Reasoning about the physical world is a central human cognitive activity. O
ne aspect of such reasoning is the inference of function from the structure
of the artifacts one encounters. In this article we present the Topologica
l iNference of Teleology (TNT) theory, an efficient means of inferring func
tion from structure. TNT comprises a representation language for structure
and function that enables the construction, extension, and maintenance of t
he domain-specific knowledge base required for such inferences. and an evid
ential reasoning algorithm. This reasoning algorithm trades deductive sound
ness for efficiency and flexibility. We discuss the representations and alg
orithm in depth and present an implementation of TNT, in a system called CA
RNOT. CARNOT demonstrates quadratic performance and broad coverage of the d
omain of single-substance thermodynamic cycles, including all such cycles p
resented in a standard text on the subject. We conclude with a discussion o
f CARNOT-based coaching tools that we have implemented as part of our publi
cly available CyclePad system, which is a design-based learning environment
for thermodynamics. (C) 1999 Elsevier Science B.V. All rights reserved.