1
Q
Cognitive processes
A
Input (masses of information from the environment) –> cognitive processes –> Output (rational behaviour (mostly))
2
Q
Categories & concepts
A
Classes of objects in the world, are concepts are mental representations of the categories.
i. e. Category: cats are a class of objects in the real world,
concept: we hold a conceptual representation of cats in our minds.
3
Q
Why do we form conceptual representations?
A
- Data reduction: storing information about everything I’ve ever encountered would be an enormous strain on my memory. It is easier to store this information in terms of generalised conceptual representation.
- Generalisation: - i can use my conceptual representation to make inferences about new members of the category ive encountered.
- i can use my conceptual representation to make inferences about novel items that bear a resemblance to members of a given category.
4
Q
Exemplars
A
Groups of exemplars form categories.
the properties of exemplars and categories are described by features.
5
Q
The classic view of concept formation
A
- dominated our understanding of conceptual representation until the 1970s.
- arose from philosophy rather than psychology.
- Based upon the presence that categories are defined by the presence or absence of specific properties
what are defining properties? - membership of the category ‘squares’ is defined by the following properties: and
- in order for a shape to be a square it is necessary for the shape to have these properties.
- Furthermore, the presence of these properties is sufficient evidence to classify a shape as being a square
- Categories are defined by NECESSARY and SUFFICIENT features.
Necessity: If any of these features are missing, it is definitely not a member of this category.
Sufficiency: If all of them are present, then it is definitely a member of this category.
It therefore follows that - there are no in-between cases, and all members are equal.
6
Q
Three main claims of the classical view of concept formation
A
- Concepts are mentally represented as definitions. A definition provides characteristics that are necessary and jointly sufficient for membership of that category.
- Every object is either in or not in a given category, there are no in-between cases
- Every member of a category is considered to be an equally representative member of the category as all other members of the category.
7
Q
Problems with this classic view of concept formation?
A
Some different categories don’t work under the classical view… sports, emotions, fruit?
- binary category membership - e.g. A fruit is a fertilised ovary of a flowering plat…
apple, pear, bananas = fruit. but tomatoes, pumpkins, cucumbers = fruit?
- equality of category members - are rollerskates and hot air balloons equally good members of the category vehicles as cars and buses?
8
Q
Empirical evidence vs the classic view
point2 - every object is either in or not in a given category, there are no in-between cases
A
Binary category membership?
- Hampton (1979) presented participants with lists of potential members of 8 categories (furniture, sport, birds etc) and asked them to rate their membership on 7 point scale.
- Category membership ratings formed a continuum ranging from 0 to 100 %
- some category members were always included or excluded, others were borderline cases.
This could be due to people having different conceptual representations…
But McCloskey and Glucksberg (1978) demonstrated that even individuals change their inclusion criteria over time:
- asked participants to make repeated category judgements (is olive a fruit? is chess a sport? etc.) for 22% of borderline cases the participants changed their minds.
therefore… category membership is not binary!
9
Q
Equality of category members?
point 3. Every member of a category is considered to be an equally representative member of the category as all other members of the category.
A
- intuitively it seems that some category members are more typical/representative category members than others: e.g. a swallow seems more typical bird than a penguin.
- Rosch (1975) asked participants to rate the typicality of members of 10 different categories. The inter-rater reliability was extremely high.
McCloskey & Gluckberg (1978) found that category membership decisions could be predicted by typicality ratings:
- tables (mean typicality =9.83) always furniture
- windows (mean typicality= 2.53) never furniture
- wastebaskets (mean typicality =4.7) furniture 30% of the time.
Rips, shoben & smith (1973) found categorisation decision times could be predicted by typicality. = e.g. people are faster to confirm that robin is a bird than penguin.
10
Q
Initial claim of the classical view: 1. Concepts are mentally represented as definitions. A definition provides characteristics that are necessary and jointly sufficient for membership of that category.
A
little harder to test.
11
Q
An alternative approach - Family Resemblance.
A
Categories are not defined by necessary or sufficiently features, but by overlapping distributions of features.
‘Members of a category come to be viewed as… typical of the category as a whole in proportion to the extent to which they bear a family resemblance to (have attributes that overlap those of) other members of the category.
12
Q
Empirical evidence vs the classic view - Rosch and mervis (1975)
A
- 20 exemplars (category members) from 6 different categories
- one group of participants rated the typicality of the exemplars (how typical is X as a member of category Y)
- Another group generated features for the exemplars (X has the feature ).
- A third group rated the applicability of the features in relation to each of the exemplars the feature ( is applicable to X, M, C, T, A & B).
13
Q
Family resemblance
A
the weighted sum of featural overlap amongst categroy members.
strong correlation between typicality and family resemblance
- the graded typicality structure that we see in the categories is well described by the featural overlap of the category members.
- importantly, the features generated by the participants tended to apply to a small sub-set of the category members. Very few features appeared to apply to ALL of the members. None of the features could be construed as necessary and sufficient.
14
Q
Graded Category Structure
A
- Typicality ratings suggest that categories have graded structure.
- Generation frequency data, and categorisation decisions and latencies also suggest that categories have graded structure.
- This graded structure is also well described by the Family Resemblance measure, a weighted measure of featural commonality amongst category members.
15
Q
Example - Blargs
A
‘these are blargs, they can be described by the following features: body shape, body colour, antannae, number of legs.’
We can use this information to calculate their family resemblance.
‘the more similar an exemplar is to other category members, the higher its family resemblance, and the more typical it is of its category’
16
Q
The Polymorphous Concept Model
A
Similar model implemented by Hampton (1979).
- in this case, the representativeness of an exemplar is a function of the degree of overlap between the features associated with the exemplar and the features associated with the category.
- the family resemblance model and the polymorphous concept model both use featural overlap to measure graded category structure.
17
Q
Similarity
A
similarity data can be collected via a number of different procedures:
- pairwise or triad similarity ratings
- card-sorting tasks
- feature by exemplar matrices
18
Q
The contrast model
A
According to the contrast model the similarity between the exemplars ‘i’ and ‘j’ can be calculated from the features common to the two exemplars, the features of i that are not present in j, and the features of j that are not present in i.
- the family resemblance and the polymorphous concept model are both special cases of the contrast model.
19
Q
Using similarity to visualise semantic structure
A
- multi-dimensional scaling (MDS) provides a visual representation of the similarity relations between different objects or entities.
- converts similarities into distances: the more similar two items are, the closer theyw ill be located. The more dissimilar two items are, the further away they will be located.
20
Q
MDS
A
- The spatial representations generated using MDS appear to reflect the structure of the categories that are being represented.
- we see this in perceptual data, and importantly, we see this also in conceptual data.
- in many cases, the spatial structure of the categories is readily interpretable.
- sometimes the structure is not so easily interpretable, particularly when the optimal dimensionality of the representation is greater than 3.
- in perceptual data, we can often see that the spatial representations reflect perceptual qualities that were not explicitly referred to in the similarity data collection process.
- in conceptual data, we often find that the spatial representations reflect measures of graded category structure such as typicality, generation frequency, etc.
21
Q
Category structure.
A
- typicality = distance from category centroid.
- same for other measures of graded category structure (generation frequency, categorisation response time).
- but not for non-structural measures such as familiarity, age of acquisition, word frequency etc.
- Typicality reflects the similarity structure of categories.
- Flying prototype
- Vector projection
22
Q
Multidimensional scaling of similarity data
A
- multidimensional scaling of similarity data can also tell us about differences in the way that different groups of people mentally represent different categories.
23
Q
Abstraction
A
- empirical evidence suggests that we store information about real world categories in the form of conceptual representations, but what sort of information are we actually storing?
- we said that conceptual representations are potentially useful because they provide a means of reducing the amount of data needed to be stored in memory… rather than remembering ever dog we see, we have a conceptual representation that stores information about dogs, some form of ‘doggy’ abstraction.
- the idea that our conceptual knowledge is stored in the form of an abstraction is the major assumption of the PROTOTYPE view.
24
Q
Prototype view
A
Under this view, on the basis of experience with category examples, people abstract out the central tendency of a category.
in other words, a category representation consists of a summary of all the examples of the category, called the prototype.
25
Exemplar view
Suggests that experience with a category does not lead to the formulation of an abstracted prototype.
Rather, it suggests that we simply store in memory every example of a given category that we encounter.
In other words, a conceptual representation consists of all the individual members of a category, known as exemplars.
26
Prototype and Exemplar view: Two ends of a continuum
At one end we have total abstraction (prototype) and at the other end we have zero abstraction (exemplar).
The prototype view is useful because it reduced memory load. BUT this reduction comes at the cost of specific information.
The exemplar view is useful because it retains specific information, BUT it comes at a cost of memory load.
27
Prototypes & exemplars
The family resemblance model predicts typicality as a function of featural overlap between category members (exemplar)
The polymorphous concept model predicts typicality as a function of featural overlap between category members and an abstracted feature list representing the category name (prototype)
Typicality can be predicted as a function of the distance between each category member in a multidimensional space and the central tendency of that category (prototype)
Typicality can also be predicted as a function of the mean distance between each category member in a multidimensional space and each other category member in that space (exemplar)
28
Category learning experiments
- tend to employ stimuli that bear little resemblance to 'real-world' categories, but can be easily manipulated. e.g. brightness, size, shape etc
- tend to have two parts: A learning phase, and a transfer phase
29
Category learning: Learning phase
In the learning phase participants are shown stimuli drawn from two categories.
They are asked if the stimulus is from category A or B.
They are given feedback.
They learn the categories over time.
30
Category learning: transfer phase
Most categorisation experiments involve a second phase: the transfer phase.
- once the category structure is learnt participants are shown a mixture of old and new stimuli, and asked to categorise them.
- This gives us insight into our ability to generalise from a stored category representation to novel stimuli.
- manipulating the category structure allows us to test different theories about the processes underlying categorisation and generalisation
31
The Generalised Context model (GCM)
The probability of a stimulus being categorised as a member of a given category is a weighted function of the distance between the target stimulus and the members of two categories in the space (exemplar)
32
The MDS-based Prototype model (MPM)
The probability of a stimulus being categorised as a member of a given category is a weighted function of the distance between the target stimulus and the prototype (central tendencies) of two categories in space.
33
Category learning
- both the GCM (exemplar model) and MPM (prototype model) do a good job of simulating human performance on category learning tasks.
- Overall, the GCM does better than the MPM.
34
Real-world category learning
- smits, storms, rosseel and de boek (2002).
- Data set: pictures of 79 well-known fruits and vegies, and 30 novel stimuli (mainly tropical fruit and veg)
- one group of participants made pairwise similarity ratings
- one group asked to categorise all 109 stimuli as either fruits or vegies
- They used MDS to generate a 3D representation of the stimuli. Based on this representation the GCM made categorisation predictions.
- the GCM was able to make a good account of the fruit and vegetable categorisation data
- A subsequent paper showed that the MPM does about equally well
35
Real-world category
- Take a long time to learn effectively
- Change over time: - over-extended words narrow over time, under-extended words broaden over time.
- Are culture, person, and time specific.
- Have a much richer structure than the types of categories used in lab-based category learning tasks.
- often follow a hierarchical structure - think of a 'tree of life'
36
Hierarchical concept structure
- our conceptual representations also often follow a hierarchical structure
- the hierarchy can be described in terms of 3 levels, the super-ordinate, basic and sub-ordinate.
- Items located on the same level of abstraction are called ordinates.
- the implication is that the basic level categories are generally more useful; because of the high level of abstraction super-ordinate lack informativeness; suborderinate categories are highly informative, but lack distinctiveness, and basic level categories appear to contain the best balance between informativeness and distinctiveness
ANIMAL
MAMMAL/ BIRD - superordinate
CAT, COW, DOG/ DUCK/MAGPIE - basic
BLUE HEELER, BORDER COLLIE - subordinate
37
Contrast categories
Contrast categories are located within a common domain at the same level of abstraction, and influence each others similarity structure.
- a bat is an atypical member of the category mammals, as it has low relative similarity to other mammals, but a high relative similarity to members of contrast categories such as birds or insects (e.g. has wings, flys etc)
38
Deductive reasoning
involves using given true premises to reach a conclusion that is also true.
- all men are mortal
- socrates is a man
- therefore, socrates is mortal
39
Inductive reasoning
inductive reasoning is probabilistic - it only states that, given the premises, the conclusion is probable.
- 7-10% of males are red-green colour blind.
- Joe is a male
- Therefore, the probability that joe is red-green colour blind is 7-10%.
40
Rips (1975) category-based induction experiment
Employed blank predicates - these are predicates that individuals would be unlikely to have strong beliefs about
Robins have sesamoid bones - birds have sesamoid bones.
- using blank predicates in this way enables Rips to understand the process underlying category-based induction in general, without having to rely on any prior knowledge regarding the predicate.
41
Category-based induction
- participants are presented with a premise and a conclusion. For example
- Premise: Ducks are susceptible to Reinholf disease.
- Conclusion: Geese are susceptible to Reinholf disease. OR. Robins are susceptible to Reinholf disease.
- the participants rate the degree to which they agree with the conclusion (0-100%).
- Rips found that the likelihood of extending a predicate from a premise to a conclusion varied within a category.
- once again, this suggests that category representations have graded structure, i.e., members of a category are not equally representative of that category
42
Rips continued.
Rips modelled the participants responses using distances in a multi-dimensional space.
-typicality was the distance from category prototype.
-similarity was the inverse of distance in the space.
The data was used to compare a set of different regression models.
On the basis of these analyses Rips concluded that the participants willingness to extend the blank predicate to the conclusion varied as a function of:
- The similarity between the premise and conclusion category.
(Participants would be more likely to accept that geese could get Reinholf disease than robins, because ducks are more similar to geese than to robins.
- the typicality of the premise category.
(-Ducks are not highly typical birds, so the premise would not tend to have a high level of extension.It is important to note that the typicality of the conclusion category appeared to play little part in the likelihood of extension. i.e., just because robins are typical doesn't mean that we are more likely to extend from the premise to the conclusion.
43
Premise monotonicity
- when more categories are added to the premise the argument is stronger.
- adding more categories should only ever increase the similarity between the premises and the conclusion, and can only ever increase the coverage of the category.
43
Premise monotonicity
- when more categories are added to the premise the argument is stronger.
- adding more categories should only ever increase the similarity between the premises and the conclusion, and can only ever increase the coverage of the category.
44
Premise diversity
The more diverse the premise categories are, the stronger the argument
- when the premises are distributed across the category (i.e., have greater coverage or diversity) we can be more confident that the property is true of the entire category.
e.g. dolphins, cows and rabbits all use Dihedron; therefore, all mammals use dihedron..
is stronger than
Dolphins, seals and whales all use Dihedron; therefore all mammals use Dihedron.
Because the second argument only covers aquatic mammals, whereas the first covers both aquatic and terrestrial mammals.
44
Premise diversity
The more diverse the premise categories are, the stronger the argument
- when the premises are distributed across the category (i.e., have greater coverage or diversity) we can be more confident that the property is true of the entire category.
e.g. dolphins, cows and rabbits all use Dihedron; therefore, all mammals use dihedron..
is stronger than
Dolphins, seals and whales all use Dihedron; therefore all mammals use Dihedron.
Because the second argument only covers aquatic mammals, whereas the first covers both aquatic and terrestrial mammals.
45
Limitations of the paradigm
1. the predicates are not entirely 'blank' (e.g. sesamoid bones). in other words, we may be relying on deeper knowledge to make our decision, not just the similarity structure of the category.
- it is possible to replace the properties with phrases such as 'has property X', but real-world properties often contain meaningfully structured information.
2. It is not always clear what the underlying similarity ratings used in the model (or by people) are based on. Biological similarity? Behavioural similarity?
Heit & Rubenstein - found that when the predicate was biological (i.e. blood potassium levels) induction was strong from biologically similar animals (e.g. rabbits and whales). But when the predicate was behavioural (i.e. foraging patterns) the induction was strongest for the behaviourally similar animals (e.g. tuna and whales).
3. There are situations in which similarity does not appear to play a strong role in induction.
- Lin and Murphy - found that is some situations induction was stronger from thematically related categories than for similar categories.
45
Limitations of the paradigm
1. the predicates are not entirely 'blank' (e.g. sesamoid bones). in other words, we may be relying on deeper knowledge to make our decision, not just the similarity structure of the category.
- it is possible to replace the properties with phrases such as 'has property X', but real-world properties often contain meaningfully structured information.
2. It is not always clear what the underlying similarity ratings used in the model (or by people) are based on. Biological similarity? Behavioural similarity?
Heit & Rubenstein - found that when the predicate was biological (i.e. blood potassium levels) induction was strong from biologically similar animals (e.g. rabbits and whales). But when the predicate was behavioural (i.e. foraging patterns) the induction was strongest for the behaviourally similar animals (e.g. tuna and whales).
3. There are situations in which similarity does not appear to play a strong role in induction.
- Lin and Murphy - found that is some situations induction was stronger from thematically related categories than for similar categories.
46
Models of category-based induction
- a number of different computational models have been developed to account for human performance on these tasks.
- Rips - Distances in multi-dimensional space
- Osherson - Featural overlap
- Smith - weighted featural overlap
- heit - bayesian model
46
Models of category-based induction
- a number of different computational models have been developed to account for human performance on these tasks.
- Rips - Distances in multi-dimensional space
- Osherson - Featural overlap
- Smith - weighted featural overlap
- heit - bayesian model
47
what about negative evidence?
so far all of the experiments have used premises based upon positive evidence..
- sharks have vertebrae, stingrays have vertebrae.
but we also learn about the world via negative evidence. (very few studies have looked at this)
- Squid don't have vertebrae
- stingrays have vertebrae.
47
what about negative evidence?
so far all of the experiments have used premises based upon positive evidence..
- sharks have vertebrae, stingrays have vertebrae.
but we also learn about the world via negative evidence. (very few studies have looked at this)
- Squid don't have vertebrae
- stingrays have vertebrae.
48
Premise monotonicity
- premise monotonicity - when negative evidence is added, the likelihood of accepting the conclusion should decrease...
pigs have sesamoid bones, wolves do not have sesamoid bones, gorillas have sesamoid bones.
should be less preferable compared to...
pigs have sesamoid bones, gorillas have sesamoid bones.
48
Premise monotonicity
- premise monotonicity - when negative evidence is added, the likelihood of accepting the conclusion should decrease...
pigs have sesamoid bones, wolves do not have sesamoid bones, gorillas have sesamoid bones.
should be less preferable compared to...
pigs have sesamoid bones, gorillas have sesamoid bones.
49
negative evidence
Heussen et al demonstrated that sometimes negative evidence can actually increase argument strength.
This is a violation of the assumption of premise monotonicity
49
negative evidence
Heussen et al demonstrated that sometimes negative evidence can actually increase argument strength.
This is a violation of the assumption of premise monotonicity
Perception & Cognition
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