Study: Kids have 'and/or' problem despite sophisticated reasoning

May 23, 2016 by Peter Dizikes
“Children seem to interpret disjunction like conjunction,” observes MIT Linguistics Professor Danny Fox. However, Fox adds, although “it has been claimed children are very different from adults in the interpretation of logical words,” the study’s larger implication is almost the opposite — namely that “the child is [otherwise] identical to the adult, but there is a very small parameter that distinguishes them.” Credit: Christine Daniloff/MIT

Imagine, for a moment, you are a parent trying to limit how much dessert your sugar-craving young children can eat.

"You can have cake or ice cream," you say, confident a clear parental guideline has been laid out.

But your children seem to ignore this firm ruling, and insist on having both cake and ice cream. Are they merely rebelling against a parental command? Perhaps. But they might be confusing "or" with "and," as children do at times, something studies have shown since the 1970s. What seems like a restriction to the parent sounds like an invitation to the child: Have both!

But why does this happen? Now a study by MIT linguistics professors and a team from Carleton University, based on an experiment with children between the ages of 3 and 6, proposes a new explanation, with a twist: In examining this apparent flaw, the researchers conclude that children deploy a more sophisticated mode of logical analysis than many experts have previously realized.

Indeed, say the linguists, children use almost entirely the same approach as adults when it comes to evaluating potentially ambiguous sentences, by testing and "strengthening" them into sentences with more precise meanings, when disjunction and conjunction ("or" and "and") are involved.

While using this common approach, however, children do not test how a sentence would change if "and" were directly substituted for "or." This more modest procedural problem is what leads to the confusion about cake and ice cream.

"Children seem to interpret disjunction like conjunction," observes Danny Fox, the Anshen-Chomsky Professor in Language and Thought at MIT and co-author of a paper detailing the study. However, Fox adds, although "it has been claimed children are very different from adults in the interpretation of logical words," the study's larger implication is almost the opposite—namely that "the child is [otherwise] identical to the adult, but there is a very small parameter that distinguishes them."

Quirky as this finding seems, it confirms a specific prediction Fox and some other researchers had made, based on previous studies in formal semantics (the area of linguistics that investigates the logic of natural language use). As such, the study reinforces what we know about the procedures both children and adults deploy in "and/or" matters.

"There's a certain kind of computation we can now say both children and adults do," says Raj Singh PhD '08, an associate professor of cognitive science at Carleton University and the lead author of the new report.

The paper, "Children interpret disjunction as conjunction: Consequences for theories of implicature and child development," is being published in the journal Natural Language Semantics. The co-authors are Singh; Fox; Ken Wexler, emeritus professor of psychology and linguistics at MIT; Deepthi Kamawar, an associate professor of psychology at Carleton University; and Andrea Astle-Rahim, a recent PhD graduate from Carleton University.

What adults do: the two-step

To understand how children conflate "or" with "and," first consider how adults normally clarify what sentences mean. Suppose you have a dozen cookies in a jar on your desk at work, and go to a meeting. When you come back, a colleague tells you, "Marty ate some of the cookies."

Now suppose you find out that Marty actually ate all 12 cookies. The previous sentence—"Marty ate some of the cookies"—may still be true, but it would be more accurate to say, "Marty ate all of the cookies."

To make this evaluation, adults compute "scalar implicatures," a technical phrase for thinking about the implications of the logical relationship between a sentence and its alternatives. For "Marty ate some of the cookies," there is a two-step computation. The first step is to think through some alternatives, such as what happens if you substitute "all" for "some" (leading to "Marty ate all of the cookies"). The second step is to realize that this alternative spells out a specific new meaning—that all 12 cookies have been eaten, not just a few of them.

We then realize the sentence "Marty ate some of the cookies" more accurately means: "Marty ate some, but not all, of the cookies." And now we have a "strengthened" version of the first sentence.

The same process applies to the sentence, "Jane ate cake or ice cream." The sentence is true if Jane ate one or the other, and still technically true if she ate both. But once we compute the scalar implicatures, we realize that "Jane ate cake or ice cream" is a "strengthened" way of saying she ate one or the other, but not both.

Fox has conducted extensive research over the last decade formalizing our computations of scalar implicatures and identifying areas where tiny differences in the logical "space of alternatives" can have far-reaching consequences. The current paper stems in part from work Singh pursued as a doctoral student collaborating with Fox at MIT.

Why "or" and "and" merge for children

The research team conducted the study's experiment by testing 59 English-speaking children and 26 adults in the Ottawa area. The children ranged in age from 3 years, 9 months, to 6 years, 4 months. The linguists gave the subjects a series of statements along with pictures, and asked them to say whether the statements were true or false.

For instance: The children were shown a picture with three boys holding an apple or a banana, along with the statement, "Every boy is holding an apple or a banana," and then asked to say if the statement was true or false. The children were asked to do this for a full range of scenarios—such as one boy holding one type of fruit and two boys holding the other—along with a varying set of "and/or" statements. The researchers repeated five sets of such trials, with the pictures changing each time.

The results suggest that children are computing scalar implicatures when they evaluate the statements—but they largely do not substitute disjunctions and conjunctions when testing out the possible meaning of sentences, as adults do.

That means when children hear "cake or ice cream," they are generally not replacing "or" in the phrase with "and," to test what would happen. Without that contrast, the children still "strengthen" the meaning of "or," but they strengthen it to mean "and." Thus "or" and "and" can blur together for children.

"They [children] don't use 'cake and ice cream' as an alternative," Fox says. "As a result, 'cake or ice cream' is expected, if we are right about the nature of the computation, to become 'cake and ' for the children."

And while we tend to think children are wrong to draw that conclusion, it is still the result of computing scalar implicatures—it just happens that, as Singh observes, those computations create divergent outcomes for children and adults.

A universal process

Other scholars say the study is a significant piece of research. Emmanuel Chemla, a scholar at CNRS in France, who has conducted previous research in this area, notes that the study's "highly counterintuitive prediction" appears to be "entirely correct." (Disclosure: Chemla has collaborated with some of the authors previously.)

Chemla also praises the study's blend of formal semantic analysis with its experimental structure, stating that this kind of interdisciplinary approach is "often highly praised and called for, but rarely taken to such a high level." And he adds that in the future, it will be "important to develop a full theory of how children arrive at this stage, and how they move from it to an adult-like competence."

The researchers say they agree with the need to examine that transition to the adult pattern of strengthening. In the meantime, they hope colleagues will consider the additional evidence the study provides about the formal logic underlying our language use.

"The computational system of language is actually telling us how to do certain kinds of thinking," Wexler suggests. "It isn't us just trying to [understand] things pragmatically."

Additionally, the scholars believe evidence from other languages besides English supports their conclusions. In both Walpiri, a language of indigenous Australians, and American Sign Language, there is a single connective word that functions as both "or" and "and" and appears subject to the strengthening process identified for children. And, Singh notes, linguists are now replicating the study's findings in French and Japanese.

In general, Fox observes, across languages, and for children and alike, "The remarkable logical fact is that when you take 'and' out of the space of alternatives, 'or,' becomes 'and.' This, of course, relies on the nature of the computation that we've postulated, and, hence, the results of the study provide confirmation of a form that I find rather exciting."

So, yes, your may not understand what you mean about dessert. Or perhaps they are just being willful. But if they confuse "or" with "and," then they are not being childish—at least not in the way you may think.

Explore further: A bigger appetite for dessert—not salty foods—predictor of body mass index for low income children, study suggests

More information: Paper: "Children interpret disjunction as conjunction: Consequences for theories of implicature and child development."— … on-April-14-2016.pdf

Related Stories

A bigger appetite for dessert—not salty foods—predictor of body mass index for low income children, study suggests

April 18, 2016
Some say there's always room for dessert - but those who follow that motto young may be more likely to gain unhealthy weight, a new study suggests.

Study concludes parents mixing languages has no impact on children's language development

June 12, 2015
Many adults speak more than one language, and often "mix" those languages when speaking to their children, a practice called "code-switching." An eye-opening study by researchers in the Department of Hearing and Speech Sciences ...

Can white kids grow up to be black? Some preschoolers think so

May 20, 2016
White preschoolers often believe a person's race can change over time. In fact, these 5- to 6-year-olds may think they can grow up to become a black adult, according to a new University of Michigan study.

BEST: Innovative technique to facilitate language development in children

November 28, 2012
A Newcastle University expert has won a prestigious award for her work to help young children with language difficulties. Dr Cristina McKean and Drs Sean Pert and Carol Stow, who both work for Pennine Care NHS Foundation ...

Most US adults say today's children have worse health than in past generations

April 18, 2016
More than half of adults believe children today are more stressed, experience less quality family time and have worse mental and emotional health than children in past generations, according to the C.S. Mott Children's Hospital ...

Recommended for you

A walk at the mall or the park? New study shows, for moms and daughters, a walk in the park is best

November 17, 2017
Spending time together with family may help strengthen the family bond, but new research from the University of Illinois shows that specifically spending time outside in nature—even just a 20-minute walk—together can ...

Risk of distracted driving predicted by age, gender, personality and driving frequency

November 17, 2017
New research identifies age, gender, personality and how often people drive as potential risk factors for becoming distracted while driving. Young men, extroverted or neurotic people, and people who drive more often were ...

When male voles drink alcohol, but their partner doesn't, their relationship suffers

November 17, 2017
A study of the effect of alcohol on long-term relationships finds that when a male prairie vole has access to alcohol, but his female partner doesn't, the relationship suffers - similar to what has been observed in human ...

Spanking linked to increase in children's behavior problems

November 16, 2017
Children who have been spanked by their parents by age 5 show an increase in behavior problems at age 6 and age 8 relative to children who have never been spanked, according to new findings in Psychological Science, a journal ...

Multiplayer video games: Researchers discover link between skill and intelligence

November 15, 2017
Researchers at the University of York have discovered a link between young people's ability to perform well at two popular video games and high levels of intelligence.

Generous people give in a heartbeat—new study

November 15, 2017
Altruistic people are said to be "kind hearted" - and new research published in the journal Scientific Reports shows that generous people really are more in touch with their own hearts.


Adjust slider to filter visible comments by rank

Display comments: newest first

4.3 / 5 (4) May 23, 2016
Now suppose you find out that Marty actually ate all 12 cookies. The previous sentence—"Marty ate some of the cookies"—may still be true, but it would be more accurate to say, "Marty ate all of the cookies."

Or Marty ate tow and Ed ate the rest.

But seriously: The article highlights something that can be seen in the comment sections over and over again. People jumping to all or nothing conclusions (black/white thinking) where it isn't warranted. Logical thinking isn't as easy as it may sound. Just take one of the many logician tests on the web and find out.
not rated yet May 23, 2016
Would you like cake or ice cream => I'd like them both => true or true => true 'yes please'. English needs a natural language word for 'exclusive or' which is the flavour of 'or' that we actually mean when we say 'you can have cake or ice cream' not the common 'or' of logic. Arguably the kids are right and the adults are jumping to conclusions in this case.
5 / 5 (1) May 23, 2016
Noted. I'll be using "xor" around my children.
not rated yet May 23, 2016
I hope they tested this with more than just cake and ice cream, because cake and ice cream always go together. (grin)

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.