arXiv subjects

Sebastian Rudolph

Publications and source records attributed to Sebastian Rudolph.

At least 19 recordsLinked to original sources

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.

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arXiv2026

Standpoint Logics with Defeasible Beliefs

In this paper, we integrate the defeasible logic of Kraus, Lehmann and Magidor (KLM) with the standpoint logic framework of G\'omez \'Alvarez and Rudolph. This is done with the goal of formally expressing knowledge taking into account multiple (possibly contradicting) viewpoints, which in turn may hold defeasible beliefs. In doing so, we utilise Defeasible Restricted Standpoint Logics (DRSL), introduced by Leisegang et al. Our work expands on previous work by providing a foundational representation result for DRSL semantics and systematically lifting several well-known entailment relations from the propositional case to the standpoint-enhanced setting. In particular, we characterise the semantics for DRSL through a set of KLM-style postulates adapted for the standpoints case. We furthermore provide a means to lift preferential entailment, and the class of entailment relations based on single ranking functions from the purely propositional to the standpoint-enhanced context, including rational and lexicographic closure. We show this can be done equivalently through semantic and algorithmic means. Furthermore, we show that, for each considered form of entailment, the complexity class of entailment checking does not change when moving from propositional KLM to DRSL.

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arXiv2025

Fitting Ontologies and Constraints to Relational Structures

We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu L}$ and $\mathcal{E\mkern-2mu LI}$ as well as several classes of tuple-generating dependencies (TGDs): full, guarded, frontier-guarded, frontier-one, and unrestricted TGDs as well as inclusion dependencies. We pinpoint the exact computational complexity, design algorithms, and analyze the size of fitting ontologies and TGDs. We also investigate the related problem of constructing a finite basis of concept inclusions / TGDs for a given set of finite structures. While finite bases exist for $\mathcal{E\mkern-2mu L}$, $\mathcal{E\mkern-2mu LI}$, guarded TGDs, and inclusion dependencies, they in general do not exist for full, frontier-guarded and frontier-one TGDs.

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arXiv2025

Putting Perspective into OWL [sic]: Complexity-Neutral Standpoint Reasoning for Ontology Languages via Monodic S5 over Counting Two-Variable First-Order Logic (Extended Version with Appendix)

Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities or agents. In these extensions, the integration between conceptual modelling and perspective annotations can vary in strength, with monodic standpoint extensions offering a well-balanced approach. They allow for advanced modelling features, such as the expression of rigid concepts, while maintaining desirable reasoning complexity. We consider the extension of C2--the counting two-variable fragment of first-order logic--by monodic standpoints. At the heart of our work is a polynomial-time translation of formulas in this extended formalism into standard, standpoint-free C2, a result that relies on intricate model-theoretic arguments. Thanks to this translation, the satisfiability problem remains at the same complexity level: NExpTime-complete, as in plain C2. Since our formalism subsumes monodic S5 over C2, this result also marks a substantial advancement in the study of first-order modal logics. From a practical standpoint, this means that highly expressive description logics such as SHOIQBs and SROIQBs--which underpin the widely adopted OWL 1 and OWL 2 ontology languages standardised by the W3C--can be extended with monodic standpoints without increasing the standard reasoning complexity. We further prove that NExpTime-hardness arises even in significantly less expressive description logics, as long as they include both nominals and monodic standpoints. Moreover, we show that if the monodicity restriction is relaxed even slightly in the presence of inverse roles, functionality, and nominals, the satisfiability problem becomes undecidable.

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arXiv2025

Semantic Web and Creative AI -- A Technical Report from ISWS 2023

The International Semantic Web Research School (ISWS) is a week-long intensive program designed to immerse participants in the field. This document reports a collaborative effort performed by ten teams of students, each guided by a senior researcher as their mentor, attending ISWS 2023. Each team provided a different perspective to the topic of creative AI, substantiated by a set of research questions as the main subject of their investigation. The 2023 edition of ISWS focuses on the intersection of Semantic Web technologies and Creative AI. ISWS 2023 explored various intersections between Semantic Web technologies and creative AI. A key area of focus was the potential of LLMs as support tools for knowledge engineering. Participants also delved into the multifaceted applications of LLMs, including legal aspects of creative content production, humans in the loop, decentralised approaches to multimodal generative AI models, nanopublications and AI for personal scientific knowledge graphs, commonsense knowledge in automatic story and narrative completion, generative AI for art critique, prompt engineering, automatic music composition, commonsense prototyping and conceptual blending, and elicitation of tacit knowledge. As Large Language Models and semantic technologies continue to evolve, new exciting prospects are emerging: a future where the boundaries between creative expression and factual knowledge become increasingly permeable and porous, leading to a world of knowledge that is both informative and inspiring.

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arXiv2024

Non-monotonic Extensions to Formal Concept Analysis via Object Preferences

Formal Concept Analysis (FCA) is an approach to creating a conceptual hierarchy in which a \textit{concept lattice} is generated from a \textit{formal context}. That is, a triple consisting of a set of objects, $G$, a set of attributes, $M$, and an incidence relation $I$ on $G \times M$. A \textit{concept} is then modelled as a pair consisting of a set of objects (the \textit{extent}), and a set of shared attributes (the \textit{intent}). Implications in FCA describe how one set of attributes follows from another. The semantics of these implications closely resemble that of logical consequence in classical logic. In that sense, it describes a monotonic conditional. The contributions of this paper are two-fold. First, we introduce a non-monotonic conditional between sets of attributes, which assumes a preference over the set of objects. We show that this conditional gives rise to a consequence relation that is consistent with the postulates for non-monotonicty proposed by Kraus, Lehmann, and Magidor (commonly referred to as the KLM postulates). We argue that our contribution establishes a strong characterisation of non-monotonicity in FCA. Typical concepts represent concepts where the intent aligns with expectations from the extent, allowing for an exception-tolerant view of concepts. To this end, we show that the set of all typical concepts is a meet semi-lattice of the original concept lattice. This notion of typical concepts is a further introduction of KLM-style typicality into FCA, and is foundational towards developing an algebraic structure representing a concept lattice of prototypical concepts.

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arXiv2024

Towards Propositional KLM-Style Defeasible Standpoint Logics

The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning new contradictory information. Standpoint logics are a group of logics, introduced to the field of Knowledge Representation in the last 5 years, which allow for multiple viewpoints to be integrated into the same ontology, even when certain viewpoints may hold contradicting beliefs. In this paper, we aim to integrate standpoints into KLM propositional logic in a restricted setting. We introduce the logical system of Defeasible Restricted Standpoint Logic (DRSL) and define its syntax and semantics. Specifically, we integrate ranked interpretations and standpoint structures, which provide the semantics for propositional KLM and propositional standpoint logic respectively, in order to introduce ranked standpoint structures for DRSL. Moreover, we extend the non-monotonic entailment relation of rational closure from the propositional KLM case to the DRSL case. The main contribution of this paper is to characterize rational closure for DRSL both algorithmically and semantically, showing that rational closure can be characterized through a single representative ranked standpoint structure. Finally, we conclude that the semantic and algorithmic characterizations of rational closure are equivalent, and that entailment-checking for DRSL under rational closure is in the same complexity class as entailment-checking for propositional KLM.

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arXiv2024

Enriching Ontologies with Disjointness Axioms using Large Language Models

Ontologies often lack explicit disjointness declarations between classes, despite their usefulness for sophisticated reasoning and consistency checking in Knowledge Graphs. In this study, we explore the potential of Large Language Models (LLMs) to enrich ontologies by identifying and asserting class disjointness axioms. Our approach aims at leveraging the implicit knowledge embedded in LLMs, using prompt engineering to elicit this knowledge for classifying ontological disjointness. We validate our methodology on the DBpedia ontology, focusing on open-source LLMs. Our findings suggest that LLMs, when guided by effective prompt strategies, can reliably identify disjoint class relationships, thus streamlining the process of ontology completion without extensive manual input. For comprehensive disjointness enrichment, we propose a process that takes logical relationships between disjointness and subclass statements into account in order to maintain satisfiability and reduce the number of calls to the LLM. This work provides a foundation for future applications of LLMs in automated ontology enhancement and offers insights into optimizing LLM performance through strategic prompt design. Our code is publicly available on GitHub at https://github.com/n28div/llm-disjointness.

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arXiv2024

The Sticky Path to Expressive Querying: Decidability of Navigational Queries under Existential Rules

Extensive research in the field of ontology-based query answering has led to the identification of numerous fragments of existential rules (also known as tuple-generating dependencies) that exhibit decidable answering of atomic and conjunctive queries. Motivated by the increased theoretical and practical interest in navigational queries, this paper considers the question for which of these fragments decidability of querying extends to regular path queries (RPQs). In fact, decidability of RPQs has recently been shown to generally hold for the comprehensive family of all fragments that come with the guarantee of universal models being reasonably well-shaped (that is, being of finite cliquewidth). Yet, for the second major family of fragments, known as finite unification sets (short: fus), which are based on first-order-rewritability, corresponding results have been largely elusive so far. We complete the picture by showing that RPQ answering over arbitrary fus rulesets is undecidable. On the positive side, we establish that the problem is decidable for the prominent fus subclass of sticky rulesets, with the caveat that a very mild extension of the RPQ formalism turns the problem undecidable again.

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arXiv2024

Supporting Risk Management for Medical Devices via the Riskman Ontology and Shapes (Preprint)

We propose the Riskman ontology and shapes for representing and analysing information about risk management for medical devices. Risk management is concerned with taking necessary precautions to ensure that a medical device does not cause harms for users or the environment. To date, risk management documentation is submitted to notified bodies (for certification) in the form of semi-structured natural language text. We propose to use terms from the Riskman ontology to provide a formal, logical underpinning for risk management documentation, and to use the included SHACL constraints to check whether the provided data is in accordance with the requirements of the two relevant norms, i.e. ISO 14971 and VDE Spec 90025.

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arXiv2023

Derivation-Graph-Based Characterizations of Decidable Existential Rule Sets

This paper establishes alternative characterizations of very expressive classes of existential rule sets with decidable query entailment. We consider the notable class of greedy bounded-treewidth sets (gbts) and a new, generalized variant, called weakly gbts (wgbts). Revisiting and building on the notion of derivation graphs, we define (weakly) cycle-free derivation graph sets ((w)cdgs) and employ elaborate proof-theoretic arguments to obtain that gbts and cdgs coincide, as do wgbts and wcdgs. These novel characterizations advance our analytic proof-theoretic understanding of existential rules and will likely be instrumental in practice.

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arXiv2023

Decidable (Ac)counting with Parikh and Muller: Adding Presburger Arithmetic to Monadic Second-Order Logic over Tree-Interpretable Structures

We propose $\omega$MSO$\Join$BAPA, an expressive logic for describing countable structures, which subsumes and transcends both Counting Monadic Second-Order Logic (CMSO) and Boolean Algebra with Presburger Arithmetic (BAPA). We show that satisfiability of $\omega$MSO$\Join$BAPA is decidable over the class of labeled infinite binary trees, whereas it becomes undecidable even for a rather mild relaxations. The decidability result is established by an elaborate multi-step transformation into a particular normal form, followed by the deployment of Parikh-Muller Tree Automata, a novel kind of automaton for infinite labeled binary trees, integrating and generalizing both Muller and Parikh automata while still exhibiting a decidable (in fact PSpace-complete) emptiness problem. By means of MSO-interpretations, we lift the decidability result to all tree-interpretable classes of structures, including the classes of finite/countable structures of bounded treewidth/cliquewidth/partitionwidth. We generalize the result further by showing that decidability is even preserved when coupling width-restricted $\omega$MSO$\Join$BAPA with width-unrestricted two-variable logic with advanced counting. A final showcase demonstrates how our results can be leveraged to harvest decidability results for expressive $\mu$-calculi extended by global Presburger constraints.

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arXiv2023

Pushing the Boundaries of Tractable Multiperspective Reasoning: A Deduction Calculus for Standpoint EL+

Standpoint EL is a multi-modal extension of the popular description logic EL that allows for the integrated representation of domain knowledge relative to diverse standpoints or perspectives. Advantageously, its satisfiability problem has recently been shown to be in PTime, making it a promising framework for large-scale knowledge integration. In this paper, we show that we can further push the expressivity of this formalism, arriving at an extended logic, called Standpoint EL+, which allows for axiom negation, role chain axioms, self-loops, and other features, while maintaining tractability. This is achieved by designing a satisfiability-checking deduction calculus, which at the same time addresses the need for practical algorithms. We demonstrate the feasibility of our calculus by presenting a prototypical Datalog implementation of its deduction rules.

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arXiv2023

Decidability of Querying First-Order Theories via Countermodels of Finite Width

We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of width measures (with treewidth and cliquewidth as popular examples). As an important special case of our framework, we identify logics exhibiting width-finite finitely universal model sets, warranting decidable entailment for a wide range of homomorphism-closed queries, subsuming a diverse set of practically relevant query languages. As a particularly powerful width measure, we propose to employ Blumensath's partitionwidth, which subsumes various other commonly considered width measures and exhibits highly favorable computational and structural properties. Focusing on the formalism of existential rules as a popular showcase, we explain how finite partitionwidth sets of rules subsume other known abstract decidable classes but - leveraging existing notions of stratification - also cover a wide range of new rulesets. We expose natural limitations for fitting the class of finite unification sets into our picture and suggest several options for remedy.

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arXiv2023

Tractable Diversity: Scalable Multiperspective Ontology Management via Standpoint EL

The tractability of the lightweight description logic EL has allowed for the construction of large and widely used ontologies that support semantic interoperability. However, comprehensive domains with a broad user base are often at odds with strong axiomatisations otherwise useful for inferencing, since these are usually context-dependent and subject to diverging perspectives. In this paper we introduce Standpoint EL, a multi-modal extension of EL that allows for the integrated representation of domain knowledge relative to diverse, possibly conflicting standpoints (or contexts), which can be hierarchically organised and put in relation to each other. We establish that Standpoint EL still exhibits EL's favourable PTime standard reasoning, whereas introducing additional features like empty standpoints, rigid roles, and nominals makes standard reasoning tasks intractable.

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arXiv2022

Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying

In our pursuit of generic criteria for decidable ontology-based querying, we introduce 'finite-cliquewidth sets' (FCS) of existential rules, a model-theoretically defined class of rule sets, inspired by the cliquewidth measure from graph theory. By a generic argument, we show that FCS ensures decidability of entailment for a sizable class of queries (dubbed 'DaMSOQs') subsuming conjunctive queries (CQs). The FCS class properly generalizes the class of finite-expansion sets (FES), and for signatures of arity at most 2, the class of bounded-treewidth sets (BTS). For higher arities, BTS is only indirectly subsumed by FCS by means of reification. Despite the generality of FCS, we provide a rule set with decidable CQ entailment (by virtue of first-order-rewritability) that falls outside FCS, thus demonstrating the incomparability of FCS and the class of finite-unification sets (FUS). In spite of this, we show that if we restrict ourselves to single-headed rule sets over signatures of arity at most 2, then FCS subsumes FUS.

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arXiv2022

How to Agree to Disagree: Managing Ontological Perspectives using Standpoint Logic

The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may require weakening in order to maintain consistency; others represent the distinct views in an entirely detached way. As an alternative, we propose Standpoint Logic, a simple, yet versatile multi-modal logic "add-on" for existing KR languages intended for the integrated representation of domain knowledge relative to diverse, possibly conflicting standpoints, which can be hierarchically organised, combined and put in relation to each other. Starting from the generic framework of First-Order Standpoint Logic (FOSL), we subsequently focus our attention on the fragment of sentential formulas, for which we provide a polytime translation into the standpoint-free version. This result yields decidability and favourable complexities for a variety of highly expressive decidable fragments of first-order logic. Using some elaborate encoding tricks, we then establish a similar translation for the very expressive description logic SROIQb_s underlying the OWL 2 DL ontology language. By virtue of this result, existing highly optimised OWL reasoners can be used to provide practical reasoning support for ontology languages extended by standpoint modelling.

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arXiv2021

AGM Belief Revision, Semantically

We establish a generic, model-theoretic characterization of belief revision operators implementing the paradigm of minimal change according to the seminal work by Alchourr\'{o}n, G\"{a}rdenfors, and Makinson (AGM). Our characterization applies to all Tarskian logics, that is, all logics with a classical model-theoretic semantics, and hence a wide variety of formalisms used in knowledge representation and beyond, including many for which a model-theoretic characterization has hitherto been lacking. Our starting point is the approach by Katsuno and Mendelzon (K&M), who provided such a characterization for propositional logic over finite signatures. We generalize K&M's approach to the setting of AGM-style revision over bases in arbitrary Tarskian logics, where base may refer to one of the various ways of representing an agent's beliefs (such as belief sets, arbitrary or finite sets of sentences, or single sentences). Our first core result is a representation theorem providing a two-way correspondence between AGM-style revision operators and specific assignments: functions associating every base to a "preference" relation over interpretations, which must be total but is - in contrast to prior approaches - not always transitive. As our second core contribution, we provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M's original work). Alongside these main contributions, we discuss diverse variants of our findings as well as ramifications for other areas of belief revision theory.

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