reasoning under rational closure

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 paper investigates the concept satisfiability problem under “pure” minimal-model reasoning in description logics (DLs), where all predicate extensions must be minimized. It first establishes undecidability of this problem in the classical DL $mathcal{EL}$, and extends this result to a restricted fragment of tuple-generating dependencies (TGDs); it further proves ExpSpace-hardness in $mathcal{DL ext{-}Lite}_{ ext{horn}}$. To restore decidability, the paper introduces and validates an acyclicity condition on TBoxes, thereby establishing a tight correspondence between minimal-model reasoning and pointwise prioritized reasoning. Combining model-theoretic analysis, complexity-theoretic lower-bound constructions, and cycle-detection techniques, the work precisely characterizes the decidability and complexity boundaries across multiple DL fragments. It provides the first systematic complexity classification for nonmonotonic DL reasoning and the first general decidability-preserving repair mechanism for pure minimal-model inference.

This study addresses the problem of query entailment under partial finite model semantics in description logics: given a knowledge base, a query, and a concept required to be interpreted as a finite set, it investigates whether the query holds in all models satisfying this finiteness constraint. To this end, the work introduces a novel framework for partial finite model reasoning that transcends the traditional dichotomy between finite and infinite model semantics, unifying both cases through techniques for constructing and pruning infinite models. Focusing on the extension of ALC with transitive roles (logic S), the paper establishes that conjunctive query entailment under partial finite semantics lies within 2-EXPTIME by reducing query entailment to query containment, and applies this result to decide query containment under closed predicates.

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.

This work addresses the satisfiability normalization problem for cyclic-restricted TBoxes in the EL description logic, presenting the first complete normalization algorithm supporting general concept inclusions (GCIs). Traditional approaches cannot handle any GCIs, whereas our method overcomes this limitation by integrating EL syntactic constraint modeling, graph-structured normalization search, explicit cycle detection, and polynomial-time TBox pre-normalization. The algorithm preserves NP-completeness while enabling efficient and complete satisfiability checking for cyclic-restricted GCIs—previously unsupported. Empirical evaluation on biomedical ontology redundancy detection demonstrates both effectiveness and practical utility. This work thus provides theoretical foundations and a practical tool for lightweight ontology engineering with GCIs.

Traditional propositional defeasible stance logic (PDSL) supports only monotonic entailment, limiting its capacity to model nonmonotonic reasoning effectively. This work addresses this limitation by incorporating KLM-style rational nonmonotonic consequence relations into a fragment of PDSL, introducing contextualized stance conditionals to enrich its syntactic expressiveness and thereby enabling nonmonotonic entailment within PDSL for the first time. By adapting techniques such as preferential semantics, ranked models, and rational closure into a modal stance logic framework, the paper establishes a faithful translation mechanism from propositional nonmonotonic logics into multi-stance contexts. The proposed approach achieves efficient nonmonotonic entailment checking while preserving the original computational complexity bounds of PDSL.

This work addresses the challenge of efficiently computing rational closures in defeasible reasoning under incomplete information, where existing approaches struggle to balance expressiveness and computational performance. Building upon the KLM framework for non-monotonic reasoning, the paper introduces a novel declarative encoding based on Answer Set Programming (ASP) that automatically constructs minimal-rank models and supports entailment queries. The proposed method preserves theoretical soundness while significantly improving computational efficiency. Experimental results demonstrate that it outperforms imperative implementations such as InfOCF, offering both superior reasoning performance and greater modeling conciseness.

This work addresses the formal representation and reasoning of defeasible beliefs under multiple perspectives by integrating Kraus–Lehmann–Magidor (KLM) defeasible logic with standpoint logic, yielding Defeasible Restricted Standpoint Logics (DRSL). By introducing preference models, ranking functions, and a KLM-style axiomatic system, the paper establishes the first foundational representation theorem for DRSL. It systematically extends classical entailment relations—such as rational closure and lexicographic closure—from propositional settings to standpoint-enriched scenarios. The resulting framework achieves a unified semantic and algorithmic treatment of multi-perspective defeasible reasoning while preserving the original computational complexity of the underlying logics.

This work proposes a novel well-founded semantics for description logic programs that addresses two key limitations of existing approaches: high consistency-checking complexity (located at the second level of the polynomial hierarchy) and the absence of a characterization via reduct transformations. By imposing a stricter evaluation mechanism on ontology atoms, the proposed semantics retains well-foundedness while reducing the consistency problem to NP-completeness. It admits precise characterizations through both a fixed-point operator and a reduct transformation, constitutes a strict subset of the prevailing semantics, and coincides with it on certain syntactic classes. To the best of our knowledge, this is the first well-founded semantics for description logic programs that simultaneously offers a reduct-based characterization, lower computational complexity, and closer alignment with logic programming principles.

This study addresses the problem of fitting Horn description logic ontologies from positive and negative ABox examples together with Boolean queries, focusing on the fragments EL, ELI, and their extensions with the bottom concept. For atomic queries (AQ), rooted conjunctive queries (CQ), and unions thereof (UCQ), the work introduces simulation relations and finite-model techniques to provide a semantic characterization of the existence of solutions and designs corresponding decision procedures. The main contributions lie in identifying novel challenges arising when moving from ALC to EL and in precisely determining the computational complexity of the fitting problem across query types: it is PTime-complete for AQ; Σ₂^P-complete for rooted CQ and UCQ in EL; and rises to ExpTime-complete in ELI. The inclusion of the bottom concept does not affect these complexity results.