorbeeld van de inhoud
Aantekeningen Human CognitionHoorcollege 1
Fundamental assumption of CogSci: cognition is a form of information
processing.
How does cognitive information processing work?
Two different models of cognitive information processing:
Physical symbol system hypothesis: information carried by physical
symbols
Artificial neural networks: information distributed across a population
of neurons
Physical symbol systems and the Language of Thought
Symbols
Numeral ‘5’ symbol for number 5 in Arabic numeral system.
Numeral ’v’ symbol for number 5 in Roman numeral system.
Letter ’b’ symbol for the sound [b] (in English alphabet, among many
others).
Word ’cat’ symbol for cats in English. Word ’chat’ symbol for cats in
French. ...
Physical symbol systems (PSS)
PSS contains a set of symbols (which are physical patterns).
Symbols can be combined to form complex symbol structures.
PSS contains processes for manipulating complex symbol structures
(which can themselves be represented by symbols).
Examples:
S → DP VP
DP → the NP
VP → V DP
NP → cat | mouse
V → ate | chased
Physical symbol hypothesis:
Newell & Simon (1976): All and only physical symbol systems are capable of
intelligent behavior
Computers are capable of intelligent behavior
Humans must be physical symbol systems
Problem solving
We generate and modify symbol structures until a solution structure is reached.
Example: Solving a chess problem.
,From physical symbol systems to intelligent behavior
How can a physical symbol system produce intelligent behavior?
The system only follows formal rules to manipulate symbol structures,
without access to what the information content they may carry (i.e.
without access to their meaning).
Fodor (1975): This does not matter, as long as the formal rules respect
the meaning of symbol structures.
In logic, formal languages that are complete and sound achieve just that.
We can postulate that humans (and other intelligent beings) have an
internal ‘Language of Thought’ with just these properties.
Before we go any further…
Searle’s (1980) Chinese room argument: A person is in a room with two
windows. They receive papers from one window, with Chinese ideograms
written on it, and pass out different pieces of papers through the other window.
In the room is a (huge) manual containing precise instructions on which pa- per
to transmit depending on the paper received. The instructions are not written in
Chinese and can be understood by anyone.
The Chinese room is meant to represent a physical symbol system, but we
wouldn’t intuitively say that the person “understands Chinese”, even if the
instructions are so well-written that it fools any native Chinese speaker.
Possible responses
See Bermudez for the systems reply and the robot reply
The distinction between simulating a mind and having a mind is ill
defined. Even if it were, it would be irrelevant because no experiments
can be proposed to distinguish between the two. Other minds reply
(Nilsson), zombie reply (Dennett), Newton’s flaming laser sword reply
(Adler)
Symbol-grounding problem (more generally):
How do symbol structures get interpreted to us, giving rise to meaningful
thinking subjective experience?
And now for something completely different…
Propositional Logic
Building blocks:
Propositions: a statement that is either true or false:
“2+2 = 4”, “It rained on Friday”, “The Earth is flat”
“2+3”, “Was it raining on Friday?”, “This sentence is false”
Propositions denoted by propositional variables, such as p, q
Meaning of propositions their truth values
, Operators: take one or more propositions as argument, return a new
proposition:
Negation (¬): takes p, returns ¬p which is 0 when p = 1 and 1 when p = 0
Conjunction (∧): takes p and q, returns p ∧ q which is 1 when p = q = 1, 0
otherwise.
Disjunction (∨): takes p and q, returns p ∨ q which is 0 when p = q = 0, 1
otherwise.
Truth tables
p ¬p p q p∧q p q p∨ q
0 11 0 0 0 0 0 0 0
1 0 0 0 1 1
0 1 0 1 0 1
1 1 1 1 1 1
If an operator takes n propositions,
the truth table has 2n rows. Truth tables allow us to evaluate the results of
complex expressions, such as ¬(p ∨ (q ∧ p)).
Using truth-tables to solve
p q p∧q p ∨ (q ∧ p) ¬ (p ∨ (q ∧ p)) complex expressions
0 0 0 0 1
0 1 0 0 1
1 0 0 1 0
1 1 1 1 0
In the end, ¬(p ∨ (q ∧ p)) is simply equivalent to ¬p.
More formally…
A set of symbols for atomic propositions: {p, q, r, . . .}
A set of symbols for operators: {¬, ∧, ∨}.
A very simple context-free grammar for the language L of well-formed
formula:
We can give semantics to this language using valuations:
v : L → {0, 1} is a valuation if it agrees with the meaning of operators:
v(¬φ)=1−v(φ)
v(φ ∧ ψ) = min (v(φ) , v(ψ)) Only true if both are true (min=en)
v(φ ∨ ψ) = max (v(φ) , v(ψ)) Only false if both are false (max=of)
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