On the Foundations of Conflict-Driven Solving for Hybrid MKNF Knowledge Bases
This work addresses the computational challenge of reasoning in hybrid knowledge bases, which is important for AI applications requiring both categorical and normative reasoning, but it appears incremental as it builds on existing conflict-driven methods from SAT and ASP.
The paper tackles the problem of developing a conflict-driven solver for Hybrid MKNF Knowledge Bases, which integrate closed-world rules and open-world ontologies, by establishing theoretical foundations through completion and loop formulas that characterize MKNF models and enable nogood-based solving.
Hybrid MKNF Knowledge Bases (HMKNF-KBs) constitute a formalism for tightly integrated reasoning over closed-world rules and open-world ontologies. This approach allows for accurate modeling of real-world systems, which often rely on both categorical and normative reasoning. Conflict-driven solving is the leading approach for computationally hard problems, such as satisfiability (SAT) and answer set programming (ASP), in which MKNF is rooted. This paper investigates the theoretical underpinnings required for a conflict-driven solver of HMKNF-KBs. The approach defines a set of completion and loop formulas, whose satisfaction characterizes MKNF models. This forms the basis for a set of nogoods, which in turn can be used as the backbone for a conflict-driven solver.