PSYCH 155/LING 155
syn
lab
UCI
COGNITIVE
SCIENCES
Psychology of Language
Prof. Jon Sprouse
Lecture 12: Storage and Computation in the
Lexicon
1
So what are we doing?
Remember our goal is to figure out what the lexemes are. In other words, we
want to know what is stored in the lexicon and what is assembled online as
needed (called computation):
We have two hypotheses under consideration:
Full-Storage Hypothesis: every word is stored in full in the lexicon
Advantage: fewer computations
Disadvantage: memory cost
qualify
prequalify
qualifies prequalifies
qualified prequalified
screen
prescreen
screens
prescreens
screened prescreened
Full-Computation Hypothesis: every morpheme is stored in the lexicon; larger
words are computed as needed
Advantage: lower memory cost
Disadvantage: more computations
qualify
screen
s
ed
pre
2
We used the Frequency Effect as a way
to probe the Full-Storage Hypothesis
The frequency effect is the fact
that more frequent words tend to be
recognized faster than less frequent
words.
The implication of the frequency
effect is that the lexicon is
organized by frequency.
This means that we can use the frequency effect to test whether a given word
is a lexeme (unit stored in the lexicon) or not: words that are lexemes
(stored in the lexicon) should show the frequency effect!
3
The problem with the Full-Storage Hyp.
slow
So these two words are consistent
with the Full Storage Hypothesis
reaction time
frequency
high
windows
kitchens
low
low
windows
slow
So these two words are inconsistent
with the Full Storage Hypothesis
reaction time
frequency
high
fast
kitchens
kitchen
window
kitchen
window
fast
4
Notice that these words were not
chosen randomly
Let’s look at these pairs a bit closer:
Crucially it is an asymmetrical pair:
We use the singular much more than
the plural because most people only
have one kitchen.
We can call this a singulardominant word.
high
frequency
Kitchen-Kitchens is clearly a singularplural pair.
low
kitchen
kitchens
5
Notice that these words were not
chosen randomly
Let’s look at these pairs a bit closer:
Crucially it is an asymmetrical pair in
the opposite direction:
We use the plural much more than
the singular because most people
have more than one window.
We can call this a plural-dominant
word.
high
frequency
Window-Windows is clearly a singularplural pair as well.
low
windows
window
6
Now let’s introduce a new type of
frequency
What we’ve been calling “frequency” up until now has really been surface
frequency:
Surface Frequency: The frequency of each individual word form
surface frequency
of “kitchen”
high
frequency
The surface frequency of a
singular-dominant word is
asymmetric in favor of the
singular form.
low
surface frequency
of “kitchens”
kitchen
kitchens
7
Now let’s introduce a new type of
frequency
What we’ve been calling “frequency” up until now has really been surface
frequency:
Surface Frequency: The frequency of each individual word form
high
surface frequency
of “window”
frequency
The surface frequency of a
plural-dominant word is
asymmetric in favor of the
plural form.
low
surface frequency
of “windows”
windows
window
8
Now watch what happens when we
combine the surface frequencies
We can add the surface frequencies of two related word forms to arrive at a
measure called the base frequency.
Base Frequency: The total frequency of all related word forms
low
high
frequency
frequency
high
kitchen
kitchens
low
windows
window
9
Now watch what happens when we
combine the surface frequencies
We can add the surface frequencies of two related word forms to arrive at a
measure called the base frequency.
Base Frequency: The total frequency of all related word forms
low
kitchens
kitchen
frequency
frequency
high
Base Frequency
of “kitchen”
high
low
Base Frequency
of “window”
windows
window
10
We chose these pairs of words because
they have the equal Base Frequency
Different word forms will have different base frequencies. The only reason that
these have equal base frequency is because we chose them this way.
We will use the equal base frequency and unequal surface frequency to test
the Full-Computation Hypothesis.
high
kitchens
frequency
sisters
windows
kitchen
sister
low
window
famines
famine
11
The primary prediction of the
Full-Computation Hypothesis
Full-Computation Hypothesis: every morpheme is stored in the lexicon; larger
words are computed as needed
Advantage: lower memory cost
Disadvantage: more computations
qualify
screen
s
ed
pre
This means that singulars and plurals will require different processes for lexical
access:
Processes for SINGULARS
Processes for PLURALS
1. Find the base in the lexicon
1. Find the base in the lexicon
2. Add -s to the singular noun
More processes means more time (assuming that the time for step 1 was equal)!
12
So this means we have two time
components to add up
Processes for SINGULARS
time per process
total time
1. Find the base in the lexicon
= time X
= time X
Processes for PLURALS
1. Find the base in the lexicon
= time Y
2. Add -s to the singular noun
= time Z
= time Y + Z
The question we face now is how to figure out time X, time Y, and time Z so that
we can make predictions using the Full-Computation Hypothesis.
The answer is that time X and time Y are determined by the base frequency,
and time Z is the same for all plurals.
13
Singular retrieval time =
Base Frequency
The crucial insight here is that the base frequency is named that on purpose -it is the frequency of the base form, which is identical to the singular form.
Notice that regardless of which form you hear (singular or plural), you must
access the singular form (the base form) in order to process it:
Processes for SINGULARS
Processes for PLURALS
1. Find the base in the lexicon
1. Find the base in the lexicon
2. Add -s to the singular noun
high
frequency
This means that the best
measure for the frequency of
the singular form is to add the
singular frequency and the
plural frequency, which is the
definition of the base
frequency
pl
base frequency =
singular + plural
sg
low
14
Getting our frequencies straight
Surface Frequency: The frequency of each individual form of the word
Base Frequency: The frequency that the base of the word (usually equivalent to
the singular form) is accessed from the lexicon. You can calculate it by adding the
surface frequencies of all of the related word forms together (e.g., singular +
plural)
Full-Storage Hypothesis:
every word is stored in full in the lexicon
Only Surface Frequency exists under this hypothesis because there is no
such thing as the “base form” of a word. Every word is its own lexeme.
Full-Computation Hypothesis: every morpheme is stored in the lexicon; larger
words are computed as needed
Only Base Frequency exists under this hypothesis. The time for singulars
is determined by base frequency, and the time for plurals is determined
by the base frequency and adding s.
15
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 1:
Kitchen and Window should be equal in decision time.
Why?
Because they have the same base frequency, which is
the correct frequency for singular forms (they are
accessed for both singulars and plurals)
slow
prediction
kitchens
windows
kitchen
reaction time
frequency
high
kitchen
low
window
window
fast
16
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 1:
Kitchen and Window should be equal in decision time.
Why?
Because they have the same base frequency, which is
the correct frequency for singular forms (they are
accessed for both singulars and plurals)
slow
actual result
kitchens
windows
kitchen
reaction time
frequency
high
kitchen
low
window
window
fast
17
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 1:
Kitchen and Window should be equal in decision time.
Why?
Because they have the same base frequency, which is
the correct frequency for singular forms (they are
accessed for both singulars and plurals)
slow
actual result
kitchens
reaction time
frequency
high
So these two words are consistent
withwindows
the Full Computation Hypothesis
kitchen
kitchen
low
window
window
fast
18
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 2:
Kitchen should be faster than Kitchens.
Why?
Because the singular only require one process: retrieve
the base. The plural form requires two processes:
retrieve the base and add -s.
slow
prediction
kitchens
windows
kitchen
reaction time
frequency
high
kitchens
kitchen
low
window
fast
19
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 2:
Kitchen should be faster than Kitchens.
Why?
Because the singular only require one process: retrieve
the base. The plural form requires two processes:
retrieve the base and add -s.
slow
actual result
kitchens
windows
kitchen
reaction time
frequency
high
kitchens
kitchen
low
window
fast
20
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 2:
Kitchen should be faster than Kitchens.
Why?
Because the singular only require one process: retrieve
the base. The plural form requires two processes:
retrieve the base and add -s.
slow
actual result
kitchens
reaction time
frequency
high
So these two words are consistent
withwindows
the Full Computation Hypothesis
kitchen
kitchens
kitchen
low
window
fast
21
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 3:
Kitchens and Windows should be equal.
Why?
Because the base forms are equal, and the plural forms
are simply the addition of two processes:retrieve the
base and add -s.
slow
low
prediction
kitchens
windows
kitchen
window
reaction time
frequency
high
kitchens
windows
fast
22
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 3:
Kitchens and Windows should be equal.
Why?
Because the base forms are equal, and the plural forms
are simply the addition of two processes:retrieve the
base and add -s.
slow
actual result
kitchens
windows
kitchen
reaction time
frequency
high
kitchens
windows
low
window
fast
23
So let’s look at some predictions of the
Full-Computation Hypothesis
Prediction 3:
Kitchens and Windows should be equal.
Why?
Because the base forms are equal, and the plural forms
are simply the addition of two processes:retrieve the
base and add -s.
slow
actual result
kitchens
reaction time
frequency
high
So these two words are inconsistent
withwindows
the Full Computation Hypothesis
kitchen
kitchens
windows
low
window
fast
24
A Re-cap of Full Computation:
frequency
high
Base Frequency is what
matters. It is the frequency that
the base form is accessed from
the lexicon.
kitchens
Processes for SINGULARS
windows
1. Find the base in the lexicon
kitchen
Processes for PLURALS
1. Find the base in the lexicon
window
low
2. Add -s to the singular noun
Comparison
Prediction
Actual Result
1.
Kitchen vs Window
Equal
Equal
2.
Kitchen vs Kitchens
Kitchen is faster
Kitchen is faster
3.
Kitchens vs Windows
Equal
Windows is faster
25
A Re-cap of Full Storage:
Surface Frequency is what
matters. The retrieval time is
directly related to surface
frequency.
frequency
high
windows
kitchen
kitchens
low
window
Comparison
Prediction
Actual Result
1.
Kitchen vs Window
Kitchen is faster
Equal
2.
Kitchen vs Kitchens
Kitchen is faster
Kitchen is faster
3.
Kitchens vs Windows
Windows is faster
Windows is faster
26
Putting the two together
Storage
Prediction
Computation
Prediction
Actual
Result
Kitchen vs
Window
Kitchen is faster
Equal
Equal
Kitchen vs
Kitchens
Kitchen is faster
Kitchen is faster
Kitchen is faster
Kitchens vs
Windows
Windows is faster
Equal
Windows is faster
Comparison
One comparison is evidence for Storage, one comparison is evidence for
Computation, and one comparison is evidence for both.
What we need is a compromise: both Storage and Computation exist in the
lexicon, such that some words are stored and some words are computed.
27
The Dual Route Model
It’s easy to say that some words are stored and others are computed...
The tricky bit is coming up with a theory that explains why certain words are
stored and why certain words are computed:
Singulars must be stored because we have to store something!
High Frequency Plurals are stored because it is more efficient to store
something that you are going to use often.
Low Frequency Plurals are computed because they aren’t used very often. It
is not worth wasting storage space on things that aren’t used very often.
28
Getting our frequencies straight!
Full-Storage Hypothesis:
every word is stored in full in the lexicon
Only Surface Frequency exists under this hypothesis because there is no
such thing as the “base form” of a word. Every word is its own lexeme.
Full-Computation Hypothesis: every morpheme is stored in the lexicon; larger
words are computed as needed
Only Base Frequency exists under this hypothesis. The time for singulars
is determined by base frequency, and the time for plurals is determined
by the base frequency and adding s.
Dual Route Hypothesis:
Singulars and HF plurals are stored, LF plurals
are computed
Both Base Frequency and Surface Frequency exist. Base frequency is
used for singulars, base frequency and add s is used for LF plurals, and
surface frequency is used for HF plurals (because they are stored
separately from singulars).
29
The Dual Route Model
Now we can use the correct types of frequencies to make predictions about the
decisions times for each type of word:
Singulars must be stored because we have to store something!
Consequence:
Decision times for singulars are due to base frequency
High Frequency Plurals are stored because it is more efficient to store
something that you are going to use often.
Consequence:
Decision times for HF plurals are due to surface frequency
Low Frequency Plurals are computed because they aren’t used very often. It
is not worth wasting storage space on things that aren’t used very often.
Consequence:
Decision times for LF plurals are due to base frequency +
adding s
30
The Dual Route Model
singulars are stored (all models need this!)
plurals are stored if they are high frequency
REMEMBER: stored is always
faster than computed!
plurals are computed if they are low frequency
kitchen is singular, so it is stored
its base frequency is high, so it is fast.
kitchens
window is singular, so it is stored
its base frequency is high, so it is fast.
windows
kitchens is LF plural, so it is computed
kitchen
computations are slow, so it is slow.
window
windows is HF plural, so it is stored
its surface frequency is high, so it is fast.
31
Explaining the results with the dual
route model
Comparison
Dual Route Prediction
Kitchen vs
Window
Both are stored, they have equal
base frequencies, so decision
times should be equal
Kitchen vs
Kitchens
Kitchen is stored, Kitchens is
computed, so Kitchen should be
faster
Kitchens vs
Windows
Kitchens is computed, Windows
is stored, so Windows should be
faster
Actual Result
Equal
Kitchen is faster
Windows is faster
32
Conclusion
Full-Storage Hypothesis:
every word is stored in full in the lexicon
Advantage: fewer computations
kitchen
window
Disadvantage: memory cost
kitchens
windows
Full-Computation Hypothesis: every morpheme is stored in the lexicon; larger
words are computed as needed
Advantage: lower memory cost
kitchen
Disadvantage: more computations
Dual Route Hypothesis:
window
s
Singulars and HF plurals are stored, LF plurals
are computed
This is a middle ground:
medium memory cost and medium
number of computations
kitchen
window
s
windows
33