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  <front>
    <journal-meta />
    <article-meta>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Gabriele Ciravegna</string-name>
          <email>gabriele.ciravegna@unifi.it</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Pietro Barbiero</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Francesco Giannini</string-name>
          <email>francesco.giannini@unisi.it</email>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Marco Gori</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Pietro Liò</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Marco Maggini</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Stefano Melacci</string-name>
          <email>mela@diism.unisi.it</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Computer Science and Technology, University of Cambridge</institution>
          ,
          <country country="UK">UK</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Department of Information Engineering and Mathematics, University of Siena</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Maasai</institution>
          ,
          <addr-line>Inria, I3S</addr-line>
          ,
          <institution>CNRS, Université Côte d'Azur</institution>
          ,,
          <country country="FR">France</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2023</year>
      </pub-date>
      <abstract>
        <p>3Consorzio Interuniversitario Nazionale per l'Informatica, CINI, (Italy) The rising popularity of deep learning has brought to light a fundamental limitation of neural network architectures: they lack the ability to provide interpretable justifications for their decisions, making them unsuitable for contexts where human experts require transparent explanations [1]. This abstract summarizes a newly introduced comprehensive approach to Explainable Artificial Intelligence (XAI), which demonstrates how a deliberate design of neural networks produces a family of interpretable deep learning models known as Logic Explained Networks (LEN) [2]. LENs only necessitate human-understandable predicates as input concepts and ofer logic explanations of the output predictions via a set of First-Order Logic (FOL) formulas build on these predicates (see an example in Figure 1). A very interesting feature of this model is its versatility, indeed LENs can be applied in many use cases, including as interpretable classifiers or to explain another black-box model. In case of interpretable classification, some design choices, like learning criterion and parsimony index, allows to achieve state-of-the-art results in the prediction accuracy while gaining transparency on the model's decision process [3]. Concerning the learning paradigms, LENs can be successfully trained to learn and provide explanations both in supervised and unsupervised learning settings [2, 4].</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>Italy
∗Corresponding author.
Explain! as a Python package on PyPI: https://pypi.org/project/torch-explain/ with an extensive
documentation that is available on read at https: //pytorch-explain.readthedocs.io/en/latest/</p>
    </sec>
    <sec id="sec-2">
      <title>CLASSIFIER</title>
    </sec>
    <sec id="sec-3">
      <title>LOGIC-EXPLAINED</title>
    </sec>
    <sec id="sec-4">
      <title>NETWORK</title>
    </sec>
    <sec id="sec-5">
      <title>INPUT</title>
    </sec>
    <sec id="sec-6">
      <title>DATA</title>
    </sec>
    <sec id="sec-7">
      <title>INPUT</title>
    </sec>
    <sec id="sec-8">
      <title>CONCEPTS</title>
    </sec>
    <sec id="sec-9">
      <title>OUTPUT</title>
    </sec>
    <sec id="sec-10">
      <title>PREDICTION</title>
    </sec>
    <sec id="sec-11">
      <title>LOGIC EXPLANATION</title>
      <p>of Black_foot_albatross
Acknowledgments
This work was supported by TAILOR and by HumanE-AI-Net, projects funded by EU Horizon
2020 research and innovation programme under GA No 952215 and No 952026, respectively.</p>
    </sec>
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