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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Clinical Documents and Their Parts</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Adrien BARTON</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Fumiaki TOYOSHIMA</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jean-François ETHIER</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Institut de Recherche en Informatique de Toulouse</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Toulouse</string-name>
        </contrib>
        <contrib contrib-type="author">
          <string-name>France</string-name>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>GRIIS, Université de Sherbrooke</institution>
          ,
          <addr-line>Quebec</addr-line>
          ,
          <country country="CA">Canada</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The medical world is replete with documents that ontologies can help to analyze and disambiguate. This paper provides a mereological analysis of such documents as structured by informational slots and fillers, completing recent work by our teams inspired by Bennett. It introduces the notion of adequate filling of an informational slot, and the representation of the layered structure of a document. An application is provided on the Prescription of drugs ontology (PDRO).</p>
      </abstract>
      <kwd-group>
        <kwd />
        <kwd>Mereology</kwd>
        <kwd>Document structure</kwd>
        <kwd>Informational slot</kwd>
        <kwd>Information content entity</kwd>
        <kwd>Drug prescription</kwd>
        <kwd>Granularity</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        The medical world is replete with documents that ontologies can help to analyze and
disambiguate, enabling better data sharing: diagnosis sheets [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], drug prescriptions [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ],
drug dispensing reports [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], laboratory test prescription and laboratory test reporting
documents [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ], consent forms [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], questionnaires and surveys [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], etc. Important
information is typically extracted from such clinical documents, such as the drugs that a
patient is likely to take, or the medical conditions he is likely to have. Nevertheless, the
semantics of the extracted information is often derived from implicit knowledge about
the structure of the document itself. This can lead to potentially serious errors of
interpretation. Therefore, an ontological analysis of clinical documents can produce
fruitful, practical and significant results in terms of quality of care. For example, it is
important to be able to distinguish the information ‘diabetes’ when it plays the role of a
therapeutic indication in a drug prescription from the information ‘diabetes’ when it
describes a past medical condition of a patient: intuitively, both have something in
common (the content ‘diabetes’), and something different (two different clinical roles
played by this content). Additionally, it would be desirable to be able to represent unfilled
templates of documents, or partially filled document.
      </p>
      <p>
        Ontological foundations for documents have been proposed [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ][
        <xref ref-type="bibr" rid="ref8">8</xref>
        ] based on the
Basic Formal Ontology (BFO) [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ] and the Information Artifact Ontology (IAO) [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
Recent work has axiomatized the mereological structure of informational entities [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ],
reconsidering classical mereological systems that are traditionally used in formal
ontology. This paper will build upon this work by introducing additional important
notions, and showing how those can be used to analyze the mereological structure of
clinical documents. Those new notions include the distinction between the adequate and
inadequate filling of documents or parts or documents; and the stratification of document
parts in hierarchized sublevels, that enables to express some axioms on how specific
kinds of clinical documents should be filled and understood. Those notions will be first
introduced on a toy example of a past medical history document, and later applied to the
ontology of drug prescriptions PDRO.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. The Mereological Structure of Informational Entities</title>
      <sec id="sec-2-1">
        <title>2.1. Former Work</title>
        <p>
          The axiomatic system will be expressed in FOL, and translated in OWL 2 when possible,
using the OWL Manchester Syntax. Classes from the Open Biomedical Ontologies
(OBO) Foundry [
          <xref ref-type="bibr" rid="ref12">12</xref>
          ] will be maximally re-used, such as IAO:Information content entity
(the prefix indicates the ontology from which the term is extracted).
        </p>
        <p>
          Classical mereology systems rest on the idea that an entity can only have a part once
[
          <xref ref-type="bibr" rid="ref13">13</xref>
          ]. However, some entities can have a part twice (or more) over, such as universals
(e.g. the universal of methane having the universal of hydrogen as part four times [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ]
[
          <xref ref-type="bibr" rid="ref15">15</xref>
          ]). Informational entity particulars share this characteristic with universals: consider
the chain of characters ‘aa’ that has the same letter ‘a’ twice over, or the sentence ‘A cat
is a cat.’ that has the same word ‘cat’ twice over. To account for this, we proposed [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]
an axiomatization of the mereological structure of documents adapted from Bennett’s
work [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ].
        </p>
        <p>
          This system introduces the unary predicate IS = “is a slot” and IF = “is a filler”, that
will be transposed here in OWL as the classes Information slot and Information filler. In
a way that is compliant with IAO [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ], fillers and slots are both information content
entities, which are defined and brought into existence by some cognitive acts (usually
coordinated inside a group whose members share a semiotic system [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ] [
          <xref ref-type="bibr" rid="ref16">16</xref>
          ]; see also
section 6.2).
        </p>
        <p>It also introduces the binary predicate F, S and P, where Sty means that t is a slot of
y (where both fillers and slots can have slots), Fxt means that x fills t, and Pxy means
that x is a part of y. Those will be written in OWL respectively as the relations fills
(inverse: filled_by), slot_of (inverse: has_slot) and part_of (inverse: has_part).</p>
        <p>
          As explained in [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ], this axiomatic system is built on a domain of fillers (with the
associate predicate IFx:=def ∃t Fxt) and slots (with the associate predicate IS), which are
disjoint: IFx → ¬ISx. Only slots are slots of something (Stx → ISt), but some slots may
not be a slot of anything (on the other hand, by definition, every filler fills a slot).
Therefore, only slots are filled, and only fillers can fill: Fxt → (ISt &amp; IFx) (but not all
slots need to be filled: there can be “empty” slots, as when a slot structure has already
been decided for a document that is not filled yet). Proper parthood is defined as filling
a slot of a filler (PPxy:=def IFy &amp; ∃s (Sty &amp; Fxt)) and parthood is defined the classical
way on this basis (Pxy:=def IFx &amp; [PPxy ∨ (x=y)]). Axioms are introduced to ensure that
no entity fills any of its slots (¬(Stx &amp; Fxt)), that there is at most one filler for a given
slot (Fyt &amp; Fzt → y=z), and that S is a strict order relation.
        </p>
        <p>
          The following axiom (named “AX8” in [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]) was accepted: if a filler x fills a slot t,
any slot of x is a slot of t, and vice versa: Fxt → (Sux ↔ Sut). From this, a theorem of
slot inheritance could be derived, that states that slots of a part of an entity are slots of
that entity too: (Stx &amp; Pxy) → Sty. On this basis, P was proven to be a partial order
relation, in line with the classical view of parthood [
          <xref ref-type="bibr" rid="ref17">17</xref>
          ] (and P is also taken to satisfy a
specific axiom akin to weak supplementation, but involving S).
        </p>
      </sec>
      <sec id="sec-2-2">
        <title>2.2. Example</title>
        <p>
          Suppose that at Princeton–Plainsboro Teaching Hospital (abbreviated PPTH), all past
medical history documents have the same structure as pmhd1=‘patient1[] condition1[]’,
where ‘patient1[]’ is a particular slot supposed to be filled with a patient name, and
‘condition1[]’ is a particular slot supposed to be filled with the name of a medical
condition (for example a disease, a disorder or a pathological process, following the
ontology OGMS [
          <xref ref-type="bibr" rid="ref18">18</xref>
          ]) that the patient got in the past (for the sake of simplicity, we omit
slots that would realistically need to be present, such as a slot to be filled by the date at
which the condition was supposed to hold, or by the name of the doctor who wrote the
document; we also suppose that each patient referred in the system has only one past
condition).
        </p>
        <p>Consider now that pmhd1 is filled such that it reads ‘John Doe / flu’. Both its
structure and content could be described with the following notation:
pmhd1=‘patient1[‘John Doe’] condition1[‘flu’]’, equivalent to the following facts:
fills(‘John Doe’, ‘patient1[]’) ; fills(‘flu’, ‘condition1[]’)
slot_of(‘patient1[]’, pmhd1) ; slot_of(‘condition1[]’, pmhd1)
One can then deduce the following facts from the definition of part_of:
part_of(‘John Doe’, pmhd1) ; part_of(‘flu’, pmhd1)
To illustrate the above-mentioned axiom AX8 with this example, if ‘John Doe’ fills the
slot ‘patient1[]’, and ‘last nameJD[]’ is a slot of ‘John Doe’ (filled by ‘Doe’), then ‘last
nameJD[]’ is also a slot of ‘patient1[]’.</p>
        <p>The apparatus of slots and fillers enables an informational entity to have a part twice
over. Suppose for example that past medical history documents at PPTH would have an
additional field to be filled with the name of the doctor writing the prescription, such that
a particular document would read ‘patient1[‘John Doe’] condition1[‘flu’]
doctor1[‘Gregory House’]’. Suppose now that Dr. House diagnoses that he has himself a
curmudgeon personality, and fills accordingly pmhd2 = ‘patient2[‘Gregory House’]
condition2[‘curmudgeon personality’] doctor2[‘Gregory House’]’ (although such
selfdiagnosis would not be possible in most real-world medical jurisdictions). Then the same
information filler ‘Gregory House’ fills two slots, namely ‘patient2[]’ and ‘doctor2[]’.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Adequate and Generalized Filling</title>
      <sec id="sec-3-1">
        <title>3.1. A Taxonomy of Relevant Entities</title>
        <p>
          We will introduce the classes as represented on Figure 1, that will be explained below
(see [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ] and Section 6.2 below for a discussion of instances of Information slot carrying
aboutness, and thus this class being a subclass of Information content entity). Note that
an IAO:Document is considered as an Information filler, and thus fills a slot. Indeed, this
class is defined as “A collection of information content entities intended to be understood
together as a whole”, and the slot it fills is precisely what makes that this collection of
information content entities is to be understood as a whole (see [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ] for more discussion
on this point).
        </p>
        <p>Given what we said earlier, we can already constrain the slot structure of a PPTH
past medical history document as follows:</p>
      </sec>
      <sec id="sec-3-2">
        <title>PPTH past medical history document SubClassOf Document and has_slot exactly 1 Patient slot and has_slot exactly 1 Condition slot</title>
        <p>We will now move to characterize slots depending on whether they are adequately filled
or not.</p>
        <p>IAO:Information content entity</p>
        <p>Information filler (IF)</p>
        <p>IAO:Document</p>
        <p>PPTH past medical history document
Human name</p>
        <p>PPTH patient name</p>
        <p>Clinical condition name
Information slot (IS)</p>
        <p>Adequately filled slot
Patient slot</p>
        <p>Adequately filled patient slot
Condition slot</p>
        <p>Adequately filled condition slot</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.2. Adequate and Generalized Filling</title>
        <p>The notion of filling needs to be refined. As a matter of fact, there are three different
ways in which a document can be inadequately filled. Suppose that the past medical
history documents at PPTH hospital have the structure presented on Figure 2 (namely
the structure described earlier, with the additional constraint that the slot for the patient
name has two slots, one for the first name and one for the last name).</p>
        <p>First, suppose that Dr. House leaves the slot last_name1[] unfilled by simply filling
medical_history1[] with ‘John / Flu’. This is what we will call “structural inadequacy”: a
slot of the document is not filled. Second, suppose that Dr. House fills condition1[] with
a filler that is not of the expected kind, such as ‘Gregory House’ (see section 6.2 for a
more general discussion of what we mean here by “expected kind”). Here, ‘Gregory
House’ is a name of a human person, whereas we would expect condition1[] to be filled
with a name of medical condition. This is what we call “semantic inadequacy”. Third,
Dr. House might fill the document as pictured on Figure 1, but still commit a mistake, if,
in fact, John Doe never had the flu in the past. This is what we call “descriptive
inadequacy”.</p>
        <p>The notion F we introduced earlier should be understood as a notion of “adequate
filling” in the structural and semantic senses mentioned above (for a short discussion
whether it should include descriptively adequate filling, see section 6.2). However, it can
be completed by a relation FG of generalized filling, used when a filler fills a slot, whether
adequately or not (such that in particular, Fxt → FGxt). On this basis, we can introduce
the notion of generalized information filler (IFG) as something that generally fills a slot
(rather than adequately fills it): IFGx:=def ∃t FGxt. Trivially, an adequate filler is a
generalized filler: IFx → IFGx. We can then define a new notion of generalized proper
parthood (PPG) as generally filling a slot (PPGxy:=def IFGy &amp; ∃t (Sty &amp; FGxt))), and define
generalized parthood (PG) between generalized fillers as being a generalized proper part
or identical (PGxy:=def IFGx &amp; [PPGxy ∨ (x=y)]).</p>
        <p>We can adapt the axioms previously exposed for F to FG and state that no entity
generally fills any of its slots (¬(Stx &amp; FGxt)) and that there is at most one general filler
for a given slot ((FGyt &amp; FGzt) → y=z). However, we do not transpose the axiom AX8
for general fillers: a general filler and the slot it fills do not necessarily have identical
slot structures (for example, ‘Gregory House’ and ‘condition1[]’ do not have the same
slot structure when the former structurally inadequately fills the later; Section 5.2 will
explain why this would be problematic). We accept axioms stating that PG is
antisymmetric and transitive (and it is trivially reflexive), and thus is a partial order (we will
not discuss here whether PG should satisfy supplementation axioms similar to those
satisfied by P).</p>
        <p>
          Our ontology admits empty slots: if the community at PPTH has decided that all past
medical history documents should have one patient slot and one condition slot, then
empty past medical history documents already have ipso facto this structure, even before
they are filled [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. Therefore, not all slots need to be generally filled (and obviously,
also not adequately filled).
        </p>
        <p>Axiomatically, we cannot state that a patient slot can only be generally filled by a
human name, since as we saw above, an agent might by mistake fill a patient slot with,
say, a condition name. However, we can state that a patient slot can only be adequately
filled by a human name. More generally, we could introduce axioms constraining what
could be adequate fillers for each kind of slot:</p>
      </sec>
      <sec id="sec-3-4">
        <title>Patient slot SubClassOf filled_by only PPTH patient name</title>
      </sec>
      <sec id="sec-3-5">
        <title>Condition slot SubClassOf filled_by only Clinical condition name</title>
        <p>We can then introduce the class of Adequately filled slot:</p>
      </sec>
      <sec id="sec-3-6">
        <title>Adequately filled slot EquivalentTo</title>
      </sec>
      <sec id="sec-3-7">
        <title>Information slot and (filled_by some Information filler)</title>
        <p>Note that an adequately filled slot is not the “composition” (in whatever sense of this
term) of a slot with its adequate filling; it is a slot that is adequately filled. We have:</p>
      </sec>
      <sec id="sec-3-8">
        <title>Adequately filled patient slot EquivalentTo</title>
      </sec>
      <sec id="sec-3-9">
        <title>Patient slot and (filled_by some PPTH patient name)</title>
      </sec>
      <sec id="sec-3-10">
        <title>Adequately filled condition slot EquivalentTo</title>
      </sec>
      <sec id="sec-3-11">
        <title>Condition slot and (filled_by some Clinical condition name)</title>
        <p>A reasoner would deduce from those two axioms that Adequately filled patient slot
and Adequately filled condition slot are both subclasses of Adequately filled slot.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Direct Slots and Direct Parts</title>
      <sec id="sec-4-1">
        <title>4.1. Definitions</title>
        <p>To clarify the slot structure of a document, we can define a hierarchy of levels among
slots. Consider a past medical history document as represented on Figure 1. Note that by
slot-transitivity, ‘first_name1[]’ and ‘last_name1[]’ are slots of ‘medical_history1[]’. But
we might want to state that the slots ‘patient1[]’ and ‘condition1[]’ are direct slots of
‘medical_history1[]’, whereas the slots ‘first_name1[]’ and ‘last_name1[]’ are not (they
are direct slots of ‘patient1[]’, however).</p>
        <p>Let’s write the relation “direct slot of” SD in FOL and direct_slot_of in OWL. Then
we can say that a direct slot of x (where x can be either a slot or a filler) is a slot of x that
is not a slot of a slot of x:
(DEF1) Direct slot of</p>
        <p>SDtx:=def Stx &amp; ¬[∃u (Stu &amp; Sux)]
We will call the inverse relation “has direct slot” and write it “has_direct_slot” in OWL.</p>
        <p>We can then define the relation “direct proper part of” PD (“direct_proper_part_of”
in OWL) as adequately3 filling a direct slot:
(DEF2) Direct proper part of
PPDxy:=def ∃t (SDty &amp; Fxt)
We will call the inverse relation “has direct proper part” and write it
“has_direct_proper_part” in OWL.</p>
        <p>Thanks to this notion, we can write, for example, that a PPTH past medical history
document has one Patient slot and one Condition slot as direct slots; and that it only has
such direct slots:</p>
      </sec>
      <sec id="sec-4-2">
        <title>PPTH past medical history document EquivalentTo Past medical history document</title>
        <p>and has_direct_slot exactly 1 Patient slot
and has_direct_slot exactly 1 Condition slot
and has_direct_slot only (Patient slot OR Condition slot)
However, a filled PPTH past medical history document can have other slots, as long as
they are not direct slots – such as the slot ‘last_name JD[]’ inherited from the filler ‘John
Doe’ that fills its patient slot.</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.2. Axiomatization of Direct Slot and Direct Parthood</title>
        <p>
          Let us now propose an axiomatization of the new relations we introduced, namely SD
(direct_slot_of) and PPD (direct_proper_part_of). Note that many of those axioms are
not (fully) representable in OWL (see [
          <xref ref-type="bibr" rid="ref19">19</xref>
          ] for a discussion), so we will write them in
FOL.
        </p>
      </sec>
      <sec id="sec-4-4">
        <title>4.2.1. Axiomatization of Direct Slot</title>
        <p>Since S is irreflexive and asymmetric (and SD implies S), SD also trivially is:
(THE1) Direct-slot irreflexivity
(THE2) Direct-slot asymmetry</p>
        <sec id="sec-4-4-1">
          <title>However, although S is transitive, SD is anti-transitive: ¬SDtt</title>
        </sec>
        <sec id="sec-4-4-2">
          <title>SDut → ¬SDtu</title>
          <p>3 Note that we might have additionally defined generalized direct parthood as generally filling a direct
slot, but such a notion will be less useful for our applied purposes that will be exposed in section 5.2.
(THE3) Direct-slot anti-transitivity</p>
        </sec>
        <sec id="sec-4-4-3">
          <title>SDxy &amp; SDyz → ¬SDxz</title>
          <p>Proof: Suppose that SDxy &amp; SDyz. Then, we do have Sxy &amp; Syz. If SDxz, then for every
u, ¬(Sxu &amp; Suz): contradiction by taking u=y. Therefore, we have ¬SDxz.
From AX8 that states that the slots of an adequate filler are identical to the slots of the
filled slot, we can prove that the direct slots of a filler are identical to the direct slots of
the adequately filled slots (that is, a slot and its adequate filler have the same direct slot
structure):
(THE4) Direct slots of an adequate filler are identical to direct slots of the filled slot</p>
          <p>Fxt → (SDux ↔ SDut)
Proof: Suppose that Fxt. SDux iff Sux &amp; ¬[∃v, (Suv &amp; Svx)] by definition of SDux.
iff Sut &amp; ¬[∃v, (Suv &amp; Svt)] by AX8.</p>
          <p>iff SDut by definition of SDut.</p>
          <p>
            We have shown in [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ] that a slot of a part of an entity is a slot of this entity. However,
this slot cannot be a direct slot of this entity:
(THE5) Inherited slot of part is not direct (Stx &amp; Pxy) → ¬SDty
Proof: Suppose that Stx &amp; Pxy. Since Pxy, there is a slot u such that Fxu and Suy.
By AX8 and Stx, we have Stu. Stu &amp; Suy contradicts SDty, therefore ¬SDty.
          </p>
        </sec>
      </sec>
      <sec id="sec-4-5">
        <title>4.2.2. Axiomatization of Direct Parthood</title>
        <p>Note first that since SD is a subrelation of S, direct parthood trivially implies proper
parthood:
(THE6) Direct proper parthood implies proper parthood</p>
        <sec id="sec-4-5-1">
          <title>PPDxy → PPxy</title>
          <p>As we have seen, PP is irreflexive, asymmetric and transitive. Therefore, from THE6,
we deduce that PPD (direct_proper_part_of) is also irreflexive and asymmetric:
(THE7) Direct proper parthood irreflexivity
(THE8) Direct proper parthood asymmetry
¬PPDxx</p>
        </sec>
        <sec id="sec-4-5-2">
          <title>PPDxy → ¬PPDyx</title>
          <p>PPD is not transitive, as a direct part of a direct part of z may not be a direct part of z:
consider a=t1[x] t2[u1[y] u2[z]] (where x, y and z are atomic), where z is not a direct part
of a, but is a direct part of u1[y] u2[z], which is a direct part of a. However, PPD is also
not anti-transitive, as a direct part of a direct part of b might be a direct part b: consider
b=t1[x] t2[u1[x] u2[y]], where x is both a direct part of b and a direct part of a direct part
of b – namely, u1[x] u2[y].</p>
          <p>
            In addition to its usefulness for writing universal restrictions, such a non-transitive
relation might be useful to mitigate undecidability issues when cardinality restrictions
are used [
            <xref ref-type="bibr" rid="ref20">20</xref>
            ].
          </p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Application to Drug Prescriptions</title>
      <p>
        Let us now illustrate how those notions can be useful on an actual ontology, the
Prescriptions of Drug Ontology (PDRO) [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. PDRO is a candidate ontology to the OBO
Foundry [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ], built in compliance with the realist methodology. It specifies generally the
structure of drug prescriptions through some relevant classes constrained by some
axioms. We will describe here how PDRO could be enriched by using the notions of
slots, adequate filling and direct slots and parts.
      </p>
      <sec id="sec-5-1">
        <title>5.1. Using Slots to Structure Drug Prescriptions</title>
        <p>
          Consider an example of prescription written by Dr. House to John Doe, similar to the
one presented in [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ], but structured using slots as in Figure 3: ‘Amoxicilin 500 mg PO
q8h x 7 days’.
        </p>
      </sec>
      <sec id="sec-5-2">
        <title>5.2. Using Universal Quantifier with Direct Slot and Direct Part</title>
        <p>In practice, drug prescriptions are further constrained according to the areas (e.g.
countries) in which they are written. In particular, in order to direct the implementation
of e-prescribing in Quebec using an application ontology, we need to constrain what kind
of parts a drug prescription can have.</p>
        <p>We want to formalize that a drug product specification in Quebec (that we will call
here a Q-Drug product specification) can be composed only with instances of Drug
active ingredient specification, Drug excipient specification, Drug dose form
specification, Drug product brand name, or Drug Identification Number. However, we
cannot use the relation BFO:has_part to express this universal restriction; just as a Drug
product specification like ‘Apo-Metoprolol 50mg tablet’ has as part a Drug product
brand name like ‘Apo-Metoprolol’, it has as part e.g. ‘mg’. Thus, it is difficult, if not
impossible, to make a list of all the possible parts of a Q-Drug product specification.</p>
        <p>To address this representational issue, we can introduce relevant slots, and use the
relation has_direct_slot to state:
(AX_QS) Q-Drug product specification slot SubClassOf has_direct_slot only
(Drug active ingredient specification slot or Drug dose form specification slot
or Drug product brand name slot or Drug excipient specification slot
or Drug Identification Number slot)</p>
        <p>This explains why we refused to adapt the axiom AX8 for generalized filling;
otherwise, an instance of Q-Drug product specification slot that would be inadequately
filled by, say, ‘John Doe’, would have the same slots as its filler, namely one for the first
name and one for the last name, and therefore axioms such as AX_QS would not hold.</p>
        <p>Combining this with the notion of adequate filling we saw earlier, we can then list
all the (adequate) direct parts an instance of Q-Drug product specification can only have:</p>
      </sec>
      <sec id="sec-5-3">
        <title>Q-drug product specification SubClassOf has_direct_proper_part only</title>
        <p>(Drug active ingredient specification or Drug dose form specification or Drug
product brand name or Drug excipient specification or Drug Identification</p>
      </sec>
      <sec id="sec-5-4">
        <title>Number)</title>
        <p>Those can be combined with axioms using existential quantification, for example
stating that an adequately filled drug product specification in Quebec has as part an active
ingredient specification or a drug product brand name, in order to specify the drug:</p>
      </sec>
      <sec id="sec-5-5">
        <title>Adequately filled Q-drug product specification SubClassOf has_direct_proper_part some (Drug active ingredient specification or Drug product brand name)</title>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Discussion</title>
      <p>
        A number of issues pertaining to the mereological structure of informational entities have
been discussed elsewhere [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] (including the possible relaxation of the axiom AX8, the
diachronic identity of informational entities, and the introduction of mereological sums).
We will add here a couple of points.
      </p>
      <sec id="sec-6-1">
        <title>6.1. Direct Parthood and Granularity</title>
        <p>
          We introduced above the has_direct_slot and has_direct_proper_part relations to
stratify the relation of parthood (between informational fillers) into several levels. This
is a way to address the vexed problem of how to represent consistently granular levels of
reality, in the particular case of informational entities (see e.g. Vogt’s [
          <xref ref-type="bibr" rid="ref21">21</xref>
          ] BFO-inspired
domain granularity framework for the life sciences). Note however that levels between
informational entities can be determined by a community of users of a semiotic system
[
          <xref ref-type="bibr" rid="ref16">16</xref>
          ], since such levels are defined by cognitive acts that can be coordinated in a
community, as explained earlier; whereas those between material objects (e.g. between
collections of cells and organisms) presumably are not defined by such cognitive acts.
        </p>
      </sec>
      <sec id="sec-6-2">
        <title>6.2. Aboutness, Semantic Adequacy and Descriptive Adequacy</title>
        <p>
          We can now suggest a few considerations on aboutness for slots and fillers, although this
question deserves more attention in future works. Note that cognitive acts are considered
in IAO as providing intentionality to information content entities [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]. Since cognitive
acts also bring information slots into existence, as mentioned earlier, it is not surprising
that they can also provide intentionality to those, the same way they do for information
fillers. In IAO [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ], ICEs can be about individuals or classes: ‘John Doe’, for example,
is about the human person John Doe; and ‘Flu’ would be about the Flu class. Similarly,
information slots can be about a class. ‘patient0[]’, for example, would be about the class
of patients from the PPTH hospital. This explains why we classified Information slot as
a subclass of ICE.
        </p>
        <p>This theory of aboutness need to be developed more systematically to express
formally the normative constraints on adequate filling that were mentioned above. In
particular, the semantic adequacy requirement for a filler was expressed as being about
an entity of the “expected kind”. We can clarify what we mean by this with two
paradigmatic cases. A first case is that ‘John Doe’ is a semantically adequate filler of
patient0[] because ‘John Doe’ is about a particular (the human person John Doe) who is
an instance of the class referred to (we take “refer to” and “being about” as synonymous
here) by patient0[], namely the class of patients from the PPTH hospital. A second case
is that ‘Flu’ is a semantically adequate filler of condition0[] because it is about a class
(the class of flu diseases) that has a non-empty intersection with the class referred to by
condition0[] (namely the class of human medical conditions; note that the former is not
a subclass of the latter: the class of flu diseases encompasses also non-human medical
condition, as some non-human animals can get the flu). A more systematic theory of
semantic adequacy will depend on the details of the endorsed theory of aboutness.</p>
        <p>A theory of aboutness could also clarify the link between descriptive adequacy and
semantic adequacy. A filler is said to be descriptively adequate if it describes a state of
affairs that obtained in the past; for example, ‘John Doe / Flu’ is descriptively adequate
if it refers to a state of affair of John Doe having got the flu in the past. But descriptive
adequacy might be seen as a form of semantic adequacy. For example, the slot
past_history0[] might be about the class of clinical state of affairs that occurred in the
past; and ‘John Doe / Flu’ is a descriptively adequate filler if it refers to a state of affair
(John Doe having had the flu) that is an instance of the class of clinical state of affairs
that obtained in the past (assuming that we would accept an ontology of state of affairs,
which is not the case currently in BFO). Thus, this would match with our definition of
semantic adequacy. Here again, interpreting descriptive adequacy as a kind of semantic
adequacy depends on the details of the theory of aboutness accepted. Moreover, even if
descriptive adequacy can be interpreted as a kind of semantic adequacy, it is
epistemically much more demanding to evaluate some descriptive adequacy than to
evaluate, say, the semantic adequacy of a filler of condition0[]. Indeed, it is relatively
easy to check whether a filler refers to a human condition (by having a dictionary or
terminology of human conditions); on the other hand, it is much more difficult (or even
impossible, if one is a strict Bayesian) to be sure that John Doe indeed got the flu in the
past.</p>
      </sec>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusion</title>
      <p>
        We have here shown how the mereology of informational entities proposed in [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] could
be extended with a normative notion of adequate filling, and a hierarchical notion of
direct slots and parts. Both are useful tools to represent clinical documents and their parts,
and could also be used to represent documents in non-clinical domains. Systematic
theories of aboutness of information fillers and information slots need to be developed
in the future to represent axiomatically the notion of adequate filling. The deontic import
of some slot (e.g., a signature slot) should also be investigated in the future. The
articulation of this ontological system with relational databases could be investigated. As
a matter of fact, a mapping might be made between an attribute in a relational database
and a class of slots (e.g., an attribute describing therapeutic indications might correspond
to a class of slots that each refer to the class of therapeutic indications); whereas identical
values in a relational database’s fields might correspond to the same filler (e.g. all values
of ‘diabetes’ could be retrieved, independently of whether they describe a therapeutic
indication or a past medical condition). Finally, similarities with the type theory in
computer science might provide some insight for this articulation with computer systems.
      </p>
    </sec>
    <sec id="sec-8">
      <title>Acknowledgements</title>
      <p>We thank Laure Vieu, Ryeyan Taseen, Paul Fabry and Cédric Tarbouriech for useful
discussions and insights on related topics, as well as audience at a seminar in Université
de Sherbrooke in July 2020. We also thank two reviewers for their useful feedback.
FT acknowledges financial support by the SPOR Canadian Data Platform (CIHR).</p>
    </sec>
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