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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>S. Alghamdi);
robert.hoehndorf@kaust.edu.sa (R. Hoehndorf)</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Ontological analysis of collection improves classification of cardinality phenotypes</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Sarah Alghamdi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Robert Hoehndorf</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Computational Bioscience Research Center</institution>
          ,
          <addr-line>Computer</addr-line>
          ,
          <institution>Electrical &amp; Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology</institution>
          ,
          <addr-line>4700 KAUST, 23955 Thuwal</addr-line>
          ,
          <country country="SA">Saudi Arabia</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0001</lpage>
      <abstract>
        <p>Phenotype ontologies formally characterize and classify phenotypes. We analyze the phenotype classes related to the presence of increased or decreased amount of entities and identify potentially misleading inferences as a consequence of the axioms used to formalize these classes. We propose an ontology design pattern to reformulate these cardinality-related phenotypes and show how these can lead to a clearer classification and higher expressivity. Furthermore, reformulating these phenotype classes in MP and HP improves predictive performance in the task of identifying gene-disease associations through semantic similarity.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Cardinality phenotypes</kwd>
        <kwd>Collections and collectives</kwd>
        <kwd>Ontology design pattern</kwd>
        <kwd>Semantic similarity</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>
        1. Introduction
Phenotype data is critical for deciphering the biological
mechanisms causing a disease. A formal ontological
description of phenotype data can assist in identifying and
interpreting these mechanisms. Many ontologies cover
the domain of phenotypes for specific organisms, such as
the Human Phenotype Ontology (HPO) [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ] and the
Mammalian Phenotype Ontology (MP) [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Most phenotype
ontologies denfie phenotypes using the Entity–Quality
(EQ) formalism [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>Here, we are interested in the phenotype ontology
axioms related to an increased or decreased amount of
entities present within a body. For example, decreased
T cell number can be defined using the EQ model as
equivalent to has_part some (’decreased amount’
and (’characteristic of’ some ’T cell’) and
(’has modifier’ some abnormal)) and decreased
lymphocyte cell number defined as has_part some
(’decreased amount’ and (’characteristic 2. Results
of’ some lymphocyte) and (’has modifier’
some abnormal)). Based on these definitions, de- We explicitly introduce collections of anatomical entities;
creased T cell number is inferred to be a subclass of de- in particular, we introduce maximal collections of entities
creased lymphocyte cell number . However, depending with respect to another entity, which we define as the
on the specific meaning of decreased T cell number and collection of all entities of a particular type that are
(spadecreased lymphocyte cell number , this may be an unin- tially) contained within another entity. For example, in
tended inference: if decreased T cell number and decreased addition to the class T cell which has individual T cells as
lymphocyte cell number refer to all T cells and lympho- instances, we introduce a class for the collection of all T
cells within a body. Based on collection classes, we can
formulate a design pattern that represents the cardinality
phenotype, where the entity in the EQ method is replaced
with the collection of entity class that we have
formulated. Restructuring MP and HPO using our ontology
design pattern improves identification of gene–disease
cyte within a body, then the inference of the subclass
axiom is not correct because the decrease or increase of
the number of T cells does not imply the
decrease/increase of the number of lymphocytes in a body. Similar
issues arise when formalizing the absence of T cells, as
the absence of T cells does not usually imply the
absence of lymphocyte. We identify 2,341 such cases in the
MP and 1,119 in the HPO. Among those classes, 490 MP
classes and 57 HP classes refer to increased or decreased
cell types.</p>
      <p>
        The underlying problem here is that cardinality
phenotypes use in their definitions a class that has individual
entities as instances whereas single entities (such as a
T cell) should not be counted; instead, cardinality is a
quality of a collection of entities. We rely on the work of
Wood and Galton [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] which previously analyzed
collections in formal ontologies.
      </p>
    </sec>
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