## TR#389: PNF Calculus: A Representation and a Fast Algorithm
for Recognition of Temporal Structure

### Claudio Pinhanez and Aaron Bobick

Submitted to AAAI'97

This paper presents a theory -- the PNF calculus -- which extends
Allen's interval algebra into handling causal propagation of the
states of temporal intervals through a network of time-connected
intervals. The basic goal is to assert whether an interval is
happening or not based on evidence dynamically provided by other
intervals. The PNF representational structure enables the design of
a fast algorithm which deduces those temporal implications of the
state of some intervals based on the state of temporally-related
intervals. The paper also contains basic results on PNF theory, and
a conjecture about the completeness of the approach. We also discuss
how to employ the PNF calculus as the foundation of methods for
human action recognition, considering actions represented as a
collection of time intervals corresponding to its sub-actions, events,
and detectable states of physical objects.