  Inferring spatial-temporal properties from data is important for many complex
systems, such as additive manufacturing systems, swarm robotic systems and
biological networks. Such systems can often be modeled as a labeled graph where
labels on the nodes and edges represent relevant measurements such as
temperatures and distances. We introduce graph temporal logic (GTL) which can
express properties such as "whenever a node's label is above 10, for the next 3
time units there are always at least two neighboring nodes with an edge label
of at most 2 where the node labels are above 5". This paper is a first attempt
to infer spatial (graph) temporal logic formulas from data for classification
and identification. For classification, we infer a GTL formula that classifies
two sets of graph temporal trajectories with minimal misclassification rate.
For identification, we infer a GTL formula that is informative and is satisfied
by the graph temporal trajectories in the dataset with high probability. The
informativeness of a GTL formula is measured by the information gain with
respect to given prior knowledge represented by a prior probability
distribution. We implement the proposed approach to classify the graph patterns
of tensile specimens built from selective laser sintering (SLS) process with
varying strengths, and to identify informative spatial-temporal patterns from
experimental data of the SLS cooldown process and simulation data of a swarm of
robots.
