Under Definition 8, when the most recent observation o t is part of an optimal plan for the expected goal g ̂ (based on the previous observation o t−1), confidence is maximised; if the plan has diverged from expectation, confidence is correspondingly reduced. This effect is particularly significant when we consider the special status typically given to the initial state. Recall from Section 3 that the core principle of cost-based goal recognition is that of cost difference ( Eq. 1): the difference between the cost of an optimal plan versus the lowest cost achievable given actions that have been observed actually to have occurred. But to estimate either of those parameters, we need to know which state the agent started from. Now, contemporary models of goal recognition such as that at Section 3 typically make the strong assumption that the initial state is fully observable (e.g., Ramirez and Geffner, 2010; Vered et al., 2016; Pereira et al., 2020). But what if the human observer has forgotten the initial state and is instead referencing their first remembered state? Now the goal recognition system and the human may be trying to solve completely different problems.

What we also learn from this neurologically is that implied movement stimulates brain functioning in much the same way as watching an actual movement. There is no initial state as such. s 0 is the first remembered state. Subsequently, s t is taken to represent the first remembered state at time-step t. In other words, something happens in front of us but because our attention is elsewhere, we don’t register having seen it. Second, magic is often described as either irrational or its own form of rationality. But premodern Europeans who used the term “magic” seemed to have believed that insofar as magic was efficacious, it worked according to the same principles explored by their theology and philosophy. Magic was not a violation of causation, but rather bounded by the same kinds of natural laws that would be explored by scientific experimentation. In this respect premodern magic was rational.It is a magician’s job to manipulate their audience’s beliefs: to find ways of persuading it that the coin is here when really it is there, that you chose the Ace of Spades of your own free will, that the lady really has been sawn in half. Lately, moreover, the practice of magic has been analysed with renewed rigour in terms of the psychological principles at work, giving rise to an emerging field of study dubbed by Kuhn (2019) amongst others, the “science of magic”. These—and related—principles provide both the inspiration for XGR and a practical demonstration of its effectiveness. Goal recognition systems use probabilistic reasoning to predict what an observer is most likely to understand from a given sequence of actions; informally, magicians have been making similar predictions for generations, performing sequences of actions such that human observers reliably draw erroneous conclusions. Importantly, magicians can rely on the conclusions people will draw. Magic works by exploiting flaws in human reasoning that are predictable; and because they are predictable, they are susceptible to probabilistic/mathematical interpretation. The past few years have seen a resurgence of interest in the scientific study of magic. Despite being only a few years old, this “new wave” has already resulted in a host of interesting studies, often using methods that are both powerful and original. These developments have largely borne out our earlier hopes ( Kuhn et al., 2008) that new opportunities were available for scientific studies based on the use of magic. And it would seem that much more can still be done along these lines. Thus, o ⃗ t may represent a different observation sequence at every time-step. Typically, the sequence is first-in-first-out. That is, oldest observations are forgotten first. If an observation is particularly intense, however (i.e., has excessive initial magnitude), it may persist long after more standard observations have been forgotten so that an observation sequence at one time-step may even have different cardinality from that at another. 5.5 The Ruse

We conclude this section by mentioning two lessons that have already been learnt: one already applied routinely in the context of goal recognition, the other already applied in a motion-planning domain. MIT Press began publishing journals in 1970 with the first volumes of Linguistic Inquiry and the Journal of Interdisciplinary History. Today we publish over 30 titles in the arts and humanities, social sciences, and science and technology.

ORIGINAL RESEARCH article

Elisabeth Loftus, Distinguished Professor, University of California, Irvine, and author of Eyewitness Testimony The ruse is a plausible, but untrue, reason, or action conveying a reason, for concealing the true purpose for doing something” which “makes it possible for the magician to do an unnatural thing naturally” ( Fitzkee, 1945). The actions involved in a ruse may receive attention at the time they take place (everyone saw the magician handle the cardboard sleeve around the bullets, the container of pens, the wine glass, the plate) but what he did with each prop seemed to have a valid purpose at the time and is likely to be forgotten once that purpose is complete. What is surprising here is that spectators, who are in a hyper-vigilant mode when watching a magic performance, are so willing to disregard and forget incidental events. This is to do with the way memories are stored and retrieved. Whereas once it was thought our memories were laid down almost like video recordings ( Chabris and Simons, 2009), available to “replay” under hypnosis, for example; we now believe that each time we recall a memory we reconstruct it from mental representations that are highly abstracted and edited down according to perceived relevance ( Loftus and Palmer, 1996). Sometime in the 15 th century, a group of university students got together in the town of Oberdorf in Bavaria to do what students have done the world over: drink beer. After they had been at it for a while, they decided that whoever fetched the next round wouldn’t have to pay for it. One student went to get beer, but on opening the door, he saw an unusually dark fog and he refused to go out. Then, a foolhardy member of the group boasted, “Even if the Devil was present, I shall fetch the drinks.” To their consternation, those in attendance all saw the man borne aloft into the air, shouting as he was carried out the door by an invisible demon in the direction of further libations. To perform human-like reasoning, the quality of stored observations should not be fixed; it should decay over time.