rc conjunctive query answering

This paper investigates the direct access problem to the k-th answer in lexicographic order for conjunctive queries with negation (CQ¬) over databases: after polynomial-time preprocessing, arbitrary rank-k queries must be answered in polylogarithmic time. To address this, we systematically extend the characterization of direct-access tractability from positive conjunctive queries to CQ¬, introducing a unified framework based on representable relation circuits. We prove that both β-acyclic and bounded nested set-width classes of negative queries are tractable within this framework, strictly generalizing prior tractability boundaries for positive and negative queries. Experimental evaluation confirms that our approach achieves polynomial preprocessing and polylogarithmic access time, subsuming all previously known tractable classes and extending beyond them.

This paper addresses inconsistent-tolerant query answering over prioritized knowledge bases—comprising logical theories, factual databases, and priority relations among conflicting facts. We systematically support query evaluation under three classical semantics—AR (cautious), IAR (intersection of all repairs), and brave—over two classes of optimal repair models: Pareto-optimal and completion-based repairs. Our key contribution is the first unified SAT encoding framework capable of handling arbitrary priority relations, enabling joint modeling and efficient solving for both repair classes and all three semantics. Based on this encoding, we implement ORBITS, a novel reasoning system. Experimental results demonstrate that ORBITS significantly outperforms baseline approaches across all semantics, highlighting the critical impact of semantic choice and solving strategy on performance. The work establishes a new paradigm for practical reasoning over inconsistent prioritized knowledge bases.

This paper investigates efficient evaluation of join queries over mixed static and dynamic relations: static relations are fixed, while dynamic relations support insertions and deletions. The central objective is to characterize *tractable* queries—those admitting constant-time updates and constant-delay enumeration. We propose three syntactically decidable classes of tractable queries, constituting the first systematic characterization of how static constraints mitigate the inherent intractability of dynamic subqueries—even when the dynamic fragment alone is intractable, the full query may remain efficiently evaluable. Our approach integrates structural query analysis, preprocessing models guided by data complexity, incremental maintenance of dynamic relations, and constraint propagation. The three classes require linear, polynomial, or exponential preprocessing time, respectively, and we provide precise, syntax-based decidability criteria for each.

This paper investigates the decidability of the widely applicable query containment problem in first-order logic, focusing on cases admitting structurally simple countermodels—characterized by bounded treewidth, cliquewidth, and a newly introduced width measure, partitionwidth. We introduce the notion of “width-bounded universal model sets” and develop a unified framework grounded in partitionwidth, systematically integrating model-theoretic methods, graph width theory, and existential rule techniques. Partitionwidth is employed as the central width parameter for the first time, subsuming and extending classical decidable classes such as Datalog± and guarded rules. We establish decidability for several classes of homomorphism-closed queries under finite-partitionwidth rule sets. Furthermore, we expose inherent limitations of finite-unification sets and propose principled repairs to restore decidability.

Existing responsibility measures struggle to handle unions of conjunctive queries with negated atoms (UCQ^¬) due to their non-monotonicity, which renders traditional positive-fact-based metrics ineffective. This work proposes the first two responsibility measures tailored for UCQ^¬: one that evaluates only the contribution of positive facts, and another that additionally accounts for the influence of negative facts. We orthogonally extend established monotonic measures—such as drastic Shapley and Weighted Minimal Support Sets (WSMS)—to this non-monotonic setting. Leveraging logical semantics, variants of Shapley values, and WSMS, we establish that the proposed WSMS-based measure is data-complexity tractable for arbitrary UCQ^¬ and achieves combined-complexity tractability for specific classes of conjunctive queries, thereby laying a theoretical foundation for responsibility analysis in non-monotonic query settings.

This work addresses the challenge of efficiently implementing defeasible reasoning based on rational closure and answering conjunctive queries in lightweight description logics, specifically DL-Lite and its core and Horn variants. To this end, the authors propose a plug-in architecture that seamlessly integrates non-monotonic reasoning on top of existing classical reasoners. This approach constitutes the first computationally efficient solution for rational closure reasoning in DL-Lite, achieving tractable instance checking and conjunctive query answering with only minimal additional overhead. By doing so, it substantially enhances the practical applicability of non-monotonic semantics in real-world knowledge representation systems.

This work addresses the challenge of achieving both confidentiality and efficiency in query answering over description logic ontologies. Focusing on DL-Lite_R ontologies, it introduces a novel semantics based on Minimal Policy Violation (MPV) for Controlled Query Evaluation (CQE), which provides a sound approximation of the ideal semantics while satisfying indistinguishability-based confidentiality requirements defined by epistemic dependencies. The proposed approach is the first to enable query entailment checking with polynomial data complexity in DL-Lite_R under such confidentiality constraints. Empirical evaluation using OWL 2 QL benchmarks demonstrates its practical feasibility, significantly enhancing the computational tractability of confidential query answering in real-world settings.

The decidability of answering conjunctive queries with safe negation over DL-Lite$_{core}$ knowledge bases has long remained an open problem. This work resolves this longstanding theoretical question in knowledge representation and reasoning by establishing the undecidability of the query entailment problem through a rigorous reduction from the halting problem for Turing machines. By demonstrating that even under the syntactic restriction of safe negation, query answering in DL-Lite$_{core}$ is undecidable, the paper precisely delineates the boundary of the language’s reasoning capabilities. This result provides a crucial theoretical foundation for future investigations into tractable fragments and extensions of description logics accommodating negation.

This work addresses the problem of efficiently rewriting atomic queries over Horn-ALCHI ontologies into UC2RPQ, a core fragment of the ISO graph query language GQL. To this end, the paper introduces a novel automata-based formal semantics for description logics and incorporates a state stratification condition to eliminate cyclic dependencies. The proposed approach establishes, for the first time, sufficient conditions under which atomic queries over Horn-ALCHI ontologies are rewritable into UC2RPQ. This result substantially extends the applicability of GQL in ontology-mediated querying and provides both a theoretical foundation and a practical pathway for the efficient evaluation of complex ontology-based queries in graph databases.

This study addresses the long-standing open problem of determining conjunctive query containment under bag semantics. It proposes a unified framework that reduces the containment problem to solving controlled systems of Diophantine inequalities. Building upon canonical models and arithmetic multiplicity representations, this framework innovatively transforms factors that typically lead to undecidability into the core of the decision procedure, precisely delineating tractable classes by uncovering their underlying unified structure. As a key contribution, this work rigorously proves the decidability of bag containment for the class of connected homogeneous queries. This result significantly generalizes previously known special cases and establishes a systematic theoretical foundation for the field.