![]() We propose that a core component of any such reasoning system is a type theory: a formal imposition of structure on the kinds of computations an agent can perform, and how they're performed. While understanding how people come up with new ideas, thoughts, explanations, and hypotheses that obey the basic constraints of a novel search space is of central importance to cognitive science, there is no agreed-on formal model for this kind of reasoning. The thought that one would respond "After 4pm" to "What would you like to eat" is either a joke or a mistake, and seriously entertaining it as a lunch option would likely never happen in the first place. Humans can generate reasonable answers to novel queries (Schulz, 2012): if I asked you what kind of food you want to eat for lunch, you would respond with a food, not a time. 0001), showing that this dissociation becomes stronger when participants are explic- itly instructed to optimize representational. 0001), despite programs in the Efficient Hierarchy condition being significantly shorter than those in the Default Hierarchy condition (t = 5.11, p <. Further, the flattened versions of solutions participants generate in the Efficient Hierarchy condition are also significantly longer than those generated in the Default Hierarchy condition (t = 4.60, p <. ![]() This dissociation reflects the trade-off between action and representational efficiency built in to the solutions and sug- gests that participants do not simply optimize action effi- ciency when generating hierarchical solutions. 0001) and Default Flat conditions (Default Hierarchy: t = 3.76, p <. 001 Efficient Hi- erarchy: t = 6.49, p <. The programs that partici- pants write in the Hierarchical conditions are, however, sig- nificantly shorter than the flat solutions provided in the Ef- ficient (Default Hierarchy: t = 3.47, p <. 0001) and Default Flat conditions (Default Hierarchy: t = 4.00, p <. Aggregating across all puz- zles, the mean normalized flattened length in the Default and Efficient Hierarchy conditions is significantly greater than in the Efficient Flat (Default Hierarchy: t = 6.55, p <. Figure 4 shows the mean lengths of the flattened versions of programs participants generate, normalized per puzzle by the min and max flat lengths. Thus, if participants generate hierarchical solutions by minimizing program complexity, we expect to see longer flattened solutions to these puzzles. Further, all of the puzzles we have used (with the exception of puzzle 2) are designed so that the flat version of the best algorithmic solution is longer than the best flat solution. ![]() If participants optimize efficiency in the number of actions their program generates, we would expect to see no difference in the length of the flattened solutions given by participants in the Hierarchy condition and participants in the Flat conditions. For example, the flattened program in Figure 1 consists of 38 instructions, whereas the hierarchical program consists of 13. ![]() A flattened pro- gram consists of all actions that a hierarchical program gener- ates. We address this question by an- alyzing the length and compressibility of the "flattened" ver- sion of participants' hierarchical programs. of flattened programs We now ask whether the hi- erarchical solutions given by participants optimize efficiency in action or representation. ![]()
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