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Three experiments investigated the frame of reference used in memory to represent vertical spatial layouts perceiv-able from a single viewpoint. We tested for the selection of three different reference systems: the body orientation, the visualvertical of the surrounding room, and the direction of gravity. Participants learned and retrieved differently colored objects ona vertical board with body and room orientations varying in relation to gravity and each other systematically. Across all threeexperiments participants were quicker or more accurate in memory recall when they saw the vertical spatial layout in the sameorientation in relation to their body vertical as during learning, irrespective of the direction of gravity or visual room upright.These results indicate that spatial long-term memories for small-scale vertical relations are mainly defined in an egocentricreference system with respect to the body vertical despite the availability of alternative highly salient allocentric referencedirections.

People reason about possibilities routinely, and reasoners caninfer “modal” conclusions, i.e., conclusions that concern whatis possible or necessary, from premises that make no mentionof modality. For instance, given that Cullen was born in NewYork or Kentucky, it is intuitive to infer that it’s possible thatCullen was born in New York, and a recent set of studies onmodal reasoning bear out these intuitions (Hinterecker,Knauff, & Johnson-Laird, 2016). What explains the tendencyto make modal inferences? Conventional logic does not applyto modal reasoning, and so logicians invented manyalternative systems of modal logic to capture valid modalinferences. But, none of those systems can explain theinference above. We posit a novel theory based on the ideathat reasoners build mental models, i.e., iconic simulations ofpossibilities, when they reason about sentential connectivessuch as and, if, and or (Johnson-Laird, 2006). The theoryposits that reasoners represent a set of conjunctivepossibilities to capture the meanings of compound assertions.It is implemented in a new computational process model ofsentential reasoning that can draw modal conclusions fromnon-modal premises. We describe the theory andcomputational model, and show how its performance matchesreasoners’ inferences in two studies by Hinterecker et al.(2016). We conclude by discussing the model-based theory inlight of alternative accounts of reasoning.

Most studies on spatial memory refer to the horizontal plane, leaving an open question as to whether findings generalize to vertical spaces where gravity and the visual upright of our surrounding space are salient orientation cues. In three experiments, we examined which reference frame is used to organize memory for vertical locations: the one based on the body vertical, the visual-room vertical, or the direction of gravity. Participants judged interobject spatial relationships learned from a vertical layout in a virtual room. During learning and testing, we varied the orientation of the participant's body (upright vs. lying sideways) and the visually presented room relative to gravity (e.g., rotated by 90° along the frontal plane). Across all experiments, participants made quicker or more accurate judgments when the room was oriented in the same way as during learning with respect to their body, irrespective of their orientations relative to gravity. This suggests that participants employed an egocentric body-based reference frame for representing vertical object locations. Our study also revealed an effect of body-gravity alignment during testing. Participants recalled spatial relations more accurately when upright, regardless of the body and visual-room orientation during learning. This finding is consistent with a hypothesis of selection conflict between different reference frames. Overall, our results suggest that a body-based reference frame is preferred over salient allocentric reference frames in memory for vertical locations perceived from a single view. Further, memory of vertical space seems to be tuned to work best in the default upright body orientation.

Individuals draw conclusions about possibilities from assertions that make no explicit reference to them. The model theory postulates that assertions such as disjunctions refer to possibilities. Hence, a disjunction of the sort, "A or B or both," where "A" and "B" are sensible clauses, yields mental models of an exhaustive conjunction of "possibly A," "possibly B," and "possibly both A and B," which each hold in default of information to the contrary. Oaksford, Over, and Cruz (this issue) are critical of the model theory and defend a probabilistic approach to reasoning. In this reply, we deal with their three main claims: (a) "Our results concern only the periphery of their probabilistic theory." We show that they refute their theory insofar as it applies to possibilities. (b) "The model theory leads to logical absurdities." We rebut this criticism as it applies to the model theory in Hinterecker, Knauff, and Johnson-Laird (2016), and explain why standard modal logics, which concern possibilities, do not set appropriate norms for inferences about them. (c) "The algorithm for reasoning based on models needs a normative theory." In fact, it has such a theory, but the demand for "a specification of a sound, complete, and decidable normative system" is chimerical for everyday reasoning. [For the article by Oaksford et al., "Paradigms, Possibilities, and Probabilities: Comment on Hinterecker, Knauff, and Johnson-Laird (2016)," see EJ1204226.]

We report 3 experiments investigating novel sorts of inference, such as: A or B or both. Therefore, possibly (A and B). Where the contents were sensible assertions, for example, "Space tourism will achieve widespread popularity in the next 50 years or advances in material science will lead to the development of antigravity materials in the next 50 years, or both." Most participants accepted the inferences as valid, though they are invalid in modal logic and in probabilistic logic too. But, the theory of mental models predicts that individuals should accept them. In contrast, inferences of this sort--A or B but not both. Therefore, A or B or both--are both logically valid and probabilistically valid. Yet, as the model theory also predicts, most reasoners rejected them. The participants' estimates of probabilities showed that their inferences tended not to be based on probabilistic validity, but that they did rate acceptable conclusions as more probable than unacceptable conclusions. We discuss the implications of the results for current theories of reasoning.

Previous behavioral and neurophysiological research has shown better memory for horizontal than for vertical locations. In these studies, participants navigated toward these locations. In the present study we investigated whether the orientation of the spatial plane per se was responsible for this difference. We thus had participants learn locations visually from a single perspective and retrieve them from multiple viewpoints. In three experiments, participants studied colored tags on a horizontally or vertically oriented board within a virtual room and recalled these locations with different layout orientations (Exp. 1) or from different room-based perspectives (Exps. 2 and 3). All experiments revealed evidence for equal recall performance in horizontal and vertical memory. In addition, the patterns for recall from different test orientations were rather similar. Consequently, our results suggest that memory is qualitatively similar for both vertical and horizontal two-dimensional locations, given that these locations are learned from a single viewpoint. Thus, prior differences in spatial memory may have originated from the structure of the space or the fact that participants navigated through it. Additionally, the strong performance advantages for perspective shifts (Exps. 2 and 3) relative to layout rotations (Exp. 1) suggest that configurational judgments are not only based on memory of the relations between target objects, but also encompass the relations between target objects and the surrounding room-for example, in the form of a memorized view. [ABSTRACT FROM AUTHOR]