**Inference from Exclusion: A More Complete View**

Studies to determine how nonhumans use inferential knowledge to make decisions commonly involve something call the “2-cup task.” The basic idea is to give the subjects two cups, A and B, let them know that nothing is in A, and see if they will infer that a treat is in B (“A or B? Not A, therefore B”).

In the simplest version, a subject sees the cups, a barrier is erected in front of the cups, the experimenter shows the subject that he or she is hiding a treat behind the barrier, then removes the barrier, shows that A is empty and asks the subject to find the treat. In a slightly more complicated version, a subject sees the experimenter hide two treats of equal value, one in A and one in B. The experimenter then erects the barrier, stealthily removes the treat from A, lifts the barrier, shows she is eating the treat herself, and then asks the subject to find the other treat.

One or both of these tasks, with appropriate controls for various types of cuing or to rule out non-inferential (i.e., associative) ways of achieving the correct result, have been given to various species—including children—and all species that have been tested succeed at least to some extent (reviewed in Voelter & Call, 2017). African grey parrots actually perform exceedingly well (Pepperberg et al., 2013). However, as is often the case in studies on cognition, someone thinks the task through in bit more detail, and argues that the task doesn’t really fully test the concept or concepts under study—here, the understanding of the combination of the logical “or” and “not” as well as the difference between certainty and mere possibility.

**2 Cups**

Researchers arguing against the 2-cup task were my colleagues at Harvard—Susan Carey and her graduate student, Shilpa Mody (Mody & Carey, 2016). They claimed that in the 2-cup task, subjects might not be thinking “Definitely A or B. Not A, definitely B!” but something more like “Maybe A, maybe B? Not A, still maybe B?” and choosing B by default. They set out to test this possibility in children; I and my students decided to see how our parrot, Griffin (who had aced the 2-cup task) would perform (Pepperberg et al., 2018). Carey and Mody designed two tasks—a 3-cup task to examine the difference between certainty and possibility, and a 4-cup task to examine inferential reasoning.

**3 Cups**

In the 3-cup task, subjects see one cup on one side (A) and two cups on the other side (B, C) and are shown that they are all empty. A barrier is erected, and two treats are hidden—one on each side. The barrier is removed, and the subjects are asked to find a treat. If they understand the task, they should go to A on every trial, because a treat *must* be in A, and there is only a 50-50 chance of finding the treat in the other side (B or C). Several trials are given each subject. If a subject could respond merely by chance at 33% (all cups being equally valid), all the children tested (2½-, 3-, 4-, and 5-year-olds) succeeded. However, if chance is considered 50%—the choice between the certain side and the uncertain side—the 2½-year-olds failed and the other children scored only between ~60-70%. Interestingly, Griffin was at about 90%! Also interesting was that on a very similar task, chimpanzees scored at the same level as the 2-½-year-olds (Hanus & Call, 2014). Although the 3-cup task didn’t test inferential abilities, the data suggested that subjects that succeeded on the 2-cup task didn’t truly understand the difference between “definitely” and “probably”.

**4 Cups**

In the 4-cup task designed to test inference (see figure below), subjects see two cups on one side (A,B) and two cups on the other side (C,D) and, again, are shown that they are all empty. A barrier is erected, and, again two treats are hidden, one on each side. The barrier is removed and the subjects are shown that one cup on one side is empty (e.g., A). If they understand the task, they should *infer* that a treat has 100% chance of being in B, only a 50-50 chance of being in C or D, and choose B. As before, several trials are given each subject. With chance set at 33% (no child chose the cup that had been shown to be empty), 2-½-year-olds failed and the older children chose the correct cup only ~60-75% of the time. Our parrot Griffin again outperformed the children, scoring close to 85%. This task has not been given to chimpanzees, and we don’t know how they might score. However, given their scores on the 3-cup task, they might again score like the 2½-yr-old children and fail. So, it looked as though Griffin was even better than children (and possibly apes) and that he truly understood inference.

However, there was one not-so-small problem. The very many children tested had each been given only four trials each, too few for them to learn the task. Griffin, though, had been given several dozen trials in order for us to acquire the same statistical power. Although Griffin didn’t appear to do better as the test proceeded, it was possible that he had somehow learned simply to go to the cup next to the one that had been shown to be empty—that is, that he had ignored one set of cups (C,D) and just focused on the two most relevant ones (A,B). To determine if that were the case, we had to perform two more experiments, which for reasons that will soon become evident, we called “gambling” trials.

**A Gamble With Skittles**

In the first experiment, we repeated the 4-cup task, but now included eight trials in which we hid nothing on one side (e.g., the A-B side). We then showed Griffin that nothing was in one of the cups on that side (A). If he understood the task, wanted a reward, and wasn’t simply going to the cup next to the one that was empty, he would have to gamble and choose one cup from the other side at random (C or D). And that’s exactly what he did on the gambling trials. He wasn’t very happy, because he often didn’t get a reward, but he understood the task. (On one trial, he actually chose the empty cup—we think he did so out of frustration, so that the trial would end and he could be given a regular trial where he knew he could get his reward by inferring, rather than guessing, where his treat would be!) Of course, one could still argue that he was simply avoiding the empty side.

Hence the second experiment. Here we also repeated the 4-cup task, but now included eight trials in which we hid a Skittle^{©} on one side. We showed him the empty cup on the side that had a nut, rather than a candy. (NB: These candies are not healthy treats, but are absolutely Griffin’s favorite food. We figured a few such candies would not be too bad for him and might really motivate him to gamble.) So, if Griffin understood the task, he knew he had a 100% chance of a nut, and a 50-50 chance of his favorite candy. He did gamble several times, showing that he wasn’t simply going to the cup next to the empty cup. Note that if he gambled and lost, he stopped gambling for a few trials, but he gambled enough to show that the effect was real.

**A Parrot’s Understanding**

So, our findings have two conclusions. First, the 2-cup task demonstrates capacities that are necessary for inference, but not sufficient for full understanding. Second, an African grey parrot understands the task at levels somewhat above those of 5-year-old children. We can’t claim that Griffin has complete understanding of the logical “or” and “not”—our data are consistent with that claim, but cannot prove it for various other reasons. We are, however, engaging in some additional studies to see how far Griffin’s understanding extends.

Hanus, D. & Call, J. (2014). When maths trumps logic: probabilistic judgements in chimpanzees. *Biol. Lett*. *10*: 20140892

Mody, S. & Carey, S. (2016). The emergence of reasoning by the disjunctive syllogism in early childhood. *Cognition* 154: 40-48.

Pepperberg, I.M., Gray, S.L., Cornero, F.M., Mody, S., & Carey, S. (2018). Logical reasoning by a Grey parrot (*Psittacus erithacus*)? A case study of the disjunctive syllogism. *Behaviour* DOI:10.1163/1568539X-00003528.

Pepperberg, I.M., Koepke, A., Livingson, P., Girard, M. & Hartsfied, L.A. (2013). Reasoning by inference: further studies on exclusion in Grey parrots (*Psittacus erithacus*). *J. Comp. Psychol*. *127*: 272-281.

Voelter, C.J. & Call, J. (2017). Causal and inferential reasoning in animals. In: *APA handbook of comparative psychology* (Call, J., Burghardt, G., Pepperberg, I.M. & Zentall, T.R., eds). American Psychological Association Press, Washington, DC, p. 643-671.