arXiv subjects

Patrick Koopmann

Publications and source records attributed to Patrick Koopmann.

At least 19 recordsLinked to original sources

arXiv2026

The More the Merrier: Combining Properties for ABox Abduction under Repair Semantics in ELbot

Abduction is a central approach to explain missing entailments from a knowledge base by providing a hypothesis, that would, if added to the knowledge base, make the missing entailment become true. Abduction under repair semantics has recently been investigated in detail, where several desirable properties and optimality criteria were considered, such as signature-restrictions and minimality in size and of introduced conflicts. Naturally, hypotheses that satisfy more than one of these properties or combine a property with an optimality criterion would be even more desirable for applications. So far, such hypotheses have not been investigated in the literature. In the present paper, we consider the ABox abduction problem for hypotheses satisfying more than one property or additional optimality criteria, for EL_bot under brave and AR semantics. Our main observation is that often requiring additional properties for hypotheses does not lead to an increase of complexity.

cs.LO↗

arXiv2026

ABox Abduction for Inconsistent Knowledge Bases under Repair Semantics

Given a knowledge base (KB) with a non-entailed fact, the ABox abduction problem asks for possible extensions of the KB that would entail this fact. This problem has many applications, ranging from diagnosis to explainability and repair. ABox abduction has been well-investigated for consistent KBs and classical semantics, but little is known for the case of inconsistent KBs, which can be caused by erroneous data. In this paper we define suitable notions of abduction in this setting and propose criteria that guide abduction towards "useful" hypotheses. To regain meaningful reasoning in the presence of inconsistencies, we use well-established repair semantics. We provide a comprehensive landscape of the complexity of ABox abduction under repair semantics, treating different variants of the abduction problem for the light-weight description logics DL-Lite and EL_bot.

cs.LO↗

arXiv2025

Interpolation in Knowledge Representation

Craig interpolation and uniform interpolation have many applications in knowledge representation, including explainability, forgetting, modularization and reuse, and even learning. At the same time, many relevant knowledge representation formalisms do in general not have Craig or uniform interpolation, and computing interpolants in practice is challenging. We have a closer look at two prominent knowledge representation formalisms, description logics and logic programming, and discuss theoretical results and practical methods for computing interpolants.

cs.AI↗

arXiv2025

Can You Tell the Difference? Contrastive Explanations for ABox Entailments

We introduce the notion of contrastive ABox explanations to answer questions of the type "Why is a an instance of C, but b is not?". While there are various approaches for explaining positive entailments (why is C(a) entailed by the knowledge base) as well as missing entailments (why is C(b) not entailed) in isolation, contrastive explanations consider both at the same time, which allows them to focus on the relevant commonalities and differences between a and b. We develop an appropriate notion of contrastive explanations for the special case of ABox reasoning with description logic ontologies, and analyze the computational complexity for different variants under different optimality criteria, considering lightweight as well as more expressive description logics. We implemented a first method for computing one variant of contrastive explanations, and evaluated it on generated problems for realistic knowledge bases.

cs.AI↗

arXiv2025

Interpolation in Classical Propositional Logic

We introduce Craig interpolation and related notions such as uniform interpolation, Beth definability, and theory decomposition in classical propositional logic. We present four approaches to computing interpolants: via quantifier elimination, from formulas in disjunctive normal form, and by extraction from resolution or tableau refutations. We close with a discussion of the size of interpolants and links to circuit complexity.

cs.LO↗

arXiv2025

Why not? Developing ABox Abduction beyond Repairs

Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. While this task has been intensively investigated for perfect data and under classical semantics, less is known about abduction when erroneous data results in inconsistent KBs. In this paper we define a suitable notion of abduction under repair semantics, and propose a set of minimality criteria that guides abduction towards `useful' hypotheses. We provide initial complexity results on deciding existence of and verifying abductive solutions with these criteria, under different repair semantics and for the description logics DL-Lite and EL_bot.

cs.LO↗

arXiv2025

Concrete Domains Meet Expressive Cardinality Restrictions in Description Logics (Extended Version)

Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete domains, which can be used to assign concrete values to individuals using so-called features. These two mechanisms have been extended towards very expressive DLs, for which reasoning nevertheless remains decidable. Number restrictions have been generalized to more powerful comparisons of sets of role successors in $\mathcal{ALCSCC}$, while the comparison of feature values of different individuals in $\mathcal{ALC}(\mathfrak{D})$ has been studied in the context of $\omega$-admissible concrete domains $\mathfrak{D}$. In this paper, we combine both formalisms and investigate the complexity of reasoning in the thus obtained DL $\mathcal{ALCOSCC}(\mathfrak{D})$, which additionally includes the ability to refer to specific individuals by name. We show that, in spite of its high expressivity, the consistency problem for this DL is ExpTime-complete, assuming that the constraint satisfaction problem of $\mathfrak{D}$ is also decidable in exponential time. It is thus not higher than the complexity of the basic DL $\mathcal{ALC}$. At the same time, we show that many natural extensions to this DL, including a tighter integration of the concrete domain and number restrictions, lead to undecidability.

cs.LO↗

arXiv2024

Planning with OWL-DL Ontologies (Extended Version)

We introduce ontology-mediated planning, in which planning problems are combined with an ontology. Our formalism differs from existing ones in that we focus on a strong separation of the formalisms for describing planning problems and ontologies, which are only losely coupled by an interface. Moreover, we present a black-box algorithm that supports the full expressive power of OWL DL. This goes beyond what existing approaches combining automated planning with ontologies can do, which only support limited description logics such as DL-Lite and description logics that are Horn. Our main algorithm relies on rewritings of the ontology-mediated planning specifications into PDDL, so that existing planning systems can be used to solve them. The algorithm relies on justifications, which allows for a generic approach that is independent of the expressivity of the ontology language. However, dedicated optimizations for computing justifications need to be implemented to enable an efficient rewriting procedure. We evaluated our implementation on benchmark sets from several domains. The evaluation shows that our procedure works in practice and that tailoring the reasoning procedure has significant impact on the performance.

cs.AI↗

arXiv2024

The Precise Complexity of Reasoning in $\mathcal{ALC}$ with $\omega$-Admissible Concrete Domains (Extended Version)

Concrete domains have been introduced in the context of Description Logics to allow references to qualitative and quantitative values. In particular, the class of $\omega$-admissible concrete domains, which includes Allen's interval algebra, the region connection calculus (RCC8), and the rational numbers with ordering and equality, has been shown to yield extensions of $\mathcal{ALC}$ for which concept satisfiability w.r.t. a general TBox is decidable. In this paper, we present an algorithm based on type elimination and use it to show that deciding the consistency of an $\mathcal{ALC}(\mathfrak{D})$ ontology is ExpTime-complete if the concrete domain $\mathfrak{D}$ is $\omega$-admissible and its constraint satisfaction problem is decidable in exponential time. While this allows us to reason with concept and role assertions, we also investigate feature assertions $f(a,c)$ that can specify a constant $c$ as the value of a feature $f$ for an individual $a$. We show that, under conditions satisfied by all known $\omega$-admissible domains, we can add feature assertions without affecting the complexity.

cs.LO↗

arXiv2023

Towards Ontology-Mediated Planning with OWL DL Ontologies (Extended Version)

While classical planning languages make the closed-domain and closed-world assumption, there have been various approaches to extend those with DL reasoning, which is then interpreted under the usual open-world semantics. Current approaches for planning with DL ontologies integrate the DL directly into the planning language, and practical approaches have been developed based on first-order rewritings or rewritings into datalog. We present here a new approach in which the planning specification and ontology are kept separate, and are linked together using an interface. This allows planning experts to work in a familiar formalism, while existing ontologies can be easily integrated and extended by ontology experts. Our approach for planning with those ontology-mediated planning problems is optimized for cases with comparatively small domains, and supports the whole OWL DL fragment. The idea is to rewrite the ontology-mediated planning problem into a classical planning problem to be processed by existing planning tools. Different to other approaches, our rewriting is data-dependent. A first experimental evaluation of our approach shows the potential and limitations of this approach.

cs.AI↗

arXiv2023

Why Not? Explaining Missing Entailments with Evee (Technical Report)

Understanding logical entailments derived by a description logic reasoner is not always straight-forward for ontology users. For this reason, various methods for explaining entailments using justifications and proofs have been developed and implemented as plug-ins for the ontology editor Prot\'eg\'e. However, when the user expects a missing consequence to hold, it is equally important to explain why it does not follow from the ontology. In this paper, we describe a new version of $\rm E{\scriptsize VEE}$, a Prot\'eg\'e plugin that now also provides explanations for missing consequences, via existing and new techniques based on abduction and counterexamples.

cs.AI↗

arXiv2023

Combining Proofs for Description Logic and Concrete Domain Reasoning (Technical Report)

Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice by showing how proofs for consequences derived by DL reasoners can be computed and displayed in a user-friendly way. However, these methods are insufficient in applications where also numerical reasoning is relevant. The present paper considers proofs for DLs extended with concrete domains (CDs) based on the rational numbers, which leave reasoning tractable if integrated into the lightweight DL $\mathcal{E}\hspace{-0.1em}\mathcal{L}_\bot$. Since no implemented DL reasoner supports these CDs, we first develop reasoning procedures for them, and show how they can be combined with reasoning approaches for pure DLs, both for $\mathcal{E}\hspace{-0.1em}\mathcal{L}_\bot$ and the more expressive DL $\mathcal{ALC}$. These procedures are designed such that it is easy to extract proofs from them. We show how the extracted CD proofs can be combined with proofs on the DL side into integrated proofs that explain both the DL and the CD reasoning.

cs.LO↗

arXiv2023

Efficient Computation of General Modules for ALC Ontologies (Extended Version)

We present a method for extracting general modules for ontologies formulated in the description logic ALC. A module for an ontology is an ideally substantially smaller ontology that preserves all entailments for a user-specified set of terms. As such, it has applications such as ontology reuse and ontology analysis. Different from classical modules, general modules may use axioms not explicitly present in the input ontology, which allows for additional conciseness. So far, general modules have only been investigated for lightweight description logics. We present the first work that considers the more expressive description logic ALC. In particular, our contribution is a new method based on uniform interpolation supported by some new theoretical results. Our evaluation indicates that our general modules are often smaller than classical modules and uniform interpolants computed by the state-of-the-art, and compared with uniform interpolants, can be computed in a significantly shorter time. Moreover, our method can be used for, and in fact improves, the computation of uniform interpolants and classical modules.

cs.AI↗

arXiv2022

Explaining Ontology-Mediated Query Answers using Proofs over Universal Models (Technical Report)

In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology, which can be formulated in a description logic (DL) or using existential rules. In the literature, there exists a multitude of complex techniques for incorporating ontological knowledge into queries. However, few of these approaches were designed for explainability of the query answers. We tackle this challenge by adapting an existing proof framework toward conjunctive query answering, based on the notion of universal models. We investigate the data and combined complexity of determining the existence of a proof below a given quality threshold, which can be measured in different ways. By distinguishing various parameters such as the shape of the query, we obtain an overview of the complexity of this problem for several Horn DLs.

cs.LO↗

arXiv2022

Finding Good Proofs for Answers to Conjunctive Queries Mediated by Lightweight Ontologies (Technical Report)

In ontology-mediated query answering, access to incomplete data sources is mediated by a conceptual layer constituted by an ontology. To correctly compute answers to queries, it is necessary to perform complex reasoning over the constraints expressed by the ontology. In the literature, there exists a multitude of techniques incorporating the ontological knowledge into queries. However, few of these approaches were designed for comprehensibility of the query answers. In this article, we try to bridge these two qualities by adapting a proof framework originally applied to axiom entailment for conjunctive query answering. We investigate the data and combined complexity of determining the existence of a proof below a given quality threshold, which can be measured in different ways. By distinguishing various parameters such as the shape of a query, we obtain an overview of the complexity of this problem for the lightweight ontology languages DL-Lite_R and EL, and also have a brief look at temporal query answering.

cs.DB↗

arXiv2022

On the Eve of True Explainability for OWL Ontologies: Description Logic Proofs with Evee and Evonne (Extended Version)

When working with description logic ontologies, understanding entailments derived by a description logic reasoner is not always straightforward. So far, the standard ontology editor Prot\'eg\'e offers two services to help: (black-box) justifications for OWL 2 DL ontologies, and (glass-box) proofs for lightweight OWL EL ontologies, where the latter exploits the proof facilities of reasoner ELK. Since justifications are often insufficient in explaining inferences, there is thus only little tool support for explaining inferences in more expressive DLs. In this paper, we introduce EVEE-LIBS, a Java library for computing proofs for DLs up to ALCH, and EVEE-PROTEGE, a collection of Prot\'eg\'e plugins for displaying those proofs in Prot\'eg\'e. We also give a short glimpse of the latest version of EVONNE, a more advanced standalone application for displaying and interacting with proofs computed with EVEE-LIBS.

cs.LO↗

arXiv2022

Evonne: Interactive Proof Visualization for Description Logics (System Description) -- Extended Version

Explanations for description logic (DL) entailments provide important support for the maintenance of large ontologies. The "justifications" usually employed for this purpose in ontology editors pinpoint the parts of the ontology responsible for a given entailment. Proofs for entailments make the intermediate reasoning steps explicit, and thus explain how a consequence can actually be derived. We present an interactive system for exploring description logic proofs, called Evonne, which visualizes proofs of consequences for ontologies written in expressive DLs. We describe the methods used for computing those proofs, together with a feature called signature-based proof condensation. Moreover, we evaluate the quality of generated proofs using real ontologies.

cs.LO↗

arXiv2022

Connection-minimal Abduction in EL via Translation to FOL -- Technical Report

Abduction in description logics finds extensions of a knowledge base to make it entail an observation. As such, it can be used to explain why the observation does not follow, to repair incomplete knowledge bases, and to provide possible explanations for unexpected observations. We consider TBox abduction in the lightweight description logic EL, where the observation is a concept inclusion and the background knowledge is a TBox, i.e., a set of concept inclusions. To avoid useless answers, such problems usually come with further restrictions on the solution space and/or minimality criteria that help sort the chaff from the grain. We argue that existing minimality notions are insufficient, and introduce connection minimality. This criterion follows Occam's razor by rejecting hypotheses that use concept inclusions unrelated to the problem at hand. We show how to compute a special class of connection-minimal hypotheses in a sound and complete way. Our technique is based on a translation to first-order logic, and constructs hypotheses based on prime implicates. We evaluate a prototype implementation of our approach on ontologies from the medical domain.

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