  Spatial-temporal reasoning is a challenging task in Artificial Intelligence
(AI) due to its demanding but unique nature: a theoretic requirement on
representing and reasoning based on spatial-temporal knowledge in mind, and an
applied requirement on a high-level cognitive system capable of navigating and
acting in space and time. Recent works have focused on an abstract reasoning
task of this kind -- Raven's Progressive Matrices (RPM). Despite the
encouraging progress on RPM that achieves human-level performance in terms of
accuracy, modern approaches have neither a treatment of human-like reasoning on
generalization, nor a potential to generate answers. To fill in this gap, we
propose a neuro-symbolic Probabilistic Abduction and Execution (PrAE) learner;
central to the PrAE learner is the process of probabilistic abduction and
execution on a probabilistic scene representation, akin to the mental
manipulation of objects. Specifically, we disentangle perception and reasoning
from a monolithic model. The neural visual perception frontend predicts
objects' attributes, later aggregated by a scene inference engine to produce a
probabilistic scene representation. In the symbolic logical reasoning backend,
the PrAE learner uses the representation to abduce the hidden rules. An answer
is predicted by executing the rules on the probabilistic representation. The
entire system is trained end-to-end in an analysis-by-synthesis manner without
any visual attribute annotations. Extensive experiments demonstrate that the
PrAE learner improves cross-configuration generalization and is capable of
rendering an answer, in contrast to prior works that merely make a categorical
choice from candidates.
