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  <front>
    <journal-meta>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Description Logic Reasoners</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Gunjan Singh</string-name>
          <email>gunjans@iiitd.ac.in</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Knowledgeable Computing and Reasoning Lab, IIIT-Delhi</institution>
          ,
          <country country="IN">India</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>OWL 2</institution>
          ,
          <addr-line>Reasoner, Benchmarking, Neuro-symbolic</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Ontologies are crucial in facilitating data sharing and integration across domains. The Web Ontology Language (OWL and its current version, OWL 2) is widely used to build expressive ontologies that capture complex relationships and semantics. However, the computational complexity of reasoning over OWL 2 ontologies increases with its expressive power. To advance the field of OWL reasoning, standardized benchmarks are needed to identify performance bottlenecks and evaluate reasoning systems. Existing real-world ontologies are limited in their coverage of OWL 2 constructs, necessitating the development of synthetic benchmarks that ofer flexibility in testing various aspects of reasoning systems. Our work addresses this need by introducing benchmarks for three types of OWL 2 reasoning systems - symbolic reasoners on static data, stream reasoners, and neuro-symbolic reasoners. These benchmarks facilitate the evaluation and comparison of reasoners' performance, promoting the development of more eficient and efective reasoners.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>CEUR
ceur-ws.org</p>
    </sec>
    <sec id="sec-2">
      <title>1. Introduction</title>
      <p>
        Ontologies enable the sharing and integration of data across diferent domains, such as
healthcare, geoscience, IoT, and e-commerce. Web Ontology Language (OWL, and its current version,
OWL 2) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] is a widely used W3C recommended standard for building ontologies that are
expressive and can capture complex relationships and semantics. One of the benefits of OWL 2 is that
it is based on Description Logics (DLs) [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], a family of logic-based knowledge representation
formalisms, which provide a way to represent knowledge in a structured and precise manner1.
This enables automatic reasoning over ontologies in a computationally tractable way. OWL
2 has diferent profiles, each with varying expressive power, from the relatively simple and
tractable profiles such as OWL 2 EL, OWL 2 QL, and OWL 2 RL to the more expressive OWL 2
DL. Expressive ontologies are required to capture complex relationships. However, there is a
tradeof between OWL 2’s expressive power and the computational complexity of reasoning.
Despite eforts to optimize reasoning methods, current reasoners face challenges in handling
large and expressive ontologies efectively [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Therefore, there is a need for more advanced
https://gunjansingh1.github.io/ (G. Singh)
      </p>
      <p>© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
and eficient reasoning techniques.</p>
      <sec id="sec-2-1">
        <title>1.1. Motivation</title>
        <p>
          To advance the field of ontology reasoning, it is important to evaluate the reasoners on diferent
ontologies and find their performance bottlenecks and improve on them. Benchmarks that can
comprehensively evaluate the reasoners can do this job. Several thousands of ontologies that
belong to diferent OWL 2 profiles are available in repositories such as the NCBO Bioportal 2,
AgroPortal3, and the ORE dataset [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ]. Although these ontologies can be used to benchmark
the reasoners, they do not quite test the limits of the reasoners because, in most cases, they
do not involve all the possible OWL 2 constructs and are either not large enough or complex
enough. Without scalable and eficient reasoners, ontology developers will not build large
and complex ontologies. Without these ontologies, it will be hard to test the performance and
scalability of the reasoners. So a synthetic benchmark addresses this chicken-and-egg problem
by ofering the flexibility to test various aspects of the reasoners by changing the configuration
parameters (such as size and complexity). Thus the strengths and weaknesses of diferent
reasoning approaches can be identified. This, in turn, enables the development of more eficient
and efective reasoning algorithms.
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>1.2. Problem Statement</title>
        <p>
          We discuss the requirements for benchmarks in three diferent types of reasoning systems.
1. Symbolic Static Data Reasoners. These are the conventional description logic
reasoners that work on static data (ontologies) and focus on reasoning tasks such as consistency
checking, classification, and realization. Several reasoners 4, such as Konclude [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ],
Openllet5, and HermiT [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ], have been developed to reason over ontologies eficiently. The
performance of these reasoners is usually evaluated in terms of reasoning time taken and
memory consumed. The benchmarks that can comprehensively evaluate these reasoners
should have the following characteristics.
        </p>
        <p>
          a) Varying size of TBox and ABox axioms. This helps determine the reasoner’s ability
to handle large ontologies and identify its limits.
b) Varying number and type of language constructs. This enables us to understand
how diferent language constructs impact reasoning performance.
c) Diferent combinations of language constructs. This facilitates evaluating the
performance of reasoners with diferent sets of language features, such as ones found
in diferent OWL 2 profiles.
2. Symbolic Streaming Data Reasoners. There are several streaming data reasoners such
as RSP4J [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] and StreamQR [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] for the real-time processing of streaming data. The key
performance indicators for these reasoners typically include latency, throughput, memory
usage, completeness, and correctness. A benchmark with the following characteristics,
2https://bioportal.bioontology.org/
3http://agroportal.lirmm.fr/
4http://owl.cs.manchester.ac.uk/tools/list-of-reasoners/
5https://github.com/Galigator/openllet
in addition to the ones discussed for static data reasoners, is required to evaluate their
performance.
        </p>
        <p>
          a) Realistic streaming data generator. The stream rate should be controllable and
inspired by real-world scenarios so that the testing reflects the system’s performance
in practical settings. It should be possible to vary the number of parallel streams
and their rates of frequencies.
b) Continuous queries. The queries should be designed to require continuous query
answering over streaming data. They should be evaluated for diferent window sizes
and multiple parallel queries. To answer each query, reasoning involving diferent
OWL 2 language constructs is required.
3. Neuro-Symbolic Reasoners. With the advancements in automated knowledge base
construction6, building large and expressive ontologies has become relatively easy.
However, these ontologies often sufer from noise and inconsistency, posing challenges for
conventional ontology reasoners [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ]. To address this, hybrid systems that combine
symbolic reasoning with neural networks are being developed. This integration aims to
enhance the performance of reasoning systems and tackle challenges such as reasoning
with incomplete or uncertain information. Neuro-symbolic reasoning systems can vary
in support for diferent OWL 2 profiles, subsets of description logics, and reasoning tasks
(classification, realization, consistency checking, class membership, class subsumption,
axiom completion). Although significant developments have taken place in the field
of neuro-symbolic reasoning space [
          <xref ref-type="bibr" rid="ref10 ref11">10, 11</xref>
          ] and advancements are ongoing, there is a
need for a common infrastructure and experiment design that will enable developers to
evaluate the performance of their systems and compare them with existing systems using
standardized performance metrics.
        </p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>2. Related Work</title>
      <p>
        The benchmarking of OWL 2 reasoners has seen limited development. Prominent benchmarks
such as LUBM (Lehigh University Benchmark) [12] and UOBM (University Ontology
Benchmark) [13] do not support OWL 2 profiles. OntoBench [ 14] covers all OWL 2 constructs and
profiles but focuses on reasoner coverage rather than scalability. Other than the aforementioned
benchmarks, there also exists an open-source java-based ORE benchmark framework7 which
was a part of OWL Reasoner Evaluation (ORE) Competition [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]. The competition was held
to evaluate the performance of OWL 2 complaint reasoners but did not consider performance
evaluation in the context of varying ontology sizes or the evaluation of SPARQL query engines
with OWL 2 reasoning support. To address these gaps, OWL2Bench [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] was proposed, which
is an extension of UOBM, enabling benchmarking of reasoners for diferent OWL 2 profiles,
ABox scalability, and query performance. However, OWL2Bench does not ofer scalable TBox
and support for customized ontologies. An extension of OWL2Bench [15] describes an ongoing
efort towards building such a customizable ontology benchmark for OWL 2 reasoners.
6https://www.akbc.ws/
7https://github.com/ykazakov/ore-2015-competition-framework
      </p>
      <p>The existing benchmarks mentioned above are primarily designed for evaluating the
performance of static reasoning systems and are not well-suited for stream reasoning systems that
handle dynamic data streams. That led to the development of benchmarks in the stream
reasoning domain, such as LSBench [16], SRBench [17], CSRBench [18], SLUBM [19], YABench [20],
CityBench [21], LASS 1.0 [22], and OWL2Streams [23]. Each of these benchmarks difers in
expressivity, supported features, and the types of datasets they use. However, out of these,
only LASS 1.0 and OWL2Streams focus on the reasoning tasks. The remaining benchmarks
only address continuous query answering under the RDFS entailment regime. However, both
LASS 1.0 and OWL2Streams are also limited in scope. LASS 1.0 includes a limited number of
OWL 2 RL language constructs, limiting its scope. On the other hand, OWL2Streams proposes
three diferent scenarios for the streaming domain, each focusing on specific requirements
but lacking a comprehensive coverage of a knowledge heavy domain that involves modeling
extensive knowledge using various OWL 2 constructs, realistic streaming data, and queries.
For example, the university domain scenario, adapted from OWL2Bench, lacks highly frequent
streams. The Smart City scenario, based on the extension of CityBench, is not knowledge-heavy.
The third scenario, based on the Smart Building Covid scenario, is neither expressive nor allows
for extensive ABox data. To fill this gap, one possibility is to extend the existing benchmarks
with expressive OWL 2 constructs. However, the existing benchmarks are not knowledge heavy.
Therefore, there is a need for a benchmark that efectively simulates real-world streaming
scenarios, stress tests existing stream reasoners, and incorporates expressive OWL 2 constructs.</p>
      <p>To the best of our knowledge, no benchmarks or evaluation frameworks have been designed
explicitly to evaluate and compare neuro-symbolic reasoning systems. Most reasoner evaluations
are performed on diferent publicly available ontologies. To evaluate neuro-symbolic reasoners
efectively, a benchmark is needed to generate ontologies tailored to specific tasks, allowing for
comparing performance and scalability.</p>
    </sec>
    <sec id="sec-4">
      <title>3. Contributions and Next Steps</title>
      <sec id="sec-4-1">
        <title>3.1. OWL2Bench</title>
        <p>OWL2Bench is an extension of the well-known University Ontology Benchmark (UOBM) [13].
It consists of three major components – a TBox for each OWL 2 profile (EL, QL, RL, and DL),
an ABox generator that can generate ABox of varying sizes for the corresponding TBox, and
22 SPARQL queries that involve reasoning. Thus, it allows users to benchmark three aspects
of the reasoners – support for diferent OWL 2 profiles, scalability in terms of ABox size, and
query performance. Moreover, the SPARQL queries also enable benchmarking SPARQL query
engines that support OWL 2 reasoning. The TBox for each profile was created by enriching
UOBM’s university ontology with the supported constructs. Two user inputs are required to
generate varying size ABox, the number of universities, and the OWL 2 profile (EL, QL, RL, or
DL) of interest. The generated instance data complies with the schema defined in the TBox of
the selected profile, and the size depends on the number of universities. For one university, by
default, approximately 50,000 ABox axioms are generated.</p>
        <p>
          To demonstrate the utility of OWL2Bench, we ran our benchmark on six reasoners, ELK [24],
1510 20
50
100
HermiT, JFact8, Konclude, Openllet, and Pellet [25] for three reasoning tasks, i.e., consistency
checking, classification, and realisation. We also evaluated two SPARQL query engines, Stardog 9
and GraphDB10, on SPARQL queries in terms of their loading time and query response time.
During our evaluation, we identified possible issues with these systems that need to be fixed
and could pave the way for further research in developing reasoners and query engines. For
example, there was a huge variation in run-time across the diferent runs on the same ontology.
The inconsistency in the results was reported to the openllet support11. The performance of
the reasoners on OWL2Bench is shown in Figure 1. For our experiments, we set the heap space
to 24 GB and the time-out to 90 minutes. Most reasoners timed out for even a few universities
(except for the QL profile). Although Konclude is much faster, it requires a lot of memory and
could not perform any reasoning task after 50 universities. For the EL profile, both Konclude
and ELK performed exceptionally well in terms of time taken, but ELK needs lower memory for
its computations. For the RL profile, most reasoners timed out on larger ontologies. In the case
of OWL 2 DL, Konclude, HermiT, and Pellet were able to complete the consistency checking
task only (for 1, 2, and 5 universities, respectively). However, we observed some inconsistency
in the results of Pellet. Other evaluations were time-outs. More details about the benchmark
and the results are available in the full version of our paper [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ].
        </p>
        <p>For the next steps, we are working towards an extension of OWL2Bench [15], which is a
customizable benchmark that can generate ontologies based on user-provided inputs such as
count and types of language constructs, as well as varying the size of TBox and ABox axioms.</p>
      </sec>
      <sec id="sec-4-2">
        <title>3.2. OWL2StreamBench</title>
        <p>We are working on OWL2StreamBench, a benchmark based on tweets from an academic
conference event. To push stream reasoning systems to their limits, it is crucial to use diverse
and scaled data that reflect real-world situations. Social media platforms like Twitter provide
an excellent source of such data, as they generate data at varying frequencies, which is ideal
for stream reasoning benchmarks. A wide range of topics and domains are discussed over
tweets, allowing users to express their thoughts and opinions on various subjects. Some popular
domains for which tweets are posted include news, personal life, and events. Unlike
newsrelated tweets, event-related tweets tend to have a longer lifespan and generate engagement
before and during the event. For instance, after the program is announced, there may be a
peak of engagement as people register for the event and plan their participation. During the
event, attendees may share their experiences, insights, and feedback on social media, generating
another peak of engagement. In contrast, news-related tweets tend to generate a peak of
engagement quickly after being posted, and the engagement may drop of rapidly. Therefore,
we generated tweets related to an academic conference event (ACE) for ABox data. ACE is an
ideal domain for benchmarking because it can produce a significant amount of data at varying
frequencies, similar to real-world data. Furthermore, tweets generated around ACE also help
design continuous queries suitable to replicate real-world scenarios. For example, one query
could be continuously monitoring tweets related to papers published on trending academic
topics like AI.</p>
        <p>Our next steps involve evaluating state-of-the-art stream reasoners using OWL2StreamBench.
However, one of the challenges we face that require careful consideration is determining how
to evaluate the correctness of these reasoners within the context of stream reasoning. Unlike
traditional reasoners, stream reasoners require a customized approach to assess correctness.</p>
      </sec>
      <sec id="sec-4-3">
        <title>3.3. NeSyBench</title>
        <p>
          We are also working on developing a benchmarking suite for neuro-symbolic reasoners. A
challenge here is the variation in support for diferent OWL 2 profiles and reasoning tasks
among the neuro-symbolic reasoners. Designing benchmarks that cover a wide range of profiles
and tasks is crucial for efective evaluation and comparison. Another challenge is the diversity
in techniques these reasoners use, such as neural language models for ontology completion [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]
and deep learning for emulating deductive reasoning [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. This involves considering appropriate
evaluation metrics. Overcoming these challenges is essential for a robust and reliable evaluation
framework that enables accurate assessments and comparisons of neuro-symbolic reasoners.
        </p>
        <p>The proposed steps for NeSyBench involve examining the current state-of-the-art in
neurosymbolic reasoning and existing benchmarks to identify desired evaluation features. These
will include generating profile-based axioms, addressing dataset biases, and representing input
axioms for neural network architectures. The performance evaluation will focus on assessing
the support for expressive logic, transferability, reasoning time, memory consumption, accuracy,
soundness, and completeness, in comparison to symbolic reasoning counterparts. Additionally,
the capabilities of neuro-symbolic reasoners to handle noisy and inconsistent ontologies will be
evaluated.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>4. Conclusion</title>
      <p>We discussed the need for benchmarks for three types of OWL 2 reasoners – conventional static
data reasoning, stream reasoning, and neuro-symbolic reasoning. We provided an overview of
our ongoing eforts in developing three benchmark frameworks – OWL2Bench,
OWL2StreamBench, and NeSyBench. Through these benchmarks, we aim to facilitate the evaluation,
comparison, and enhancement of reasoning systems. This, in turn, facilitates the progress of ontological
reasoning research.</p>
      <p>Acknowledgements. I am grateful to my supervisors, Dr. Raghava Mutharaju and Dr. Sumit
Bhatia, for their guidance and support. I would also like to acknowledge the partial support of
the Infosys Center for Artificial Intelligence (CAI), IIIT-Delhi.
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