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        <article-title>An Interdisciplinary Approach to Legal Terminology: Challenges of the “Algorithmic Turn” in Legal Science</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Giorgio Maria Di Nunzio</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Angela Condello</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Information Engineering, University of Padova</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Law Department, University of Messina</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>In this paper we aim to discuss the current challenges of legal science caused by the diffused use of AI software in various legal operations (verification, drafting, risk analysis and prediction). Working on the threshold between legal philosophy and computer engineering, we are going to address especially one problem, i.e. how the meaning of terms used in legal documents might be fixed differently because of the progressive and increased use of AI software by legal professionals (lawyers, judges, notaries). To do so, we are going to refer to Herbert Hart's idea that all legal concepts - via the terms referring to them - always have a core of settled meaning, but are also characterized, as well, by a penumbra of debatable cases in which words are neither obviously applicable nor obviously ruled out. These are so-called “hard cases”. Here are some questions that we aim to address: is it possible to anticipate the potential emergence of hard cases and hence prepare legal software to deal with the core-penumbra problem in legal meaning? How can machines perceive the relevance of the context and of societal change (fundamental aspects in Hart's legal theory of meaning)? 0000-0001-9709-6392 (G.M. Di Nunzio); 0009-0009-6299-5991 (A. Condello)</p>
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    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        In recent years, the "algorithmic turn" in legal science has gained traction, significantly altering
the landscape of legal operations with the adoption of AI across a multitude of functions, from
document automation and contract drafting to complex judgment predictions and risk analyses [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ].
This paper adopts an interdisciplinary approach, drawing from both legal philosophy and computer
engineering, to investigate the impact of AI-driven tools on legal semantics and interpretation.
      </p>
      <p>In examining the integration of AI within legal operations, we confront both “direct” and
“indirect” consequences that affect legal reasoning. Direct consequences, such as errors, biases, and
so-called hallucinations in AI outputs, highlight immediate risks of embedding prejudices within
predictive algorithms. However, a concern lies in the indirect consequences, notably the risk of
semantic un-flexibility which could suppress the interpretative adaptability that legal concepts
require for responding to complex concepts.</p>
      <p>Given these challenges, this paper seeks to add to the growing discussion about AI’s role in legal
science by asking whether AI systems can be developed to accommodate the different degrees in the
interpretive needs of legal contexts. Can these technologies effectively distinguish between clear-cut
cases and more ambiguous ones, and adapt to evolving contexts and interpretive shifts? We explore
how an approach combining legal theory, terminology, and computer engineering may help address
these issues, allowing AI to support the interpretive complexity of legal work while preventing the
risks of overdetermined or overly narrow legal meanings.
3rd Workshop on Augmented Intelligence for Technology-Assisted Review Systems (ALTARS 2024): Evaluation Metrics and
Protocols for eDiscovery and Systematic Review Systems. March 28, 2024, Glasgow, UK.</p>
      <p>giorgiomaria.dinunzio@unipd.it (G.M. Di Nunzio); angela.condello@unime.it (A. Condello)</p>
    </sec>
    <sec id="sec-2">
      <title>2. Background</title>
      <p>
        In this paper, we explore the multifaceted challenges facing legal science in light of the
widespread adoption of AI software across legal operations such as document automation and
verification, contract drafting, risk analysis, judgment, and prediction.2 In this interdisciplinary
context, between legal philosophy and computer engineering, the focus of our proposal will narrow
down onto a pivotal issue: the evolving dynamics of legal terminology and the consequences for
legal interpretation and argumentation, due to the pervasive and ever-increasing use of AI software
by legal professionals, including lawyers, judges, notaries, police forces, and labor consultants (see,
among others, [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]).
      </p>
      <p>
        Central to our investigation is Herbert Hart's theoretical framework [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], which posits that legal
concepts, mediated through the terms that denote them, exhibit a dual nature. While, in theory, they
possess a core of settled meaning, they are also surrounded by a “penumbra” of debatable cases,
known as “hard cases” [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], wherein the application of words is neither evidently applicable nor
categorically ruled out. As [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] explain, legal rules derive their dynamic nature in part through the
dynamic, open-textured nature of the terms used in the rules. As new situations arise, interpretation
of the meaning of these terms changes as well. Hart’s theoretical framework is particularly
interesting from the point of view of the intersection between legal theory, legal terminology and
computer engineering because it brings the focus on the potential changes in the use of terms (be
them simpler, like his famous example on ‘vehicle’, or more complex, like terms referring to concepts
– ‘dignity’, ‘freedom’, ‘self-determination’).
      </p>
      <p>The integration of AI software in legal practice raises critical questions that we want to explore;
in particular, whether it is conceivable to anticipate the potential emergence of hard cases and deep
interpretive disagreements (see [6]) and, subsequently, prepare legal software to navigate the
intricate core-penumbra problem inherent in legal meaning, considering both the vagueness and the
often necessary indeterminacy of legal terms, which are necessary for the adjustment of general
prescriptions to singular cases. [7] Working at the intersection between legal theory, terminology
and computer engineering is timely in particular given the supranational dimension in which legal
actors and decision-making bodies operate. In addition, the increasing sophistication of digital
technologies and their availability have generated two divergent narratives about their potential
implications, as described by [8]. These narratives alternately express excitement about legal
technology’s potential to make the law more efficient and improve access to justice, or concern about
the ways in which it may actually exacerbate existing biases or otherwise systematically harm
justice.</p>
      <p>From our transdisciplinary point of view, two types of issues are generated by the widespread
adoption of AI software across legal operations: some of them can be considered as “direct”
consequences, while others are more “indirect”. Hallucinations, errors, discrimination fall into the
first category, i.e., they are direct consequences of the use of AI software: since the software can
confuse situations or judge the potential events of the future in relation to past events, it can also
reproduce prejudice and more technically generate biases towards certain categories of subjects.
Although these are the consequence more often discussed by legal scholars and practitioners, we
believe that working on the terminology (via Hart’s theoretical framework) can demonstrate the
focal importance also of what can be described as “indirect” consequences. These are the effects of
the probabilistic logic underlying AI software that might produce, across time, a narrowing of
meaning and rigidity in legal terms, something that might generate a scientific revolution in law in
terms of the determinacy/indeterminacy of legal meaning [9]. Such semantic is, though, essential to
the evolution of legal concepts through time and is often the consequence of legal interpretation in
cases of deep disagreement and political conflict (see [10]).
2
https://joinup.ec.europa.eu/collection/justice-law-and-security/solution/leos-open-source-software-editinglegislation/discussion/smart-leos-which-new-functionalities-should-be-implemented-next-and-what-can-be-learntcorrigenda</p>
      <p>Our research extends beyond the theoretical questions and addresses practical considerations tied
to the intersection of AI and legal semantics. In this context, one main issue arises: can automatic
systems be trained to foresee the contours of hard cases and adapt to the subtle distinctions of legal
meaning? Can we measure the uncertainty of legal concepts and argumentation to handle the
conflicts between different interpretations of norms [11]?</p>
      <p>This challenge involves understanding how AI systems can effectively discern the relevance of
contextual complications as well as societal changes, a task that is very important in the context of
Hart's legal theory of meaning and well as in further developments of legal interpretivism until
today.</p>
      <p>As we examine the implications of AI software on legal terminology, our analysis recognizes the
transformative impact on traditional legal practices. The diffusion of AI technologies introduces a
paradigm shift, necessitating a reevaluation of established legal methodologies. We explore the
potential repercussions of this shift on the interpretation of legal documents and the inherent
stability (or instability) of legal concepts. The balance between settled meanings and the penumbra
of hard cases becomes increasingly important in a field where AI contributes to legal
decisionmaking processes not only via software of predictive justice (simulating the act of judging) but also
via semantic searches in jurisprudential materials and operations aimed at clarifying or specifying
the content of legal concepts. By examining the core-penumbra problem through the lens of Hart's
legal theory of meaning, we shed light on the challenges and opportunities posed by the integration
of AI in legal science. Through this interdisciplinary analysis, we contribute to the ongoing discourse
on the evolving nature of legal semantics in an era marked by the influence of augmented
intelligence. We aim to show that cases such as Loomis (2017, US Supreme Court) or Deliveroo (2020,
Bologna Court of First Instance) or the UK Post Office scandal (also known as the Horizon IT scandal)
might be avoided, in the near future, thanks to a continuous cooperation between legal theory,
terminology and computer engineering aimed at working through direct and indirect risks and
consequences of the use of AI software in legal operations. In particular, we aim at (i) foreseeing
upcoming potential legal conflicts (via a screening of the typical aspects of hard cases) and (ii)
preserving the “penumbra” and the essential indeterminacy of legal concepts.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Representing “Penumbra”</title>
      <p>In this section, we briefly list some possibilities to represent the concept of penumbra from a
machine learning point of view. Particularly, in the context of natural language processing (NLP)
and decision-making algorithms, the penumbra can be linked to areas of uncertainty or ambiguity
where the model's predictions may not be unequivocal.</p>
      <p>In exploring the concept of "penumbra" within legal interpretation, we draw parallels to machine
learning models that face similar challenges of ambiguity and uncertainty. Just as legal penumbra
deals with cases that do not fit neatly into established categories, machine learning models often
encounter "gray areas" in their predictions and decisions. The following sections examine this
relationship more closely, highlighting how machine learning approaches—whether dealing with
prediction uncertainty, boundary cases, context sensitivity, or interpretability—can mirror the
interpretative demands of legal reasoning. By analyzing these facets, we would like to uncover how
probabilistic and context-dependent models reflect the indeterminate nature of certain legal terms
and cases, emphasizing the shared need for flexibility in interpreting complex scenarios.</p>
      <sec id="sec-3-1">
        <title>3.1. Uncertainty in Model Predictions:</title>
        <p>In machine learning models, especially those based on probabilistic frameworks like Bayesian
models, predictions are often associated with a degree of uncertainty [12]. The model may provide a
probability distribution over possible outcomes rather than a definitive answer. This uncertainty
may reflect the penumbral aspect, where certain instances may fall into a gray area, making it
challenging for the model to make a clear-cut decision.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Boundary Cases:</title>
        <p>Much like legal penumbra involving hard cases, machine learning models may struggle with
boundary cases [13]. These are instances that lie on the edge of the decision boundary, where small
changes in input features can lead to different predictions. These boundary cases represent situations
where the model's confidence is lower, and decisions may be less straightforward.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Context Sensitivity:</title>
        <p>In legal terms, the interpretation of a term may vary based on the context in which it is used.
Similarly, machine learning models, specifically NLP models, often rely on context to make accurate
predictions [14]. The model's understanding of certain terms or features may exhibit variability based
on the surrounding context, introducing a level of interpretation flexibility analogous to the legal
penumbra.</p>
      </sec>
      <sec id="sec-3-4">
        <title>3.4. Interpretable Machine Learning:</title>
        <p>Interpretable machine learning models aim to provide transparency into how decisions are made
[15]. Despite efforts to achieve interpretability, there may still be instances where the model's
reasoning is not entirely clear. This lack of clarity aligns with the penumbral nature, where certain
cases may defy straightforward interpretation.</p>
        <p>In essence, the concept of penumbra in legal science, with its shades of interpretation ambiguity,
can find in machine learning models dealing with uncertainty, boundary cases, context sensitivity,
and adaptability.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Final Remarks</title>
      <p>By incorporating the penumbra concept, an eDiscovery system may predict and prioritize hard
cases within debatable scenarios and deep interpretive disagreements especially in the case of
contested concepts (such as, for instance, life, dignity, self-determination, autonomy). The same idea
(“difficult” concepts that are designated by multiple quasi-synonym terms) may be applied to the
case of medical review systems. This approach promises to enhance the efficiency of such kinds of
systems but, at the same time, may ensure that users are supported, not replaced, in the
decisionmaking process, maintaining accountability for actions taken.</p>
    </sec>
    <sec id="sec-5">
      <title>Acknowledgements</title>
      <p>This work is part of the initiatives carried out by the Center for Studies in Computational
Terminology (CENTRICO) of the University of Padua and in the research directions of the Italian
Common Language Resources and Technology Infrastructure CLARIN-IT.
[6] V. Villa, Deep Interpretive Disagreements and Theory of Legal Interpretation, in Pragmatics and
Law. Philosophical Perspectives, A. Capone and F. Poggi (eds.), Springer 2016, pp. 89-119.
https://doi.org/10.1007/978-3-319-30385-7_5
[7] A. Marmor, Defeasibility and Pragmatic Indeterminacy in Law, in Pragmatics and Law.</p>
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