arXiv subjects

Mantas Šimkus

Publications and source records attributed to Mantas Šimkus.

9 recordsLinked to original sources

arXiv2026

sheval: An RDF data shapes evaluation tool and test-suite for recursive shapes

Two different languages have been developed to validate RDF data based on the concept of a shape: ShEx and SHACL. In each language it is possible to define a shape that refers to itself, which is called a recursive shape. While in the case of ShEx, the semantics of recursive shapes is well defined and is part of the specification, in the case of SHACL, the semantics of recursive shapes is left to the implementation of the different SHACL engines. Consequently, the different SHACL engines show different behaviours when confronted with recursive shapes. In this paper we present sheval: an evaluation framework consisting of a tool and a test suite that can be used to compare the behaviour of different shapes technologies when confronted with recursive definitions. The tool has been used to evaluate and understand the differences in the implementation of recursive shapes in ShEx and SHACL. It provides a framework for testing and comparing the behaviour of different shape engines, helping to identify inconsistencies and potential issues, and providing a basis for further research and development in the field of shape-based validation of RDF data.

cs.DB↗

arXiv2026

The Triguarded Fragment

A prominent research question in computational logic is how to restrict first-order predicate logic (FO) in such a way that the satisfiability problem becomes decidable. Among others, past efforts have identified two prominent decidable FO fragments of high expressivity: the guarded fragment (GF), and the two-variable fragment (FO2). These fragments are of high interest and crucial importance as they provide significant insights into decidability and expressiveness of other prominent (computational) logics like Modal Logics (MLs)} and various Description Logics (DLs)}, which play a central role in Verification, Knowledge Representation, and other areas. In this article, we show that GF and FO2 can be combined into a new fragment that subsumes both, while maintaining decidability of the satisfiability problem. This fragment, called the triguarded fragment (denoted TGF), is obtained by relaxing the standard definition of GF by requiring guardedness of quantification only for subformulae with three or more free variables. We show that, when restricting the use of equality, satisfiability in TGF is N2ExpTime-complete, dropping to NExpTime-complete when the maximum predicate arity is fixed (a natural assumption in the context of MLs and DLs). We further establish that the problem is NP-complete in terms of data complexity, which is again in line with data complexity results for basic expressive DLs. We observe that many natural extensions of TGF, including the liberal use of equality, lead to undecidability. We also establish that TGF has the finite model property (providing a tight doubly exponential bound on the model size), whence finite satisfiability coincides with satisfiability.

cs.LO↗

arXiv2026

Common Foundations for Recursive Shape Languages

As schema languages for RDF data become more mature, we are seeing efforts to extend them with recursive semantics, applying diverse ideas from logic programming and description logics. While ShEx has an official recursive semantics based on greatest fixpoints (GFP), the discussion for SHACL is ongoing and seems to be converging towards least fixpoints (LFP). A practical study we perform shows that, indeed, ShEx validators implement GFP, whereas SHACL validators are more heterogeneous. This situation creates tension between ShEx and SHACL, as their semantic commitments appear to diverge, potentially undermining interoperability and predictability. We aim to clarify this design space by comparing the main semantic options in a principled yet accessible way, hoping to engage both theoreticians and practitioners, especially those involved in developing tools and standards. We present a unifying formal semantics that treats LFP, GFP, and supported model semantics (SMS), clarifying their relationships and highlighting a duality between LFP and GFP on stratified fragments. Next, we investigate to which extent the directions taken by SHACL and ShEx are compatible. We show that, although ShEx and SHACL seem to be going in different directions, they include large fragments with identical expressive power. Moreover, there is a strong correspondence between these fragments through the aforementioned principle of duality. Finally, we present a complete picture of the data and combined complexity of ShEx and SHACL validation under LFP, GFP, and SMS, showing that SMS comes at a higher computational cost under standard complexity-theoretic assumptions.

cs.LO↗

arXiv2025

Graph Learning via Logic-Based Weisfeiler-Leman Variants and Tabularization

We present a novel approach for graph classification based on tabularizing graph data via new variants of the Weisfeiler-Leman algorithm and then applying methods for tabular data. The variants are obtained by modifying the underlying logical framework, and we establish a precise theoretical characterization of their expressive power using a novel generalization of the bisimulation game for generalized quantifiers. We then test our method on 14 datasets that span a range of application domains. The experiments demonstrate that on datasets with up to 40 000 samples, our approach generally matches the predictive performance of graph neural networks and graph transformers, without requiring a GPU or extensive hyperparameter tuning. Even when our method's tuning time is included and the baselines' is not, our method is 5-20 times faster. When tuning time is included for all methods, the gap is significantly greater in favour of our method.

cs.LG↗

arXiv2025

Minimal Model Reasoning in Description Logics: Don't Try This at Home!

Reasoning with minimal models has always been at the core of many knowledge representation techniques, but we still have only a limited understanding of this problem in Description Logics (DLs). Minimization of some selected predicates, letting the remaining predicates vary or be fixed, as proposed in circumscription, has been explored and exhibits high complexity. The case of `pure' minimal models, where the extension of all predicates must be minimal, has remained largely uncharted. We address this problem in popular DLs and obtain surprisingly negative results: concept satisfiability in minimal models is undecidable already for $\mathcal{EL}$. This undecidability also extends to a very restricted fragment of tuple-generating dependencies. To regain decidability, we impose acyclicity conditions on the TBox that bring the worst-case complexity below double exponential time and allow us to establish a connection with the recently studied pointwise circumscription; we also derive results in data complexity. We conclude with a brief excursion to the DL-Lite family, where a positive result was known for DL-Lite$_{\text{core}}$, but our investigation establishes ExpSpace-hardness already for its extension DL-Lite$_{\text{horn}}$.

cs.AI↗

arXiv2020

An ExpTime Upper Bound for $\mathcal{ALC}$ with Integers (Extended Version)

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called $\omega$-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of $\mathcal{ALC}$ with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of $\mathcal{ALC}$ with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard $\mathcal{ALC}$. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

cs.AI↗

arXiv2019

Ontology Focusing: Knowledge-enriched Databases on Demand

We propose a novel framework to facilitate the on-demand design of data-centric systems by exploiting domain knowledge from an existing ontology. Its key ingredient is a process that we call focusing, which allows to obtain a schema for a (possibly knowledge-enriched) database semi-automatically, given an ontology and a specification of the scope of the desired system. We formalize the inputs and outputs of focusing, and identify relevant computational problems: finding a schema via focusing, testing its consistency, and answering queries in the knowledge-enriched databases it produces. These definitions are fully independent of the ontology language. We then instantiate the framework using selected description logics as ontology languages, and popular classes of queries for specifying the scope of the system. For several representative combinations, we study the decidability and complexity of the identified computational problems. As a by-product, we isolate (and solve) variants of classical decision problems in description logics, that are interesting in their own right.

cs.LO↗

arXiv2018

Relaxing and Restraining Queries for OBDA

In ontology-based data access (OBDA), ontologies have been successfully employed for querying possibly unstructured and incomplete data. In this paper, we advocate using ontologies not only to formulate queries and compute their answers, but also for modifying queries by relaxing or restraining them, so that they can retrieve either more or less answers over a given dataset. Towards this goal, we first illustrate that some domain knowledge that could be naturally leveraged in OBDA can be expressed using complex role inclusions (CRI). Queries over ontologies with CRI are not first-order (FO) rewritable in general. We propose an extension of DL-Lite with CRI, and show that conjunctive queries over ontologies in this extension are FO rewritable. Our main contribution is a set of rules to relax and restrain conjunctive queries (CQs). Firstly, we define rules that use the ontology to produce CQs that are relaxations/restrictions over any dataset. Secondly, we introduce a set of data-driven rules, that leverage patterns in the current dataset, to obtain more fine-grained relaxations and restrictions.

cs.LO↗

arXiv2013

Shape and Content: Incorporating Domain Knowledge into Shape Analysis

The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting shapes from program source code. Many real world programs however manipulate complex data whose structure and content is most naturally described by formalisms from object oriented programming and databases. In this paper, we look at the verification of programs with dynamic data structures from the perspective of content representation. Our approach is based on description logic, a widely used knowledge representation paradigm which gives a logical underpinning for diverse modeling frameworks such as UML and ER. Technically, we assume that we have separation logic shape invariants obtained from a shape analysis tool, and requirements on the program data in terms of description logic. We show that the two-variable fragment of first order logic with counting and trees %(whose decidability was proved at LICS 2013) can be used as a joint framework to embed suitable fragments of description logic and separation logic.

cs.PL↗