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The Meaning of Every
Every bear is an animal
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The Meaning of Some Part I
Some bears are white animals
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The Meaning of Some Part II
Some bears are animals
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The Meaning of No
No frog is a white animal
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Exclusive OR
Point to a frog or a bear (but not both)
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Inclusive OR
Point to a frog or a bear (or both)
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The Meaning of AND
Point to a frog and a bear
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Truth Tables
A, B A and B A orEXCL B A orINCL B T T
T F T T F F
T T F T F T T F
F F F F
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Subsets and Supersets
A, B A and B A orINCL B T T
T T T F F T F T
F T F F F
F Whenever A and B is True, so is A orINC B But
A orINC B is also True in other circumstances
So A and B is True in a subset of the
circumstances corresponding to A orINC B. Using
logical notation A and B ? A orINC
B
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Logical Words Some and Or

• Judgments about the truth of sentences with
  logical words such as some and or depend on two
  systems
• semantic knowledge
• (permitting judgments of truth in felicitous
  contexts)
• pragmatic knowledge
• (e.g. Grices Principle of Cooperation,
  articulated into specific maxims of
  relevance, quantity, etc.)
• Prediction As soon as children become
  cooperative, they will display adult-like
  behavior in their use of logical words

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Scalar Implicatures
Scalar Terms some, many, most, every
The truth conditions for some and every are
related E.g., if every (also, many, most) boy
swam, then, some boy swam
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Scalar Implicatures
The truth conditions for some and every are
in a subset/superset relation
Some boy swam is true in many
circumstances Circumstances every boy
swam ... two boys swam one boy
swam Every boy swam is true in just one of
these circumstances Circumstance every boy
swam
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Scalar Implicatures
Scalar Terms or, and
The truth conditions for and and or are also in a
subset/superset relation Fred bought a
hamburger and a hot dog Fred bought a
hamburger or a hot dog
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Semantics of Logical Expressions
Entailment A sentence S1 entails another
sentence, S2, iff S2 is true in a superset of
circumstances corresponding to S1
S1 Fred bought a hamburger and a hot dog
entails S2 Fred bought a hamburger or a hot
dog
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Semantics of Logical Expressions
Entailment A sentence S1 entails another
sentence, S2, iff S2 is true in a superset of
circumstances corresponding to S1
S1 Every boy swam entails S2 Some boy
swam
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Scalar Implicatures
Information Strength If a sentence S1
asymmetrically entails another sentence, S2, then
S1 makes a stronger statement than S2
S1 Fred bought a hamburger and a hot dog S2
Fred bought a hamburger or a hot dog
Because S1 entails S2, S1 makes a stronger
statement
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Scalar Implicatures
Strength If a sentence S1 entails another
sentence, S2, then S1 makes a stronger statement
S1 Every boy swam makes a stronger
statement than S2 Some boy swam
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Pragmatics of Logical Expressions
Co-operation Use a sentence that makes the
strongest statement that is consistent with what
you know to be true
S1 Fred bought a hamburger and a hot dog
makes a stronger statement than S2 Fred
bought a hamburger or a hot dog If you know S1
to be true, then do not use S2 Use S2 only if you
are uncertain that S1 is true
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Pragmatics of Logical Expressions
Co-operation Use a sentence that makes the
strongest statement that is consistent with what
you know to be true
S1 Every boy swam makes a stronger
statement than S2 Some boy swam If you know
S1 to be true, then do not use S2 Use S2 only if
you are uncertain that S1 is true
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Pragmatics of Logical Expressions
Co-operation Use a sentence that makes the
strongest statement that is consistent with what
you know to be true
There was pizza or ice cream at the party
There will be pizza or ice cream at the
party A scalar (conversational) implicature.
If you know there was pizza and ice cream, then
using or instead of and is odd. Use of or is
felicitous in circumstances of uncertainty. A
or B conversationally implies not A and B
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Pragmatics of Logical Expressions
Co-operation Use a sentence that makes the
strongest statement that is consistent with what
you know to be true
Some boy swam Some boy will be
swimming A scalar (conversational) implicature.
If you know every boy swam, then using some
instead of every is odd/infelicitous. some N
VP conversationally implies not every N VP
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Entailments

• (1) Some student brought wine and cheese
• (2) Some student brought wine and some student
  brought cheese
• (1) entails (2) but not vice versa
• Adults see easily that if (2) is true, (1) isnt
  necessarily true
• They have some difficulty seeing that if (1) is
  true, (2) is also true

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Spelling out the Entailment
(1) Some student brought wine and cheese(2) Some
student brought wine and some student brought
cheese The following reasoning helps adults see
that (1) entails (2) Look, if some student
brought wine and cheese, then (a) is certainly
true moreover (b) is certainly true (a) Some
student brought wine (b) Some student brought
cheese But if the two sentences (a) and (b) are
true separately, then their conjunction must
also be true Some student brought wine and
some student brought cheese
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The Implicature of Disjointness
Some student brought wine and some student
brought cheese The implicature of disjointness
arises from two occurrences of the indefinite
NP, some N. If the speaker knows that the same
person performed both actions, there is a more
cooperative way of saying so Some student
bought wine and cheese
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The Disjointness Implicature

• The implicature can be suspended in certain
  contexts, e.g., when there is uncertainty about
  the outcome
• In such contexts, it is easy to see that (1)
  entails (2)

Suppose theres going to be a party at Johns
house. John says I expect that some
student will bring Coke, some student will
bring wine, and some student will
bring cheese.
Actual Outcome At the party, one student brings
coke, and somebody else, say, Mary, brings wine
and cheese. Question Was John right?
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Or The Scalar Implicature
Disjunction (or) triggers a scalar implicature
in certaincontexts. For example, if you are
instructed to Pick a red circle or a blue
triangle out of the box. What would you do?
Pick just one. Why? Because if the speaker
intended for you to pick both, she would have
said Pick a read circle and a blue triangle
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Semantics and Pragmatics Or

• Semantics
• The semantics of disjunction or is such that
  A or B is true if A is true or B is true, or both
• The semantic operator or corresponds to the
  inclusive interpretation, not the exclusive
  interpretation
• Pragmatics
• The use of A or B triggers a scalar implicature
  in certain contexts the implicature is not both
  A and B
• It is more cooperative to use A and B in such
  contexts

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Conversational Implicatures

• The indefinite NP some N triggers a scalar
  implicature and a disjointness implicature in
  certain contexts
• The disjunction operator or triggers a scalar
  implicature in certain contexts
• These contexts which trigger the implicatures
  will be called implicature raising contexts

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When the Implicature is NOT Raised
The scalar implicature does not arise in many
contexts,which we can call implicature erasing
contexts 1. Conditions of Uncertainty Making a
Bet Ill bet you five dollars John will put a
red circle or a blue triangle into the
box Suppose John puts both into the box. Do I
win or lose the bet? If I win, or has been
assigned the inclusive reading.
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Implicature Erasing Contexts
The scalar implicature does not arise in certain
contexts 2. Conditions of Uncertainty Making a
Prediction I predict that John will put a
red circle or a blue triangle into the
box Suppose John puts both into the box. Was I
right? If so, or has been assigned the inclusive
reading.
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When the Implicature is NOT Raised
The scalar implicature does not arise in certain
contexts, 3. Disapproval I forbid you to
eat noodles or shrimp This means that I forbid
you from eating either one. (Inclusive)
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Implicature Erasing Contexts
The scalar implicature does not arise in certain
contexts 4. Linguistic When or is inside the
scope of NEGATION John didnt put a red
circle or a blue triangle into the
box Entails that John put neither one into the
box. (Inclusive)
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Implicature Erasing Contexts
The scalar implicature does not arise in certain
contexts 5. Linguistic When or is inside the
scope of the Universal Quantifier Every
soldier is holding a cat or a dog. This is true
if every soldier is holding a pet, some cats and
some dogs. (Inclusive) NOT It is a cat that
every soldier is holding or it is a dog that
every soldier is holding.
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Implicature Erasing Contexts
The scalar implicature does not arise in certain
contexts 6. Minimum Requirements (Conditional
Statements) If there is a red circle or a blue
triangle on the table, then put a coin into the
box Suppose both objects are on the table. The
listener puts a coin into the box, right?
(Inclusive)
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Implicature Erasing Contexts
The scalar implicature does not arise in certain
contexts 7. Minimum Requirements
(Advertisements) Wanted Someone with a PhD in
Computer Science or programming
skills Suppose the applicant has a PhD and
programming skills. Is she qualified for the
job? (Inclusive)
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Childrens Logical Reasoning

• These observations led us to reexamine the
  conclusion that childrens logical reasoning does
  not conform to classical logic
• Previous studies which drew this conclusion used
  implicature raising contexts
• The findings leave open the possibility that
  children know both
• The semantics of logical operators and The
  pragmatic conditions that govern their use

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Childrens Logical Reasoning Revisited

• Hypothesis Children will behave differently in
  implicature raising contexts and implicature
  erasing contexts
• Research Strategy Test children in both contexts
  to see
• If childrens interpretation of some and or
  conforms to classical logic
• If children know principles of pragmatics

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Experimental Design
Prediction Children will behave differently in
implicature raising and in ones that suspend
implicatures Current Research 1. Descriptions of
Events Description Mode versus 2. Conditions
of Uncertainty - Prediction mode - Betting
Mode3. Linguistic Conditions (Inside scope of
NEGATION, UQ)4. Conditions that Establish
Minimum Requirements - Conditionals
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Truth Value Judgment Task

• Puppet and child watch a story that is acted-out
  with toys and props
• The puppet tries to describe the events of the
  story
• The child judges the puppets description of
  the story as true or false Yes No
• If the child judges the puppets description of
  the story to be false, she is asked to explain
  to the puppet What really happened (to
  check understanding of the events)

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Methodology
Description Mode Kermit the Frog describes the
story after the acted-out vignettes Prediction
Mode Child hears part of the story, then the
magician puppet predicts how it will end. The
prediction is repeated at the conclusion of the
story, if necessary
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Experiment 2 Or Description Mode

• A troll decides what to eat for lunch
• The troll considers 3 options hamburger, slice
  of pizza, ice-cream
• Troll chooses pizza and ice-cream, but not
  hamburger
• Kermit I know what happened. The troll ate a
  slice of pizza or an ice-cream
• Results 13 children tested in this mode
  judged Kermit to be incorrect on 83 of trials

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Experiment 2 Or Prediction Mode

• Similar story to Description Mode
• A troll decides what to eat for lunch
• Considers 3 options hamburger, slice of pizza,
  ice-cream
• Magician I know what will happen. The troll
  will eat a slice of pizza or an ice-cream
• Story finishes with troll eating pizza and ice
  cream
• Results 8 children tested in this mode
  judged the magician to be correct on 100 of
  trials

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Conclusions

• Preliminary results
• Childrens semantic knowledge is consistent
  with classical logic
• Children are sensitive to certain pragmatic
  principles