Minimality Criteria in Spatial Belief Revision

Minimality Criteria in Spatial Belief Revision Leandra Bucher (leandra.bucher@psychol.uni-giessen.de) Justus Liebig University, Experimental Psychology and Cognitive Science, Otto-Behaghel-Strase 10F, 35396 Giessen, Germany Paul D. Thorn (thorn@phil-fak.uni-duesseldorf.de) Heinrich Heine University, Institute for Philosophy, Universitaetsstr. 1, 40204 Duesseldorf, Germany Knauff, 2011; Bucher & Nejasmic, 2012; Knauff, Bucher, Krumnack, & Nejasmic, 2013; Mikheeva, Bucher, Nejasmic, & Knauff 2013; Nejasmic, Bucher, & Knauff, 2013). Such work follows the general approach of positing mental models as the basis for relational reasoning (Johnson-Laird & Byrne, 1991; Knauff, 2009). In a prototypical task that is used to study spatial belief revision, participants are provided with two (or more) statements, S i , about object arrangements. For example: Abstract Agents typically revise their beliefs when confronted with evidence that contradicts those beliefs, selecting from a number of possible revisions sufficient to reestablish consistency. In cases where an individual’s beliefs concern spatial relations, belief revision has been fruitfully treated as a decision about which features of an initially constructed spatial mental model to modify. A normative claim about belief revision maintains that agents should prefer minimal belief revisions. Yet recent studies have rebutted the preceding claim, where minimality is understood to consist in modifying the position of the fewest objects, showing instead that reasoners prefer revisions that modify the position of an object x while retaining the position of an object y, when the agent’s new evidence is a relational statement of the form ‘xRy’. We here present cases where the preceding effect is reduced, and show an effect of minimality as measured by the number of initial premises preserved. (S 1 ) “The apple is left of the mango. ” (S 2 ) “The mango is left of the pear. ” The example description results in the arrangement (or mental model M): (M) Apple – Mango – Pear Participants are then told that they cannot be entirely sure that the description is correct, but that a third statement (the “fact”, F) – subsequently given (and partly contradicting) the initial description – is incontrovertibly true and has to be taken into account. For example: Keywords: Relational reasoning; Spatial reasoning; Spatial cognition; Belief revision; Mental models Belief Revision as Variation of Spatial Mental Models (F) “The pear is left of the apple. ” Whenever one’s beliefs are contradicted by compelling evidence, one is apt to revise one’s beliefs in order to maintain the consistency. For example, suppose, you believe that Bob is a baker from Bavaria, and you then come across conclusive evidence that Bob is not from Germany. Presumably, you will adopt the belief that Bob is not from Germany, and retract the belief that Bob is from Bavaria. Although there are many possible revisions that would allow you to achieve consistency in this case, it is very likely that you will continue to believe that Bob is a baker. If you revise your beliefs in this way, then your revision will be accord with a normative principle that states that one should minimize the changes made to one’s belief set when revising one’s beliefs in the face of new (contradicting) evidence (Gardenfors, 1992; Harman, 1986; Krumnack, Bucher, Nejasmic, & Knauff, 2011). In the domain of spatial belief revision, and particularly in research concerning the revision of beliefs about spatial relations between objects, belief revision has been described as a process of modifying of spatial mental models (Bucher, Krumnack, Nejasmic, & Knauff, 2011; Bucher, Nejasmic, Bertleff, & Knauff, 2013; Krumnack, Bucher, Nejasmic, & The task of the participants is to revise the initially constructed model (M) such that it coheres with the “fact” (F). Multiple revisions (R i ) are possible in order to reestablish consistency, and take the fact into account, e.g.: (R 1 ) Pear – Apple – Mango (R 2 ) Mango – Pear – Apple Both revised arrangements (R 1 and R 2 ) preserve the initially constructed model (M) to the same extent, and each revision preserves one of the initial statements: R 1 preserves S 1 , and R 2 preserves S 2 . From the viewpoint of logic, R 1 and R 2 are equally acceptable. Nevertheless, multiple studies (discussed below) have found that reasoners have a clear preference for R 1 . Preferred Spatial Model Revision The preference for R 1 , in the preceding example, is based on linguistic cues that are provided in the expression of binary relations of the form xRy, in particular by the functional asymmetry between x and y (with the “pear” as x, and the “apple” as y, in the above example). The asymmetry is often