On the Foundations of Conflict-Driven Solving for Hybrid MKNF Knowledge Bases

TL;DR

This paper explores the theoretical foundations for conflict-driven solving of Hybrid MKNF Knowledge Bases, integrating rules and ontologies, and introduces formulas and nogoods for solver development.

Contribution

It defines completion and loop formulas for HMKNF-KBs, enabling conflict-driven solving by characterizing MKNF models through nogoods.

Findings

Defines completion and loop formulas for HMKNF-KBs

Establishes a basis for conflict-driven solver development

Characterizes MKNF models via nogoods

Abstract

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.