Dependently-Typed Formalisation of Typed Term Graphs

We employ the dependently-typed programming language Agda2 to explore formalisation of untyped and typed term graphs directly as set-based graph structures, via the gs-monoidal categories of Corradini and Gadducci, and as nested let-expressions using Pouillard and Pottier's NotSoFresh library of variable-binding abstractions.Comment: In Proceedings TERMGRAPH 2011, arXiv:1102.226

The impetus theory in judgments about object motion: A new perspective

Several tendencies found in explicit judgments about object motion have been interpreted as evidence that people possess a naive theory of impetus. The theory states that objects that are caused to move by other objects acquire force that determines the kind of motion exhibited by the object, and that this force gradually dissipates over time. I argue that the findings can better be understood as manifestations of a general understanding of externally caused motion based on experiences of acting on objects. Experiences of acting on objects yield the idea that properties of the cause of motion are transmitted to the effect object. This idea functions as a heuristic for explicit predictions of object motion under conditions of uncertainty. This accounts not only for the findings taken as evidence for the impetus theory, but also for several findings that fall outside the scope of the impetus theory. It has also been claimed that judgments about the location at which a moving object disappeared are influenced by the impetus theory. I argue that these judgments are better explained in a different way, as best-guess extrapolations made by the visual system as a practical guide to interactions with the object, such as interception