  Logic-based problems such as planning, theorem proving, or puzzles, typically
involve combinatoric search and structured knowledge representation. Artificial
neural networks are very successful statistical learners, however, for many
years, they have been criticized for their weaknesses in representing and in
processing complex structured knowledge which is crucial for combinatoric
search and symbol manipulation. Two neural architectures are presented, which
can encode structured relational knowledge in neural activation, and store
bounded First Order Logic constraints in connection weights. Both architectures
learn to search for a solution that satisfies the constraints. Learning is done
by unsupervised practicing on problem instances from the same domain, in a way
that improves the network-solving speed. No teacher exists to provide answers
for the problem instances of the training and test sets. However, the domain
constraints are provided as prior knowledge to a loss function that measures
the degree of constraint violations. Iterations of activation calculation and
learning are executed until a solution that maximally satisfies the constraints
emerges on the output units. As a test case, block-world planning problems are
used to train networks that learn to plan in that domain, but the techniques
proposed could be used more generally as in integrating prior symbolic
knowledge with statistical learning
