Appendix A Proof for Proposition

We restate the proposition 1 and its proof here. Given Beta embedding S, S is a fixed point of N N: N (N ( S)) = S. 2. Given Beta embedding S, we have I ({S, S,..., S}) = S. Proof. Then we naturally have S = I ( {S,..., S}) . Here we discuss the computation complexity of representing any given FOL query using the De Morgan's laws (DM) and the disjunctive normal form (DNF). Then for each query structure, we use pre-order traversal starting from the target node/answer to assign an entity/relation to each node/edge iteratively until we instantiate every anchor nodes (the root of the query structure). Table 7: Number of training, validation, and test queries generated for different query structures.