Midterm 2

Question 1

Hume on causality

Answer 1

Causal connections are the product of
observation:
Ø Spatial/temporal contiguity (happen at the same time)
Ø Temporal succession (the causer has to happen before what it causes)
Ø Constant conjunction (has to always cause this thing to happen)
Important: causation is a relation between experiences rather than one between facts

Question 2

Challenge to Hume’s causality

Answer 2

Causality is not directly in the input, nothing in our system ensures that flicking the switch will turn on the light.
Big problem: cause knowledge has to emerge from non-causal input

Question 3

Causal inference

Answer 3

Infer causal relations from patterns of data.
Difficult because the data is often incomplete, and other models (such as a third party) could be the cause.
Dominant theory: people estimate the strength of causal relations on the basis of covariation between events (do they happen more often together or separately?)

Question 4

Delta-P rule

Answer 4

Probability of causality = probability that result happens with cause - probability that the result happens without the cause.
If result positive = Generative cause
If result negative = Preventative cause
If result is 0 = non-causal, independent

Question 5

Crime reasoning experiment

Answer 5

Subjects more
likely to supply interpretation
most supported by the data
when doing so affirmed their
political position
More numerate subjects use
their quantitative-reasoning
capacity selectively to conform
their interpretation of the data to
the result most consistent with
their political outlooks
An Experiment in Motivated
Reasoning (Kahan et al 2016)

Question 6

Alien experiment

Answer 6

People require disproportionate evidence in favor of the complex
explanation before it can rival the simpler alternative

Question 7

Axiomatic system

Answer 7

formal system consisting of a set of axioms and inference rules
Goal is to codify knowledge in some domain
Axiom: A statement accepted as true
Inference rule: logical form or guide consisting of premises (or hypotheses) and draws a conclusion

Question 8

Propositions in axiomatic system

Answer 8

Statement that is stated precisely enough to be either true or false
Proof of a proposition: a sequence of steps that ends with the proposition

Question 9

Consistency in axiomatic system

Answer 9

A consistent axiomatic system is one that can never derive
contradictory statements by starting from the axioms and following the
inference rules (2 contradictory statement cannot both be true).
If a system can generate both P and not P for any proposition P, the
system is inconsistent.
If a formal system cannot generate any contradictory pairs of
statements it is called consistent.

Question 10

Completeness in axiomatic system

Answer 10

A complete axiomatic system can derive all true
statements by starting from the axioms and following the
inference rules.
That is, if a given proposition is true, some proof for
that proposition can be found in the system.

An ideal axiomatic system would be complete and
consistent:
It would derive all true statements and no false
statements

Question 11

Principia Mathematica

Answer 11

Whitehead and Russel
An attempt to formalize mathematical reasoning, attempted to derive all true statements

Question 12

Gödel’s Incompleteness
Theorem

Answer 12

no axiomatic system
could be both complete and consistent:
No matter what the axiomatic system is, if it is
powerful enough to express a notion of proof,
it must also be the case that there exist
statements that can be expressed in the
system but cannot be proven either true or
false within the system.

Question 13

Deductive
Reasoning

Answer 13

conclusion follows logically from premises
conclusion is guaranteed to be true

Question 14

Inductive reasoning

Answer 14

conclusion is likely based on premises.
involves a degree of uncertainty

Question 15

Deductive Inference Rules

Answer 15

§ If the premises are true, the conclusion is necessarily
true.
§ The premises provide conclusive evidence for the
conclusion.
§ It is impossible for the premises to be true and the
conclusion to be false.
§ It is logically inconsistent to assert the premises but
deny the conclusion.

“Modus Ponens”
If p then q
p
Therefore q

“Modus Tollens”
If p then q
~q
Therefore ~p (need to solve Wason selection task)

Question 16

Syllogistic Reasoning

Answer 16

The logical validity of the conclusion is determined after
‘accepting’ the premises as true (that is a conclusion that
necessarily follows from the premises)
Major Premise
Minor Premise
Conclusion
Syllogistic reasoning is often subject to belief bias

Question 17

Ideological belief bias in
syllogistic reasoning

Answer 17

• Liberals are better at identifying flawed arguments
  supporting conservative beliefs
• Conservatives are better at identifying flawed
  arguments supporting liberal belief

Question 18

Induction tasks

Answer 18

People do better when
contrasting two viable
alternatives than when
evaluating the truth of a single
hypothesis

Question 19

Radiation problem

Answer 19

Without base problem that hints the solution: only 20% solved it, vs 75% when shown it
These results show that noticing the analogy is a separate step
from constructing the analogy. (Condition 3 > Condition 2.)

Question 20

Analogical transfer

Answer 20

Reasoning from base problem (previously solved) to target problem, solving problem in one domain based on solution in another domain
* Recognition: identify a potential analog or ‘base’
domain
* Abstraction: abstract general principle from base
problem
* Mapping: apply principle to target

Question 21

Analogical inference

Answer 21

generalizing
properties/relations from one domain to another

Question 22

Structure-mapping theory of analogy

Answer 22

An ANALOGY is when two conceptual
domains share relational similarity
Comparisons involve an alignment of relational structures
One-to-one mapping
Ø e.g., “sun” à“nucleus”
Parallel connectivity
Ø e.g., “sun”to“nucleus” & “planets” to “electrons”
Systematicity: Deeply nested relational structures make better
analogies

Question 23

War choices experiment

Answer 23

Results: Superficial Features Affect
Availability of Analogies
Subjects’ preferred policy was significantly more
interventionist when scenario contained WW II features
than when it contained Vietnam features

Question 24

Cross-matching experiment in children

Answer 24

When trying to match sequence of shapes, 68& succeeded if it was within dimension, but only 48% did if if needed to cross-match

Question 25

Near vs. Far Transfer

Answer 25

• near transfer - apply knowledge from a closely
  related base domain to the target domain
  furnace:coal :: woodstove:wood (ie water pump)
• far transfer - apply knowledge from seemingly
  distant base domain to target domain
  furnace:coal :: stomach:food (ie velcro)

Question 26

Three ways to think about syntax

Answer 26

1 Syntax aims to model and explain the implicit knowledge speakers
have of their language
2 Syntactic models as a generative and explanatory model of language
3 Syntactic claims are claims about language variation

Question 27

definition of syntax

Answer 27

Syntax is the descriptive study of the grammar, or the set of systematic
rules, underlying a particular language

Question 28

Prescriptivism vs. Descriptivism

Answer 28

Prescriptive:
Normative statements about how one ought to use one’s langauge
Descriptive:
Statements about what speakers of a language know and do naturally

Question 29

2 types of language

Answer 29

i-language, or big-L Language, is the internal system underlying our
linguistic knowledge. The object of study for linguists.
e-language, or little-l language, is the external manifestation of our
linguistic knowledge. We study these in order to study i-Language

Question 30

Phrase Structure Grammar

Answer 30

when we learn languages, we are generalizing over
categories of words
we make “infinite use of finite means”

Question 31

Why Phrase Structure Grammar does not work for english

Answer 31

Undergeneration: The grammar and lexicon fail to account for the
range of English sentence types
Overgeneration: Since we didn’t constrain which lexical items occur
where, we generate sentences that speakers will judge to be
ungrammatical.

Question 32

Levels of adequacy pf grammar models

Answer 32

Observational: the model can capture each discrete data point.
Descriptive: the model produces all and only the attested/attestable
data, in a general way.
Explanatory: the model provides a compelling way of explaining
why it is the way it is, and provides a principled way of deciding
between it and a competing descriptively adequate model.

Question 33

Universalist view of grammar

Answer 33

• Universalist assumptions:
  Most generative linguists adopt some version (with lots of
  variation) of the latter, where:
  a proper fine-grained analysis of a single language makes an
  implicit typological claim: we expect the parts used in our
  analysis of English (or Swahili or Nahuatl) to be available in
  principle to every other natural language spoken by humans
• Universalist goals:
  Since we’re interested in Language, looking at a language in
  comparison to other languages gives us the best chance of
  revealing the more general character of what makes up syntactic
  knowledge
  Looking at several languages together reveals similarities and
  differences that will help us uncover how Language works

Question 34

4 elements of problem solving

Answer 34

• Initial State
• Goal State
• Operators (actions that
  can be taken, which serve to alter
  the current state of the problem)
• Path constraints (additional
  conditions on a successful path to
  solution, beyond simply reaching
  the goal (for instance, the constraint
  of finding the solution using the
  fewest possible steps))

Question 35

State Spaces and Search

Answer 35

• Problem space consists of
  the set of all states that can
  potentially be reached by
  applying the available
  operators .
• A solution is a sequence of
  operators that can transform
  the initial state into the goal
  state in accord with the path
  constraints .
• A problem-solving method is
  a procedure for finding a
  solution (search technique)

Question 36

Search tree

Answer 36

Considerations:
* completeness
does it always find the
goal state?
* optimality
does it always find the
shortest (lowest-cost)
path?
* “time complexity”
how long did it take?
* “space complexity”
need to keep track of
which states you’ve visited

factors that affect time
and space complexity:
* B - ”branching factor”, breadth
* D – depth in tree of
goal state

Question 37

Types of search

Answer 37

§ Breadth-first search: always
guaranteed to find the shortest
path (go for shortest path first)
§ Depth-first search: If the solution
is very ‘deep’, turning up this path
might take many steps (explore states in order)
Both brute force (can cause NP-hard problem)

Question 38

combinatorial explosion

Answer 38

The exponential increase in
the size of the possible search
space with the increasing tree
makes many problems
impossible to solve by
exhaustive search of all
possible paths

Question 39

Heuristic search techniques

Answer 39

Focus on promising areas
Uses evaluation tool to find them
Hill-Climbing: always choose the next
state with the best (lower)
score provided by the
evaluation function
Best first search: perform a brute-force
(exhaustive) search such as
depth-first or breadth-first but
prioritize states with better
scores

Question 40

Forward vs. Backward Search

Answer 40

• Forward search involves applying
  operators to the current state to
  generate a new state
  Starts at the initial state and searches
  for a path to the goal
• Backward search involves finding
  operators that could produce the
  current state.
  Starts at the goal and searches for a
  path to the initial state

Question 41

Means-ends analysis

Answer 41

Involves a mixture of forward and backward search.
The key idea underlying means-ends analysis is that
search is guided by detection of differences between the
current state and the goal state

1. Compare the current state to the goal state and
   identify differences between the two. If there are
   none, the problem is solved; otherwise, proceed.
2. Select an operator that would reduce one of the
   differences.
3. If the operator can be applied, do so; if not, set a new
   subgoal of reaching a state at which the operator
   could be applied. Means-ends analysis is then
   applied to this new subgoal until the operator can be
   applied or the attempt to use it is abandoned.
4. Return to step 1

Question 42

The “Sussman Anomaly”

Answer 42

In the process of achieving a new sub-goal during the
planning process, means-end analysis might entail
reversing or ‘undoing’ a goal it had already achieved
A remedy: don’t perform any actions which would
undo a previously achieved goal or sub-goal

Question 43

The Frame Problem

Answer 43

When representing actions we make the assumption
that the only effects our operator has on the world
are those specified by the ‘add’ and ‘delete’ lists.
* In real-world planning this is a hard assumption to
make as we can never be certain of the extent of the
effects of an action
Plans must constantly adapt based on incoming sensory
information about the new state of the world, otherwise the
operator preconditions will no longer apply

Question 44

Constraint Satisfaction Problems
(CSPs)

Answer 44

problems whose states and goal test conform to a
standard, structured, and very simple representation.
§ This representation views the problem as consisting of a
set of variables in need of values that conform to certain
constraint(s).
Goal: Assign a value to every variable such that all
constraints are satisfied

Question 45

Idealized neurons (or “units”)

Answer 45

Key components:
1. A set of synapses
(i.e. inputs) brings in
activations from other
neurons.
2. A processing unit
sums the inputs, and
then applies an
activation function
3. An output line
transmits the result to
other neurons

Inputs are weighted: an input with more
weight between the input unit j and the
unit i will have a bigger effect on the
activation of unit i
Summing total input by how much each input neuron is weighted

Unit i has a threshold of 1;
so if its total input exceeds
1 then it will activate with
+1, but if the net input is
less than 1 then it will
respond with –1

Question 46

Neural Networks: Key Concepts

Answer 46

• Units contain:
  – Activation = Activity of unit
  – Weight = Strength of the connection between two units
• Learning = changing strength of connections
  between units
• Excitatory and inhibitory connections
• correspond to positive and negative weights
  respectively

Question 47

Perceptron

Answer 47

The arrangement that has one layer of input
neurons feeding forward to one output
layer of McCulloch-Pitts neurons, with full
connectivity
Can, in principle, compute any linear
function!

Question 48

Logic gates

Answer 48

AND “Are both input units
active?”. You can use a straight line to separate the YES
(active) cases from NO (inactive) cases
OR “Is at least one input
unit active?”. You can use a straight line to separate the YES
(active) cases from NO (inactive) cases
NOT “Flip (or negate) the
activation of the input
unit”

XOR “is only one input active?”. To solve the XOR problem you need a more complex neural network that
is able to generate more complex decision boundaries. Solution: multi-layer network

Question 49

Hebbian Learning

Answer 49

Information is stored in the connections between neurons in neural
networks, in the form of weights
If two units on either side of a connection are activated
simultaneously (i.e. synchronously), then the strength of that
connection weight is selectively increased.
Or: ‘units that fire together, wire together’.

two
learning methods are possible:
* With unsupervised learning there is no
teacher: the network tries to discern
regularities in the input patterns
* With supervised learning an input is
associated with a output correct output and
the network’s job is to learn this input-output
mapping

Question 50

localist representation

Answer 50

Each unit represents just one item
§ Easy to understand
Network output is human-understandable
and can be easily coded ‘by hand’
§ Easy to learn and associate with other
representations or responses.
§ Inefficient in situations with
“componential structure”

Localist networks suffer catastrophically if damaged, since loss
of a given unit will render its referent unrepresented

Question 51

Distributed Representations

Answer 51

Each unit is involved in the representation of multiple items
§ Efficiency / Capacity
Solve the combinatorial explosion problem: With n
binary units, 2 n different representations possible.
§ Hard to interpret
ØNetwork outputs are usually not human-readable

Question 52

Attending unexpected findings

Answer 52

Always attend to it when it happens late in the experiment
Does not attend it if early and not related to core hypothesis

Question 53

Intelligence of AI reading

Answer 53

4 things to be considered intelligent: the ability to acquire knowledge, to master knowledge, to create knowledge, to output knowledge to the outside world
All performed worse than a 6 yo
2 types of general intelligence: fluid (solve noel problems) and crystallized (effective use of accumulated knowledge)