Plausibility and Visualizability in Relational Belief Revision

Plausibility and Visualizability in Relational Belief Revision Leandra Bucher (leandra.bucher@psychol.uni-giessen.de) Jelica Nejasmic (jelica.nejasmic@psychol.uni-giessen.de) Sabine Bertleff (sabine.bertleff@psychol.uni-giessen.de) Markus Knauff (markus.knauff@psychol.uni-giessen.de) Justus-Liebig University, Experimental Psychology and Cognitive Science, Otto-Behaghel-Str. 10F, 35394 Giessen, Germany Abstract Belief revision is required when new facts are incompatible with existing beliefs. In the present experiment, participants changed their mind about the spatial and non-spatial relations between objects. The participants received information about relations, which were subsequently contradicted by irrefutable counterfacts. The task was to decide which of the initial relations to retain and which ones to give up. Previous experiments showed that these decisions are guided by the linguistic asymmetry between located (LO) and reference objects (RO). Reasoners have a strong preference to relocate the LO of the counterfactual relation. Our experiment explores whether this robust effect can be overwritten by the plausibility of revised beliefs; and how visualizability of problems affects revision. We found the LO-preference to be robust even when the resulting representation is implausible; and that revision is impeded when problems are easy to visualize. The results shed new light on relational belief revision in humans. Keywords: Relational reasoning; Spatial reasoning; Belief revision; Mental models, Visual impedance Relational Reasoning and the Revision of Beliefs Imagine you involuntarily put on some weight over the Christmas holidays. That is why, for the next couple of months, in order to get rid of the additional pounds, you consider nutrition which is low in fat and calories. You know that pasta, buckwheat, potatoes, and fruits are all low in fat, and further that potatoes are higher in calories than buckwheat is, and that pasta provides more energy than potatoes and fruits. Your ability to rank these, and even more, different types of food according to the amount of energy they provide enables you to conclude that fruits are a good choice when you want to pursue your aim of weight loss. This little example demonstrates that reasoning with relations is essential in our daily life. In fact, it is ubiquitous and it plays a vital role in higher cognitive processing, for instance, in planning and categorizing (Halford, Wilson, & Phillips, 1998; 2010; Hummel & Holyoak, 2005). Now, imagine you learn about avocado fruits that they contain high amounts of fat. You presumably integrate this fact with ease into your knowledge base, although it is not coherent with what you thought you knew about fruits (that they were low in fat). The process of integrating non- consistent pieces of information into already existing belief sets is referred to as belief revision (e.g. Gardenfors, 1988; Elio & Pelletier, 1997; Wolf, Rieger, & Knauff, 2012). Reasoners usually revise their beliefs about the state of the world when confronted with contradicting evidence. Indeed, we frequently encounter new facts that do not cohere with our beliefs. When the source of a new piece of information is reliable and the fact itself somewhat indisputable, we might consider taking it into account. In case we do, it entails that we update knowledge bases and revise current sets of beliefs. Frequently, there are multiple ways in which the revision could be performed, implicating different decisions about which beliefs to maintain and which ones to discard. Consider your belief that fruits are a good choice when you want to lose weight: do you maintain it in the face of the fact that avocados are high in fat; or will you discard at least avocados from the diet menu? Do you still think of avocados as fruits after all? It is clear that belief revision is often accompanied by uncertainty and ambiguity. The current study relies on recent work done in the field of relational belief revision. A recent finding in studies that looked at belief revision about spatial relations is that the revision is based on the variation of spatial mental models (Bucher, Krumnack, Nejasmic, & Knauff, 2011; Krumnack, Bucher, Nejasmic, & Knauff, 2011; Bucher & Nejasmic, 2012; Knauff, Bucher, Krumnack, & Nejasmic, 2013). Often, there are multiple (logically equal) alternatives for variations that would all re-establish consistency. However, human reasoners hold strong preferences for specific alternatives. These preferences can rely on linguistic cues provided by relational statements. The experiment presented here was designed to investigate whether reasoners still rely on these cues during revision, even when the resulting object relations are implausible. Furthermore, we compared reasoners´ performance in problems that were easy to visualize and easy to spatially represent. Preferences in Spatial Belief Revision Our recent experimental studies have focused on the revision of object arrangements. Imagine a person has reason to think that the objects X, Y, and Z are arranged in this linear order. The spatial mental model that is constructed can be sketched as: X – Y – Z Let us assume the reasoner then learns from a reliable and trustworthy source that as an incontrovertible fact, “object Z is to the left of object X”. This fact is inconsistent with the