Managing Change in Graph-structured Data Using Description Logics (long version with appendix)

In this paper, we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider an action language in which actions are finite sequences of conditional insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the above data management problems as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.

💡 Research Summary

The paper addresses the problem of managing and reasoning about graph‑structured data (GSD) that evolves through user‑initiated or application‑driven updates. The authors propose a unified framework that combines a rich description‑logic (DL) formalism with an expressive action language, enabling both static verification of integrity constraints after updates and planning of action sequences that achieve or avoid certain states.

First, the authors view GSD as interpretations of a DL knowledge base (KB). The ABox corresponds to a possibly incomplete instance of the graph, while the TBox encodes domain knowledge and integrity constraints. To capture the needs of dynamic updates, they introduce an extension of ALC HOI Q called ALC HOI Q_br. This language adds Boolean combinations of axioms, role constructors for singletons, unions, differences, and role restrictions, as well as variables that can serve as placeholders for individuals. The resulting logic retains the same NEXPTIME‑complete finite satisfiability as standard ALC HOI Q, while being powerful enough to express complex graph patterns.

The action language is built on top of this DL. Basic actions consist of conditional insertions (⊕) or deletions (⊖) of individuals into concepts or of pairs into roles. Complex actions are formed by sequencing basic actions and by guarded conditional constructs of the form K ? α₁ J α₂ K, where K is an arbitrary DL formula. Variables appearing in actions are treated as parameters that must be instantiated (grounded) before execution. The semantics of actions is defined via interpretation updates: for a ground action α, a mapping S_α transforms any interpretation I into a new interpretation obtained by applying the specified insertions/deletions, possibly conditioned on the current satisfaction of K.

The central technical contribution is the transformation TR_α(K), which rewrites a KB K by “pushing back” the effects of an action α. Intuitively, TR_α(K) describes the set of pre‑states I such that after applying α, the resulting interpretation satisfies K. The transformation proceeds recursively on the structure of α: for an insertion (A ⊕ C) it replaces every occurrence of A in K by A ⊔ C; for a deletion (A ⊖ C) it replaces A by A ⊓ ¬C; for role updates it uses set union or set difference; and for conditional actions it combines the two branches with the logical formula (¬K₁ ∨ TR_α₁·α(K)) ∧ (K₁ ∨ TR_α₂·α(K)). The authors prove (Theorem 2) that for any ground action α and any interpretation I, S_α(I) ⊨ K iff I ⊨ TR_α(K). Consequently, reasoning about the effect of actions reduces to ordinary DL reasoning on a single KB.

Using this reduction, the paper studies several decision problems. The static verification problem asks whether, for every finite model of a given KB K, the execution of a prescribed action sequence α preserves K. By applying TR_α to K and checking finite satisfiability, the problem becomes a standard DL satisfiability test. The authors show that static verification is NEXPTIME‑complete for ALC HOI Q_br and CoNP‑complete for a DL‑Lite variant, matching known lower bounds.

The planning problems are more involved. The authors consider (i) existence of a plan (a sequence of actions) that drives a known initial graph into a goal state defined by a DL formula, (ii) existence of a plan when the initial graph is only partially described (i.e., any model of a given KB), and (iii) universal planning, where a given action sequence must guarantee the goal for all possible initial states. Since unrestricted plan existence is undecidable even for lightweight DLs, the paper focuses on bounded‑length plans. For bounded plans, they provide tight complexity results: for DL‑Lite the bounded planning problem is PSPACE‑complete, while for the expressive ALC HOI Q_br it is EXPSPACE‑complete. These results are obtained by reducing bounded planning to finite satisfiability of the transformed KBs, and by constructing appropriate automata‑based decision procedures.

The framework is deliberately generic. Because the underlying DL can encode RDF, RDFS, and OWL ontologies, the same techniques apply to semantic‑web data. Moreover, via standard reification, the approach can be used for relational schemas, UML class diagrams, and object‑oriented data models, thereby unifying a wide range of data‑management scenarios under a single logical umbrella.

From a practical standpoint, the authors argue that their action language mirrors database transaction primitives, making the approach suitable for integrity‑preserving updates, security policy enforcement, and automated migration of graph data. The transformation‑based reduction means that existing DL reasoners can be leveraged without building dedicated model‑checking engines.

In summary, the paper delivers a comprehensive theory for dynamic graph‑data management: it defines a powerful DL for modeling constraints, an action language for expressing updates, a sound and complete transformation that captures action effects, and a suite of algorithms with optimal complexity for static verification and bounded planning. The results bridge the gap between description‑logic reasoning and AI planning, offering a solid foundation for future tools that need to reason about evolving graph‑structured information.