Description Logic Knowledge and Action Bases
Description logic Knowledge and Action Bases (KAB) are a mechanism for providing both a semantically rich representation of the information on the domain of interest in terms of a description logic knowledge base and actions to change such information over time, possibly introducing new objects. We resort to a variant of DL-Lite where the unique name assumption is not enforced and where equality between objects may be asserted and inferred. Actions are specified as sets of conditional effects, where conditions are based on epistemic queries over the knowledge base (TBox and ABox), and effects are expressed in terms of new ABoxes. In this setting, we address verification of temporal properties expressed in a variant of first-order mu-calculus with quantification across states. Notably, we show decidability of verification, under a suitable restriction inspired by the notion of weak acyclicity in data exchange.
💡 Research Summary
The paper introduces a novel framework called Knowledge and Action Bases (KAB) that integrates description‑logic (DL) knowledge bases with dynamic actions capable of modifying the stored information over time. While earlier KAB proposals relied on lightweight DL‑Lite and assumed the Unique Name Assumption (UNA), this work relaxes UNA and allows explicit equality and inequality assertions between individuals, thereby supporting reasoning about when two identifiers denote the same real‑world object.
Actions are specified as sets of conditional effects. The conditions are “epistemic queries” that are evaluated against the whole knowledge base (both TBox and ABox), meaning that an action may fire only if the logical consequences of the current ontology satisfy the query. Effects are expressed as new ABox fragments that can insert, delete, or modify facts, and they may also introduce fresh individuals. This design captures realistic scenarios where new entities (e.g., new orders, new patients) appear during execution.
A central technical challenge is that unrestricted creation of fresh objects can lead to an infinite transition system, making verification of temporal properties undecidable. To tame this, the authors import the notion of weak acyclicity from data‑exchange theory. They construct a dependency graph that records how actions’ pre‑conditions and effects refer to each other and to newly created objects. If the graph satisfies weak acyclicity—i.e., any cycle does not involve a “creation” edge—then the reachable state space can be finitely abstracted. Under this restriction the authors prove that the transition system generated by a KAB is effectively finite modulo bisimulation.
The verification target is a variant of first‑order μ‑calculus (FO‑μ‑calculus) that permits quantification over individuals across states and includes the usual temporal operators (next, until, fix‑point). Although FO‑μ‑calculus combined with DL reasoning is generally undecidable, the weak‑acyclicity condition restores decidability. The authors present a model‑checking algorithm that builds the finite abstraction, evaluates the μ‑calculus formula on it, and show that the overall decision problem lies in EXPTIME.
To demonstrate practicality, two case studies are presented. The first models a medical record system where patients, diagnoses, and treatments are encoded in a DL‑Lite TBox; actions such as “add diagnosis” or “start treatment” are conditioned on epistemic queries that respect the domain constraints, and equality assertions handle cases where the same patient appears under different identifiers. The second case study concerns a logistics scenario with orders, shipments, and warehouse locations; actions can generate new order IDs and update shipment status. Both examples satisfy weak acyclicity, and the authors successfully verify safety properties like “every order eventually reaches a delivered state” and liveness properties such as “if a shipment is in transit, a delivery action will eventually be enabled.”
In summary, the paper makes four major contributions: (1) extending DL‑Lite‑based KABs to support equality reasoning by dropping UNA, (2) introducing epistemic queries as action guards, (3) applying weak acyclicity to guarantee a finite abstraction despite unbounded object creation, and (4) establishing decidability and an EXPTIME model‑checking procedure for FO‑μ‑calculus properties over such KABs. These results advance the theoretical foundations for building semantically rich, dynamically evolving knowledge‑driven systems that can be rigorously verified.