Explaining preferred mental models in Allen inferences with a metrical model of imagery

We present a simple metrical representation and algorithm to explain putative imagery processes underlying the empirical mental model preferences found by Knauff, Rauh and Schlieder (1995) for Allen inferences (Allen, 1983). The computational theory is compared with one based on ordinal information only (Schlieder, in preparation). Both provide good fits with the data. They differ psychologically in background theories, visualisation strategies motivated by these, and model construction processes generating models with the properties indicated as desirable by the strategies. They differ computationally in assumptions about knowledge strength (ordinal: weaker) and algorithmic simplicity (metrical: simpler). Our theory and its comparison with the ordinal theory provide the basis for a discussion of issues pertaining to imagery in general: Using the assumption of imagery inexactness, we develop a sketch theory of mental images and motivate a new visualisation strategy ('regularisation' ). We demonstrate systematic methods of modelling imagery processes and of analysing such models. We also outline some criteria for comparison (and future integration?) of cognitive modelling approaches. Allen inferences, preferred mental models, and a computational theory based on ordinal information Allen relations are the 13 ' qualitative' relations which can hold between two intervals, corresponding to relations between the startand endpoints of the two intervals, between which only the ordinal relations ' is before/smaller than' , ' is equal to' , and ' is after/larger than' are distinguished, see fig. 1. They have been discussed by Allen (1983) in a logic for reasoning about temporal events and have been used also as a basis for spatial reasoning calculi , e.g. in (Guesgen, 1989; Mukerjee & Joe, 1990). Qualitative relations are of interest to Cognitive Science because they might be employed in programs like Geographical Information Systems (GIS) to model human temporal/spatial reasoning more adequately than models based on numerical specifications. Allen inferences are compositions of Allen relations answering the following question: If the Allen relation between intervalsA and B isR1 and that between intervalsB andC is R2, then which Allen relation(s) R3 can hold between A and C? In some cases, there is only one possible answer (relation R3); in others, there are several. For example, if A finishes-inverse B andB beforeC, thenA can only be beforeC. IfA finishesinverse B and B during C, it is possible that A starts C, name