This paper describes a formal framework for perceptual categorization that can account for the salient qualitative predicates human observers are willing to ascribe to a closed class of objects, and consequently the simple groupings they can induce from small sets of examples. The framework hinges on the idea of a generative process that produces a given set of objects, expressed as a sequence of group-theoretic operations on a primitive element, thus ascribing algebraic structure to perceptual organization in a manner similar to Leyton (1984). Putatively, perceivers always seek to interpret any stimulus as a formally generic result of some sequence of operations; that is, they interpret each object as a typical product of some generative process. The principle formal structure is a "mode lattice," which a) exhaustively lists the qualitative shape predicates for the class of shapes, and b) defines the inferential preference hierarchy among them. The mechanics are worked out in detail for the class of triangles, for which the predicted qualitative features include such familiar geometric categories as "scalene," "isosceles," and "right," as well as more "perceptual" ones like "tall" and "short." Within the theory it is possible as well to define "legal" vs. "illegal" category contrasts; a number of examples suggest that our perceptual interpretations tend to regularize the latter to the former.

When integrating information in real time from multiplemodalities or sources, such as when navigating with the helpof GPS voice instructions along with a visual map, a decision-maker is faced with a difficult cue integration problem. Thetwo sources, in this case visual and spoken, have potentiallyvery different interpretations or presumed reliability. Whenmaking decisions in real time, how do we combine cues com-ing from visual and linguistic evidence sources? In a sequenceof three studies we asked participants to navigate through aset of virtual mazes using a head-mounted virtual reality dis-play. Each maze consisted of a series of T intersections, ateach of which the subject was presented with a visual cue and aspoken cue, each separately indicating which direction to con-tinue through the maze. However the two cues did not alwaysagree, forcing the subject to make a decision about which cueto “trust.” Each type of cue had a certain level of reliability(probability of providing correct guidance), independent fromthe other cue. Subjects learned over the course of trials howmuch to follow each cue, but we found that they generallytrusted spoken cues more than visual ones, notwithstandingthe objectively matched reliability levels. Finally, we showhow subjects’ tendency to favor the spoken cue can be mod-eled as a Bayesian prior favoring trusting such sources morethan visual ones.

How effective do observers expect other problem solvers to be? What makes a decision seem "human"?" We addressed this question in the context of the Traveling Salesman Problem (TSP), a decision problem in which a perfectly optimal solution is intractable, but for which various kinds of approximate solutions are available. We conducted a series of experiments involving both "production tasks" in which we asked subjects to solve the TSP, and "perception tasks", in which we asked subjects to judge others' solutions to the TSP, rating them for intelligence or humanness. Results suggest that observers expect human solutions to be less optimal than algorithmic solutions: observers expect human problem solvers to exhibit a combination of local and global solution criteria, and to use a short look-ahead window when choosing a solution. These results shed light on human models of other humans' minds, a fundamental problem in social interaction and robotics.

Although the Traveling Salesman Problem (TSP) is an NP-hard problem, human schedulers can find strategies that are comparable if not better than existing algorithms. However, it is still unclear what heuristics they adopt in order to select an approximate solution (Schaefer, 2018). In solving a navigational problem in 3D, the directional heading is an essential factor because changes of direction require additional energy expenditure. In our study, we focus on the connection between local choices minimizing distance and local choices minimizing the turning angle. We then examine human solutions to the TSP in light of the tradeoff between local and global optimization of distance and turning angle. We conducted two experiments showing that while subjects were more likely to move to the nearest node when they plan the next step ahead, they also take the turning angle into consideration and overall adopt a strategy that combines local and global heuristics.