  One of the main obstacles for developing flexible AI systems is the split
between data-based learners and model-based solvers. Solvers such as classical
planners are very flexible and can deal with a variety of problem instances and
goals but require first-order symbolic models. Data-based learners, on the
other hand, are robust but do not produce such representations. In this work we
address this split by showing how the first-order symbolic representations that
are used by planners can be learned from non-symbolic inputs that encode the
structure of the state space. The representation learning problem is formulated
as the problem of inferring planning instances over a common but unknown
first-order domain that account for the structure of the observed state space.
This means to infer a complete first-order representation (i.e. general action
schemas, relational symbols, and objects) that explains the observed state
space structures. The inference problem is cast as a two-level combinatorial
search where the outer level searches for values of a small set of
hyperparameters and the inner level, solved via SAT, searches for a first-order
symbolic model. The framework is shown to produce general and correct
first-order representations for standard problems like Gripper, Blocksworld,
and Hanoi from input graphs that encode the flat state-space structure of a
single instance.
