The techniques introduced in this paper, particularly the concepts of #-hypertree decompositions and the associated tractability results, can be extended to handle more expressive query languages by adapting the structural properties and decomposition methods to accommodate the additional complexity introduced by unions of conjunctive queries (UCQs) and the presence of negation and disequalities.
For unions of conjunctive queries, one approach is to analyze the hypergraph representation of the union as a combination of the hypergraphs of individual conjunctive queries. This requires developing a framework that can efficiently manage overlapping solutions across different conjunctive queries while ensuring that the counting process does not overcount shared solutions. Techniques such as view-based approaches, where views represent subqueries, can be employed to maintain the integrity of the counting process.
When dealing with queries that include negation and disequalities, the structural properties of the hypergraphs must be carefully examined. The introduction of additional constraints necessitates a more nuanced understanding of how these constraints interact with the existing structural parameters. For instance, the concept of frontier hypergraphs can be extended to account for the implications of negation, ensuring that the relationships among variables are accurately represented. Moreover, the hybrid decomposition approach can be adapted to incorporate these additional constraints, allowing for a more comprehensive analysis of the query structure.
Overall, extending the techniques to handle more expressive query languages involves a combination of refining the existing structural decomposition methods and developing new algorithms that can efficiently count solutions while respecting the complexities introduced by UCQs, negation, and disequalities.