=Paper=
{{Paper
|id=Vol-3637/paper26
|storemode=property
|title=Filling with Nothing – An Ontological Analysis of Empty Information
|pdfUrl=https://ceur-ws.org/Vol-3637/paper26.pdf
|volume=Vol-3637
|authors=Adrien Barton,Laure Vieu,Jean-Francois Ethier
|dblpUrl=https://dblp.org/rec/conf/jowo/BartonVE23
}}
==Filling with Nothing – An Ontological Analysis of Empty Information==
https://ceur-ws.org/Vol-3637/paper26.pdf
Filling with Nothing –
An Ontological Analysis of Empty Information
Adrien Barton 1,2, Laure Vieu 1,3 and Jean-François Ethier2
1
IRIT, CNRS, Université de Toulouse, France
2
GRIIS, Université de Sherbrooke, Canada (QC)
3
LOA, ISTC-CNR, Italy
Abstract
We often think about information as having some kind of substantial content. Texts and their
parts (sentences, words, letters…), pictures and musical scores are all substantial in some sense.
However, some pieces of information seem to be less substantial, such as a space between two
words, a portion of canvas left unpainted, a silence during the performance of a piece of music
or a field in a form that is left unfilled. To analyze them, we build on slot mereology applied
to informational entities, which introduces two entities: informational slots and informational
fillers that may fill those slots. We identify three heterogeneous ways in which one may speak
of “empty” information: first, a concretization of information that involves some absence, such
as an empty pattern or a silent process; second, informational slots that can act as receptacles
for fillers; third, empty informational fillers indicating that some information is voluntarily not
provided. The introduction of such empty informational fillers makes it possible to satisfy an
important axiom of company in slot mereology applied to informational entities.
Keywords 1
Informational entity, Slot mereology, Absence, Template, Cognitive representation
1. Introduction
We often think about information as having some kind of substantial content. Texts and their parts
(sentences, words, letters…), pictures, musical scores, are all substantial in some sense. This is apparent
in the fact that typically, information is conveyed by some marks (on a paper, a screen, etc.) – consider
e.g. an ink pattern forming the letter “a”, the picture of a rabbit, or a musical note. However, there is
another kind of important information conveyor, which seems less substantial. Consider e.g. a space in
a written text between two words; a portion of canvas on a painting that is left unpainted; a silence
during the performance of a musical piece; or a field in a form that is left unfilled. There is no doubt
that such features can be relevant. Is there something in common shared by all of them? Because such
information is typically represented by some absence rather than a presence, its existence is unclear:
are there “empty” pieces of information? Or should we refrain from positing the existence of absent
information as an entity? And more fundamentally, what does it mean for a piece of information to be
“empty”? A particularly important example of empty informational entities concerns relational
databases, namely the NULL value. In electronic health records, for example, absent data points (that
is, data generated during a procedure but that are not present in a data source) are a pervasive and
complex phenomenon to deal with. Finding ontological correlates of such values is important when
using e.g. ontologies associated with such records (such as ontologies of drug prescriptions PDRO [1]
or laboratory tests LABO [2]) and matching them with a relational database structure [3].
FOUST VII: The 7th Workshop on Foundational Ontology, 9th Joint Ontology Workshops (JOWO 2023), co-located with FOIS 2023,
19-20 July, 2023, Sherbrooke, Québec, Canada
EMAIL: adrien.barton@irit.fr (A. 1); laure.vieu@irit.fr (A. 2); ethierj@gmail.com (A. 3)
ORCID: 0000-0001-5500-6539 (A. 1); 0000-0003-0303-0531 (A. 2); 0000-0001-9408-0109 (A. 3)
© 2023 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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This paper will thus argue that it is important to distinguish and represent at least several kinds of
empty information2 in ontologies. In particular, it will distinguish 1) “empty representations” (or, more
technically, “empty concretizations” of some informational entities), where it is the physical trace or
process materializing the informational entity that has some empty dimension (absence of a mark, of a
sound, etc.) from 2) some inherently empty informational entities, encompassing in particular: 2-a) slots
that determine the mereological structure of an informational entity, and 2-b) “empty informational
fillers” that specify that the information that is expected to be indicated in such a slot is not provided.
This analysis will clarify the philosophical status of informational slots that were introduced in former
work [4,5], and the introduction of empty informational filler will enable the satisfaction of an axiom
of company in slot mereology applied to informational entities.
The next section will present some philosophical work on nothingness and emptiness. The third
section will expose the motivation and methods, presenting in particular the analysis of informational
entities in the Informational Artifact Ontology (IAO) [6] based on BFO [7]. The fourth section will
propose an ontological analysis of scenarios that could be informally characterized as involving empty
information, and will distinguish three different kinds of such “emptiness” as explained above: empty
concretizations, informational slots and empty informational fillers. The fifth section will show how
the introduction of some empty informational fillers enables to satisfy an important axiom of company
in slot mereology applied to informational entities. A sixth section will conclude the paper.
2. Philosophical and ontological work on nothingness and emptiness
A first field of study that is important to distinguish from our present topic of interest is the
philosophical study of nothingness. It will be helpful though to say a few words on this topic.
Parmenides famously argued that “nothing” cannot exist: one can only speak of a thing that exists. From
this, he deduced the impossibility of change: we cannot speak of a thing in the past (as it does not exist
anymore), and thus the supposed change from a thing in the past to a thing now does not exist. For
Heidegger, the fundamental question of metaphysics was “Why are there beings at all, instead of
Nothing?” [8].
A related branch of philosophy is “meontology”, namely the branch of philosophy that study non-
existence. Philosophy is replete with ontological deflationist theses: idealism claims the inexistence of
the material world (pace the materialists), nominalism claims the inexistence of universals (pace the
realists about universals), illusionism denies the existence of consciousness (pace Descartes),
mathematical anti-platonism denies the existence of mathematical objects, etc.
Our focus of interest here will be, in a sense, the opposite: where some philosophers claim that some
things that “obviously” seem to exist (such as the material world or consciousness) do not in fact exist,
we will claim that some things that might seem not to exist – namely, empty information – do, in fact,
exist. As often in applied ontology (but also sometimes in philosophy [9]), our argument will be
practically guided: we will show the usefulness of ontologies that assume the existence of empty
information – and leave open the question of how those practical considerations should influence a
bona fide philosophical ontology of the world.
Some forms of Buddhism allow Śūnyatā (emptiness) [10] – by contrast to “nothingness”. More
recently, Casati and Varzi proposed an ontology of holes [11] and Hahnmann and Brodaric an ontology
of voids [12]. Thus, our position will find place in this tradition that gives an ontological status to
apparently empty entities, in the specific context of empty information. What is the status of e.g. a space
character in a text, a silence in an utterance, a blank portion of canvas or an unfilled field in a form? As
we will argue, it will be useful to give an ontological status to “empty information”, but we will show
that this informal term can encompass ontologically heterogeneous categories.
2
In this paper, “empty information” should be understood as a shorthand for “empty informational entities” or “empty concretizations of
informational entities” (as will be clarified later), and should not be interpreted as zero-information messages conveyed by logical tautologies
in the context of Shannon’s theory of information.
3. Background and Methods
3.1. Background: Empty Information and its Meaning
By separating chains of characters into words, space characters play naturally a role in the meaning
that we can assign to a given text: “xxxyyy” and “xxx yyy” will typically not be understood the same
way. Moreover, whether we admit its existence in a strong sense or not, so-called “empty information”
can certainly carry meaning thanks to the pragmatics of communication – consider e.g. the following
dialogue: “How do you like my new shirt?” “It’s… [long pause]3 interesting…” Think about a silence
in a musical symphony: an instrument that stops playing, or a plain, total silence. Such silences can
typically carry meanings of quietness; a feeling of achievement – or, on the opposite, of expectation;
embarrassment; anxiety; trouble; death; and so on.
Calligrams by Apollinaire [14] are poems where letters and spaces are arranged to represent
common shapes, such as a bird or a fountain; such spaces might be seen as empty informational units
that act as building blocks for shape depiction. The painting White on White (1918) by Malevich raises
the issue of the status of a white portion on a painting, where the contrast between two kinds of whites
might evoke floating, infinity or movement. Relatedly, the play Art by Yasmina Reza [15] questions
the artistic value of a canvas painted in white. However, ontologically speaking, a portion of canvas
painted in white is not so different from a portion of canvas painted in blue or red – although it may
make an important artistic or psychological difference. More relevant for our current discussion is a
portion of canvas left unpainted on a painting, which may certainly carry meaning (a message, an
emotion…) at some level – whatever our theory of meaning of art is. In traditional Chinese and Japanese
art, “yohaku” refers to the use of empty space: blank spaces were considered to play an important role
in the composition, and to be as important as painted spaces. It could represent light or pictorial depth,
concrete entities like snow, or more abstract notions such as emptiness or time flow [16].
On the musical side, John Cage realized a full piece of music of total silence4 named 4’33” [17] –
that was “performed” on some occasions. If there is no such thing as a musical silence, then one would
have to conclude that he did not create anything with this work; he certainly thought differently.
If empty information can carry meaning, it is only a small step to suppose that there might indeed
exist pieces of empty information that are about something, and in linguistic terms have a syntactic, a
semantic, or a pragmatic role (see e.g. the null subject phenomenon [18]). The conveyor of information
in such situations might not be empty information though, but a more general entity that encompasses
this apparent empty information. For example, in the dialogue mentioned above, the doubt about the
shirt might not be carried by the silence by itself, but by the whole dialogue encompassing the silence.
As we will see though, it will be useful to posit the existence of such empty information.
Note that if empty information exists, then there is arguably not only one instance of empty
information, not even only one type of empty information: the space in a written text, the blank on a
painting canvas or a box on a form left empty are all different kinds of information. I cannot use a
musical silence on a painting; I cannot move a space that appears between two words to a musical score
between two notes. Those kinds of information have very different nature.
3.2. Methods
A variety of ontological frameworks have analyzed the status of informational entity [19], with a
focus on “substantial” informational entities, such as words, sentences or figures. We will show how
such empty information can fit in the theory of information content entities in the context of BFO and
IAO, with occasional inputs from other ontologies.
3
We consider here the case where this pause is an authentic silence, but in real life, such “pauses” are often filled with sounds such as “er” [13]
4
Although according to John Cage, the environmental sounds that are thereof heard during its performance are supposed to be part of this
performance.
3.2.1. Representations and Information Content Entities in IAO
The entities used in this paper are represented on figure 1. In particular, all the axioms reflecting the
taxonomic structure will be accepted, that is, if A is a subclass of B, we accept Aa → Ba.
In BFO, dependent continuants are divided into specifically dependent continuant (SDC, that inhere
in a specific independent continuant) and generically dependent continuant (GDC, that “can migrate
from one bearer to another through a process of copying” [[7] p. 179]). An important subclass of SDC
is Quality. The Information Artifact Ontology (IAO) [6] introduces the class Information Content Entity
(ICE) as a subclass of GDC: documents, databases, paintings, etc. ICEs are about some “portion of
reality”, a label which encompasses all the BFO particular entities (including ICEs) but also universals,
relations, and “configurations” (e.g., the cat being on the mat). ICEs can be “concretized” by one (or
several) “information quality entity” (IQE), but also by one (or several) processes (e.g. an utterance or
a music performance) since BFO-2020 [20].
Smith & Ceusters [6] define Representation as “a quality which is about or is intended to be about
a portion of reality”. Where an ICE must be about some portion of reality, a representation is “more
comprehensive in scope”: it can intend to be about something without actually being about something
(in BFO’s acceptance, which only admits entities recognized by science) – such as a unicorn drawing
by a child who believes that unicorns exist.
The mental functioning ontology further defines Mental quality as “a quality which specifically
depends on an anatomical structure in the cognitive system of an organism” and Cognitive
representation as “a representation which is a mental quality”. Cognitive representations have
constituent parts named “representational units”.
Independent continuant
Material entity
Site
Dependent continuant
Specifically dependent continuant
Quality
Information quality entity
Mental quality
Representation
Cognitive representation
Empty pattern
Generically dependent continuant
Informational entity [IE]
Information content entity [ICE]
Informational slot [IS]
Unattached slot (U-slot)
Slot of slot (S-slot)
Slot of filler (F-slot)
Informational filler [IF]
Empty informational filler [EIF]
Figure 1: Taxonomies of continuants in BFO and IAO, with classes added by us underlined5
IAO then introduces two binary relations. First, “x is_a_representation_of y” means that “x is a
representation & x is_about y” (where y is a portion of reality; note that not all representations are
about something – consider e.g. the unicorn drawing mentioned above). Second, “x is_conformant_to
y” means that “x is an information quality entity & y is a cognitive representation & there is some GDC
g such that x concretizes g and y concretizes g.” For example, if John has a cognitive representation y
of some configuration and writes a concretization x on a piece of paper reflecting this representation
(and thus describing this configuration), then there is an ICE g concretized by both x and y, such that x
is conformant to y.
5
Cognitive representation is also a subclass of Mental quality. IE, IS (and its subclasses) and IF are introduced in former works [4,5].
3.2.2. Proposed Extension of IAO
To account for the fact that some informational entities (such as letters) are not about anything,
contrarily to ICEs, but may be building blocks of ICEs, Barton et al. [4] introduced the class
Informational entity (IE) – which can be elucidated as “A GDC that is a building block of information
or a combination of such building blocks”. For example, the word ‘cat’ (which is an ICE) is an IE, but
so are the letters ‘c’, ‘a’ and ‘t’ (which are arguably not about anything and thus not ICEs). ICEs are
concretized by qualities (although those are not always IQEs, which by definition can only concretize
ICEs). Like ICEs, informational entities can be concretized by mental qualities – although those
qualities are by definition not cognitive representations when they concretize an IE which is not about
anything. Note that we can also easily extend IAO’s notion of conformance to concretizations of such
informational entities that are not necessarily about anything, by introducing the relation
“x is_conformant+_to y” meaning that “x concretizes an informational entity & y is a mental quality &
there is some GDC g such that x concretizes g and y concretizes g.”
A first step towards empty information has been made by some former work on the ontology of
information templates [4,5]. Such templates can be filled with information content entities, but are
considered to exist even if unfilled: think for example of a Latex template, which is an entity in its own
right. A template has some “empty” dimension (even if it can of course be constituted by very
substantial computer language), in the sense that it is a receptacle for more substantial information,
typically a document.
Informational slots have been introduced [4] to account for the fact that an informational entity can
have several times the same informational entity as part, something impossible in classical mereology.
For example, the string ‘the cat’6 has as part twice the letter ‘t’. Substantial informational entities such
as ‘the cat’ or ‘t’ are called “informational fillers”. Their mereological structure can be described by
slots, more precisely, “F-slots” [5] or “slots of fillers”, where a slot is linked to its owner by the relation
“slot-of” (S). Fillers can then fill slots themselves by the relation “fills” (F)7. For example, the string
filler ‘the cat’ has several F-slots, two of which are filled by the same filler ‘t’. The mereological relation
of parthood is analyzed in terms of the relations S and F: a filler x is a direct proper part of the filler y
iff x fills an F-slot of y. Thus, the string ‘the cat’ has the letter ‘t’ as part twice. More generally, any
part of an informational entity occupies a slot of that informational entity – so there exists also, for
example, a slot for ‘the’ and a slot for ‘cat’ in ‘the cat’.
Not only fillers can have slots though. In particular, templates are composed by informational slots,
that are also receptacles for proper parts of the document. Because they are not encompassed into
something bigger, templates8 are called “unattached slots” (U-slots), and the slots that compose them
(for example a field for a first name or an address) are called “slots of slots” (S-slots), and related to
their slot-owners by the same relation S [5]. Thus, slot mereology is an important tool for both the
mereological structure of documents and templates.
Slot of slots can be related to their slot-owner by two subrelations of S: mandatory-slot-of (MS) and
optional-slot-of (OS). Mandatory slots of a slot must be filled for this slot to be filled; but a slot can be
filled without all its optional slots being filled. For example, a slot for an American full name would
have a slot for the last name and a slot for the first name that must be filled for the full name slot to be
filled, and a slot for middle name that may be filled. The two formers are mandatory, the latter is
optional.
It is important for any ontology to analyze the ontological nature of the entities it introduces,
typically by characterizing it pre-formally in a first step. We should not introduce entities motivated
only by their formal convenience (contrast with other work on void entities [12], which introduces a
“unique zero region of no extent and no location”, whose ontological nature seems difficult to
characterize). The importance of such a pre-formal analysis should not be underestimated in any
authentic ontological analysis of the real world. Thus, this paper will give a specific attention to
6
Informational entities will be written with single quote marks.
7
In this paper, “filled” should be understood as “adequately filled” in the sense defined in [21]: structurally adequate (the filler has the right
structure as constrained by the slot it fills), semantically adequate (the filler is about the right sort of things as expected by the slot it fills) and
descriptively adequate (the filler describes a configuration of the world that obtains) when applicable.
8
Here, we call “template” strictly the entity composed by various fields, not the informational entities that might help to read and use this
template (such as boxes encompassing those fields, labels of those fields, etc.)
characterize precisely the real correlates in the world of the formal elements of the theory, which might
be especially difficult to pinpoint when dealing with “empty” informational entities.
4. Ontological Analysis of Scenarios Involving Empty Information
We will now provide an ontological analysis of two sets of scenarios involving seemingly empty
information. The first set (section 4.1) will concern space in a text, a canvas left blank and a silence in
a musical piece. The second set (section 4.2) will concern fields in a form. We will then consider
(section 4.3) how adding informational slots to the picture can provide a fuller account of the situation,
and introduce (section 4.4) empty informational fillers.
4.1. First Set of Scenarios: Space Character, Blank Canvas and Silence
To clarify the nature of so-called “empty information”, we will consider several scenarios presented
in Table 1 below (note that T1-T3 happen in succession, as well as P1-P2 and M1-M2). In scenario T1,
there is an ink pattern written by John on a paper that reads ‘the cat’, which is a representation of (say)
his cat Felix, and concretizes a specific ICE. But there is also an informational entity corresponding to
the space between ‘the’ and ‘cat’, that we will call “IET”. Thus, IET is a part of the first ICE, and we
can suppose that both are concretized by mental qualities in John’s mind. However, John does not leave
any kind of ink mark on the paper to concretize IET: he merely takes his pen up at the end of writing
“the”, moves it to the right, and put it back down to write the word “cat” (assuming he writes them all
on the same line). If we suppose that there is a concretization on paper conformant+ to all relevant
mental qualities, then there must be a concretization of IET on paper. This would be the pattern qT on
the sheet of paper approximately delimitated on its left by the concretization (an ink pattern) of the ‘e’
of ‘the’ and on its right by the concretization (another ink pattern) of the ‘c’ of ‘cat’; we can call such a
pattern an “empty pattern”9. Therefore, the empty pattern qT is ontologically dependent on the ink
patterns (concretizing the ‘e’ and the ‘c’) that approximately delimit its shape. Such patterns belong to
what DOLCE categorizes as “features” (that also include e.g. edges, bumps, etc.) [22]. Empty patterns
that concretize information content entities can thus be called “empty concretizations”.
Table 1
First set of scenarios: Text, painting and music
Scenario Scenario description
T1 John writes by hand on a paper “the cat”.
T2 After T1, John reads aloud distinctively the words he wrote “the
cat”.
T3 After T2, John copies the words “the cat” he wrote earlier on a
computer using a text editor.
P1 On a physical painting on which he has been working, John leaves
a portion of canvas blank and states his work is finished.
P2 After P1, John digitizes his work of art; the portion of blank canvas
is represented on a screen by white pixels.
M1 On a musical score, John leaves a sign between two notes to
indicate a silence (a pause between two notes).
M2 After M1, the musical score is performed by an orchestra.
9
A subtle question concerns the difference between such empty patterns and BFO:sites [5], which are independent continuants typically
demarcated by material entities and their surrounding medium and “which can thus change location, shape and size as their material hosts
move or change shape or size” [20] (such as a grotto or the hold of a ship). It might be the case than such an empty pattern delimitates a site.
Note however that if some informational entities could be concretized by sites, there would be a significant heterogeneity between those
concretized by qualities (which are specifically dependent continuants) and those concretized by sites (which are independent continuants) –
hence the preference for “empty patterns” here. See also the related work on the ontology of holes [11] and voids [12].
In scenario T2, when John reads aloud distinctively ‘the cat’, he produces a sequence of sounds,
including a pause (no sound) between the sounds concretizing ‘the’ and the sounds concretizing ‘cat’
(note that this is the case because he reads the words distinctively; in daily life, we often do not make a
pause between two pronounced words, in which case the space IET is arguably concretized by the non-
silent transition between two sounds). The process of this pause is then the concretization of IET. Such
silences, here again, can be called “empty concretizations”.
In scenario T3, it seems that John copies IET on his computer the same way he copies the other, more
“substantial” characters such as ‘t’, ‘h’, ‘e’, ‘c’, ‘a’ and ‘t’: by pressing a key of his keypad. This
character is (typically) concretized on the screen by some pixels being lit in white (or black in dark
mode), while other characters are typically concretized by some pixels being unlit (or lit in black) and
others lit in white. It is also concretized in the memory system of the computer by some bits (or an
electronic quality at a finer level of granularity – to put it simply), the same way all characters are
concretized. For example, the ASCII code of ‘the cat’ reads ‘116 104 101 32 99 97 116’, where the
space is represented by the code ‘32’, in a similar way to (say) the character ‘t’ being represented by
the code ‘116’. In this scenario, the space IET is concretized similarly to more “substantial” characters,
contrarily to what happened in scenario T1 where IET was concretized by an empty pattern, whereas
other characters were concretized by more substantial ink patterns. As it happens, there is a large variety
of “invisible” characters [23] and although their concretizations are sometimes similar (e.g. a series of
white pixels), some of their other concretizations are different (e.g. Unicode, “show non-printing
characters” mode or bits) and the underlying informational entities are definitely different10.
Scenario P1 is to painting what scenario T1 is to text. One can argue that there is an informational
entity IEP concretized at least by a mental quality in John’s cognitive system, which represents the space
left unpainted on his canvas. Like IET in scenario T1, we can consider it to be concretized by an empty
pattern on the painting (delimitated by neighboring painted areas), which is then conformant+ to John’s
mental quality. In scenario P2, the same blank part on the canvas might be concretized in the computer
system by some electronic quality (and then concretized on screen, e.g. by white pixels).
Let’s now turn to scenario M1 and M2. A silence symbol on partition concretizes some information
entity IEM that can be also concretized by a process of abstaining from playing any note11. Of course,
IEM would also be concretized by some mental qualities in the cognitive systems of the conductor and
the players. Thus, the nature of a silence is not so different from the nature of musical note: it is
concretized by some mental quality when read, and it is concretized by (say) some ink pattern on the
printed partition in M1. Its only “empty” aspect is when it is concretized by a process of the instruments
playing the score staying silent rather than making sounds – as we can see in M2.
Let’s make a quick summary of what we learned so far from those first examples. Some IEs might
be concretized by empty patterns, as illustrated by scenarios T1 and P1; and by silent processes, as
illustrated by scenarios T2 and M2. Those concretizations can be called “empty concretizations”. Thus,
the apparent “empty” character of some empty informational entities characterizes their concretization
rather than those informational entities themselves. Scenarios T3, P2 and M1 show indeed how a space
character, a blank part of a painting or a musical pause can be concretized exactly the same way as
respectively a letter, a painted portion of a canvas or a musical note. That is, we can have two
concretizations of the same IE where one is an empty concretization and the other is a non-empty
concretization. Let us now turn to scenarios involving templates and their fields, which will reveal other
forms of emptiness that characterize the information itself.
4.2. Second Set of Scenarios: Filling a Form
Consider the scenarios in Table 2 (contrarily to earlier scenarios, F1-F4 are alternative possibilities
and do not occur in a succession). John is married in scenarios F1 and F3, and unmarried in scenarios F2
10
There is even a programming language named Whitespace that uses exclusively invisible characters: Space and Tab (and Linefeed). A code
in Whitespace looks thus uniformly blank for a human user on a screen, but is quite clearly defined at the computer memory level, very
similarly to a code written with 0, 1 and linefeeds.
11
Alternatively, one may consider that such a silence symbol would direct a process of not playing anything – that is, (arguably) directing the
absence of an action rather than an action. We will however not investigate in this paper “empty” directive informational entities, and consider
more simply that musical informational entities can be directly concretized by processes of performance (see [24] for more details on directive
informational entities).
and F4. In all scenarios, a questionnaire features a box with the legend “tick the box if you are married”.
Let’s call “qF” the empty pattern that is surrounded by the box. In scenarios F1 and F2, John misses
reading the question asking him whether he is married or not.
Table 2
Second set of scenarios: Form
F1 John is married. He misses the question and leaves the box empty
inadvertently.
F2 John is unmarried. He misses the question and leaves the box
empty inadvertently.
F3 John is married. He reads the question and ticks the box by writing
an “x” in it.
F4 John is unmarried. He reads the question and leaves the box empty
on purpose.
In scenarios F1 and F2, John misses the question. Thus, he does not represent the configuration that
he is married or unmarried in the part of his cognitive system that deals with this form (but such an
information is concretized elsewhere in his cognitive system, as he probably remembers in some way
whether he is married or unmarried). Therefore, there is no informational entity concretized on paper
indicating his marital status.
In scenario F3, when prompted to indicate whether he is married or not, John actively represents in
his cognitive system the configuration that he is married by an informational entity IEF3, concretized by
the cognitive representation qJohnIEF3. He then concretizes IEF3 on paper by the “x” ink pattern
approximately spatially co-localized with qF that we will call qPaperIEF3.
In scenario F4, John also actively represents in his cognitive system the configuration that he is
unmarried by some informational entity IEF4, concretized by the cognitive representation qJohnIEF4. Like
in the case of text, IEF4 would then be concretized by the empty pattern qF. Since qF already existed
before John started filling the form, this implies that it becomes the concretization of IEF4 when John
consciously chooses to leave it unfilled12.
If John did not tick the box, there is no way for an external observer by just looking at the filled form
to know whether he is in a scenario F1/F2 (that is, John missed reading the question and did not create
an informational entity to represent his marital status) or F4 (that is, John left the box empty on purpose
and there is an informational entity IEF4); but if asked later, John can help to clarify whether the situation
was F1/F2 or F4. John might e.g. explain that he had not seen this question, or that he had seen this
question and left it blank on purpose as he is unmarried. Thus, it is important to be able to represent a
scenario like F4 differently from a scenario like F1 or F2. Accepting an informational entity such as IEF4
is a way to do so. Like other entities analyzed in former scenarios, however, the empty dimension does
not concern IEF4 intrinsically, but rather the pattern qF that concretizes it.
In scenario F2, the visible status of the form is, by chance, not misleading: although John missed the
question, he is unmarried, so the form looks correct to an agent aware of his marital status, and an
external reader not previously aware of his marital status is going to make a right inference about John’s
marital status based on this form. In scenario F1, on the other hand, the visible status of the form is
misleading: an external reader might infer incorrectly from it that John is unmarried. However, from an
ontological point of view, the form is incorrectly filled in both scenarios F1 and F2: indeed, in F2, for
the form to be correctly filled, there should have been a conscious decision to leave the field empty like
in F4 (for more details about the difference between correctly filling and incorrectly filling, see [21]).
Such distinctions have clear applications for clinical documents. Similar to the distinction between
scenarios F1 and F4, forgetting to fill in your allergy to penicillin versus leaving the relevant field empty
12
Of course, we do not suppose that there is some kind of magical interaction between John and the paper as soon as he decides that he will
not tick the box. The fact that such physical entity concretizes such informational entity is just an ontological rephrasing of the cognitive and
communicational nature of language and meaning.
because you do not have such allergy can obviously lead to vastly different consequences, and therefore
need to be distinguished.
As we are now going to see, slot mereology applied to informational entities introduces another type
of entity that needs to be analyzed: informational slots.
4.3. Refining the Analysis with Informational Slots
The informational entities IET, IEP, IEM, IEF3, IEF4 presented above belong to the class of
informational fillers. However, as explained earlier, there is another kind of informational entity,
namely informational slots. For example, the string ‘the cat’ comprises seven F-slots s1-s7, filled
respectively by the informational entities ‘t’, ‘h’, ‘e’, ‘ ’, ‘c’, ‘a’ and ‘t’. If a painting is digitally
represented as an array of pixels, each pixel can also be represented as concretizing an informational
entity filling an F-slot. Finally, a form is an especially important case of application of informational
slots. In scenarios F1-F4, the whole questionnaire template would comprise various S-slots: the one that
interests us and that can be filled to indicate a marital status of “married”, but also e.g. one for the first
name, one for the last name, etc.
If we take a broadly realist stance towards ontology, then slots should appear in reality; and if they
are bona fide informational entities, they should be concretized. How are such slots concretized? In ‘the
cat’, the slot s2, for example, which is filled by the letter ‘h’, might be concretized on the paper by the
empty pattern between the concretization of the first ‘t’ and the concretization of the ‘e’. Thus,
informational slots might also be concretized by empty patterns. But what about the concretization of
the slots s4 filled by the space ‘ ’? Arguably, the empty pattern qT between the letters ‘e’ and ‘c’
concretizes the slot s4. Thus, if we also accept as explained earlier that qT does concretize the space
character IET, it means that it concretizes both s4 and its filler IET.
Similarly, on the form in scenarios F1-F4, the slot ISF for indicating the marital status is concretized
by the empty pattern qF. If we accept that an empty pattern can also concretize an informational filler,
then qF concretizes both ISF and the information filler IEF4 indicating that John is unmarried in
scenario F4. In scenarios F1 and F2, however, where John did not create an empty informational entity
concerning his marital status, qF only concretizes the (unfilled) S-slot ISF.
Within this framework, we have thus a duplication of “empty” informational entities: the slot ISF is
always concretized in scenarios F1-F4 (by the empty pattern qF on paper in all four scenarios, and by a
cognitive representation of John in scenarios F3 and F4), and an information filler is also concretized
(by a different cognitive representation and the same empty pattern qF on paper) in scenario F4.
Although it might seem at first sight an expensive ontological price to pay, this ontology enables the
differentiation of scenarios F1/F2 from scenario F4, which is important for the reasons explained above.
Also, this ontology enables to have an external representation on paper of the filler that is conformant+
to the mental quality concretizing this filler.
Figure 2 presents some of the entities involved in each scenario (instantiated classes are written in
italics below the instance names). To represent the difference between scenarios F1 and F2, one would
need to represent the married or unmarried status of John, as well as the true or false beliefs [25] of the
readers of the form: in F2, a reader may have a true belief that John is unmarried, whereas in F1, a reader
may have a false belief that John is unmarried.
Similarly, all kinds of slots (U-slots, S-slots and F-slots) can be concretized, in particulars by empty
patterns. We could imagine other kinds of concretizations: when Jane asks to John “Are you married?”,
she arguably concretizes a slot for John to provide his answer, and the concretization is a process of her
staying silent after asking the question. Note however that slots might be concretized in a more
substantial way. A slot for inputing one’s marital status, for example, might be represented in a
computer in a quite similar way as any filler – namely by a sequence of bits or an electronic
configuration. Here again, there is an “empty” dimension we might spontaneously assign to some slots
that rather characterize some of their concretizations. However, all slots still have inherently another
fundamental “empty” (or “hollow”) dimension, namely their status of possible receptacles of fillers.
Figure 2: Informational entities and their concretizations in each scenario (C: concretized_by)
4.4. Empty informational fillers
Finally, we need to introduce a third important kind of “empty” dimension. This one characterizes
directly some informational fillers, namely fillers that indicate that the information expected to be
provided in a slot is not provided, whatever the reason – e.g. because a question does not apply to the
respondent, because he doesn’t know the answer, or because he does not want to answer it13. We will
call such entities “empty fillers”. Consider for example a form with a slot for the respondent to indicate
his middle name, should he have one. It might be filled either by a chain of characters constituting the
middle name of the person, or by an empty filler indicating that no middle name is provided – which is
not the same as indicating that the person has a middle name, and that their middle name is a chain of
blank characters (in that very hypothetical case, the filler would not be intrinsically empty, only its
concretization might be). If a field of a form is filled and the answer is then erased for confidentiality
reasons, then the original (non-empty) filler is replaced by an empty filler indicating that the expected
information is not provided (anymore). To take another example, the missing part of the book that I am
writing could correspond to an empty filler filling a slot of the template of my book that is concretized
in my cognitive system.
In scenarios F1 and F2 above, John did not fill the slot corresponding to the box; in scenario F3, he
filled it with a (non-empty) informational filler concretized by an “x” sign; and in scenario F4, he also
filled it with a non-empty informational filler (since it does provide information), which is concretized
by an empty concretization.
We could imagine additional scenarios to F1-F4 to clarify further the distinction between empty and
non-empty informational fillers. For example, John might be married but deceptively decides to leave
the box unchecked. Depending on what he plans to say, should he be confronted about his answer (“I am
married but I did not see the field” or “I am unmarried and this is why I left the box unchecked”), he
either left the slot unfilled (a case of inadequate filling [21]), or filled the slot with a filler that has an
empty concretization and misrepresents reality (since in this latter case he deceptively communicated
that he is unmarried); note that in this case, like in F4, this filler is not an empty filler (since it does aim
at providing information). Alternatively, John might not know whether he is married, e.g. if he suffers
from dementia; in such a case, he might fill the slot with an empty informational filler indicating that
the information is voluntarily not provided (because he does not have access to this information
himself). Or he might refuse to communicate whether he is married: here again, he would fill the slot
with an empty informational filler.
Of course, we might not know whether John missed the field or saw it, whether he intended to tell
the truth or intended to lie, and whether he has access to the relevant information or not – to take a few
examples. Nevertheless, as soon as John represents something in his cognitive system, the associated
informational entities exist and it is thus important for an ontological theory to be able to account for
them. In case the ontologist does not know whether John represented such entities in his cognitive
system, he can just abstain from representing the relevant particulars, since ontologies are traditionally
written following the open-world assumption. Should John clarify his position, the ontologist could
then introduce in the ontology the representation of the relevant particulars. Being able to represent
such entities can in itself be a useful guide to design better forms that are able to more effectively
capture these different situations.
13
Note that IEF4 above was not an empty information filler in this sense, as it did answer the question, by stating that John is not married;
only its concretization could be said to be “empty”.
An important case of empty filler for information systems is the NULL value in relational database.
A problem with NULL is its ambiguity: in particular, it might denote non-applicability of the
information (the “nonexistent interpretation”) or unknowability (the “unknown interpretation”) [26].
An ontology of empty fillers could thus introduce several subclasses of the class Empty filler, bringing
additional semantics. Such subclasses would encompass respectively empty fillers denoting non-
applicability of the information (that is, inexistence of the entity that is supposed to be referred to by
the filler of a slot), or those denoting unknowability, or – in the context of relational databases – other
aspects as listed on [27]. Thus, an instance of Empty filler might be later reclassified into one of its
subclasses, should additional information be provided (as in some examples considered in our paper).
More specifically, our theory is expected to provide the semantics supporting mappings between a
relational database that accepts NULL value and an ontology of information including such subclasses
of Empty filler. Even further, it can support the creation of relational databases on the basis of this
ontology that enables to clarify, for each occurrence of the NULL value, which interpretation of it
should be retained (or clarify that we do not know which interpretation of it should be retained for some
occurrences of NULL). We will now see that the introduction of such empty fillers is also important
from a theoretical and technical point of view to satisfy an axiom in slot mereology.
5. Empty Fillers at the Rescue of Informational Slot Mereology
To explain the important role of empty fillers, we need first to remind that although S-slots describe
the mereological structure of templates and F-slots describe the mereological structure of fillers, the
former might constrain the later. More specifically, the mandatory slot structure of a slot should be
mirrored in the slot structure of the filler that fills it [5]. So for example, if a slot full_name0[] has as
mandatory S-slots first_name0[] and last_name0[], then a filler of it (say ‘John Doe’) must have a
similar mereological slot-structure with two “mirrored” F-slots (say “first_nameJS[]” and
“last_nameJS[]”), such that an S-slot and its mirrored F-slot must be filled by the same filler. However,
this kind of constraint only holds for the mandatory slots: if full_name0[] has as optional slot
middle_name0[], then it is not compulsory for a filler of full_name0[] to have a mirrored slot of
middle_name0[] (and indeed, ‘John Doe’ has no part that would be a middle name – see Figure 3 for
an illustration).
Such a representation raises an issue though. Consider now the case of Afghan names, that must
each contain a first name and can, but must not, contain a last name – as not all Afghan persons have a
last name. This means that a template for Afghan names Af_full_name0[] would have two slots: a
mandatory slot Af_first_name0[] and an optional slot Af_last_name0[]. Consider now an Afghan
person named ‘Ali’ who doesn’t have any last name, and let’s write x his complete name (see Figure 4a).
x fills Af_full_name0[], thus the mandatory slot structure of Af_full_name0[] must be mirrored in x:
x has a mirrored slot of Af_first_name0[] that we will call First_nameAli[]. However, there is no other
F-slot in x: this violates an important “axiom of company” according to which any F-slot of an entity
should be accompanied by another F-slot14. Such an axiom is especially important, as its violation
implies the violations of axioms of weak (and strong) slot supplementation [28].
14
Note that the classical mereological axiom of company, according to which any proper part of an entity should be accompanied by a different
proper part, is not true in slot mereology: the string ‘xx’ has ‘x’ as proper part, but there is no informational filler different from ‘x’ that is a
part of ‘xx’; however ‘xx’ has two different F-slots, each filled with ‘x’.
Figure 3: The mirroring of the slot structure of a slot into the slot structure of its filler
Empty fillers offer a way out of this problem. In the former axiomatic system [5], if a slot is filled,
then all its mandatory slots are also filled:
(A13) Mandatory slots of a filled slot are also filled ∃y Fyt → ∀u (MSut → ∃x Fxu)
We can instead impose that all slots of a slot must be filled (for this slot to be filled), but optional
slots can be filled by an empty filler. Thus, we replace A13 by the following:
(EA13) Slot is filled iff all its slots are filled ∃y Fyt ↔ ∀u (Sut → ∃x Fxu)
Of course, EA13 trivially implies A13, but it implies more. First, the optional slots of a filled slot
are also filled; however, they can be filled by an empty filler. Second, it is sufficient for a slot to be
filled that all its slots are filled (keeping in mind that its optional slots might be filled by empty fillers).
If we introduce the class “empty informational filler” represented by the predicate EIF, we can also add
the axiom:
(EA14) Fillers of mandatory slots are not empty MSut & Fyt & Fxu → ¬EIFx
This means that we could now impose an axiom according to which all slots of a slot s (not only its
mandatory ones) are mirrored by F-slots in the filler of s. In the Ali example, this means that the full
name of Ali (let’s write it 'Ali ∅’15) encompasses not only the information about his first name ‘Ali’,
but also the information that he has no last name (see Figure 4b).
Figure 4: a) Violation of F-slot-company ; b) A reformulation of the theory with empty informational
entities
15
Note that there could be several approaches to the identity of empty fillers. Maybe there is a specific empty filler for a middle name not
being applicable, a different one for a last name not being applicable, etc. A more radical approach would be to assume that there is a unique
empty filler denoting non-applicability, whose meaning is contextually determined by the slot it fills (synonym to: ‘the information expected
in this slot is not applicable’). This question would need to be addressed within a wider analysis of the identity of informational entities. In
any case, it is important to realize that would two persons named “Ali” fill the last-name slot with the same empty filler indicating non-
applicability, the fact that they use the same empty filler would not imply that they have the same last name; rather, it implies that both indicate
they do not have a last name.
6. Conclusion
We have identified three heterogenous ways in which an information-related entity can be
informally qualified as “empty”. First, some concretizations of informational entities (whether fillers
or slots) are empty in the sense that they are empty patterns or (partial) silence processes, by contrast to
more “substantial” entities such as ink patterns or non-silent processes. However, the same
informational entity can be concretized by either empty or more substantial concretizations, for example
digitally by a sequence of bits or an electronic configuration; thus, this does not characterize inherently
empty information. Second, informational slots themselves might be qualified as “empty” in the sense
that they can be receptacles of informational fillers. Third, some informational fillers are empty in the
sense that they indicate that the expected information is not provided – such as an empty filler of a slot
for middle name indicating that the person who filled the form does not have a middle name, or does
not want to communicate it. NULL values in relational databases are such a case of empty informational
fillers, and introducing subclasses of empty informational fillers might help to clarify the signification
of various NULL values.
Note that some concretizations of informational slots or empty informational fillers are empty
concretizations, but not all of them are. For example, both an informational slot and an empty
informational filler might be concretized by a sequence of bytes in a computer system, and an empty
informational filler might be concretized by a pen stroke in a box. Also, the scenario of John indicating
no middle name is especially relevant as it illustrates the three kinds of information emptiness: in that
scenario, 1) the slot for the middle name is “empty” insofar as it is a slot, 2) the filler indicating that no
middle name is provided is an empty filler, and finally 3) both this slot and its filler are concretized by
the same empty pattern (which is thus an empty concretization).
As we saw, it is important to accept an ontology such that when an informational slot is processed
in the way it is supposed to be, it is always filled – be it by an “empty” informational filler. Indeed, such
a representation enables the satisfaction of an important mereological axiom of slot-company. Thus,
our former theory in terms of mandatory slots that need to be filled for the parent slot to be filled and
optional slots that can remain unfilled needs to be adapted. In the revised theory, all slots of a filled slot
must be filled, and mandatory slots must be filled by non-empty informational fillers whereas optional
slots can be filled by empty informational fillers. However, a slot can remain inadequately filled (as
analyzed by [21]), a particular case of which would be for the slot to remain unfilled. Overall, this work
on empty information is an important step towards the creation of a full theory of mirrored slots in the
context of slot mereology for informational entities, that would combine former works on the
mereological structure of fillers [29] and on mandatory and optional slots [5].
7. Acknowledgments
We thank several anonymous reviewers for their useful comments on this paper. AB thanks Therese
Granholm for inspiring discussions on the use of empty space in art.
8. References
[1] J.-F. Ethier, A. Barton, R. Taseen, An ontological analysis of drug prescriptions, Applied Ontology
13 (2018), 273–294.
[2] A. Barton, P. Fabry, L. Lavoie, J.-F. Ethier, LABO: An Ontology for Laboratory Test Prescription
and Reporting, in: A. Barton, S. Seppälä, D. Porello (Eds.), Proceedings of the Joint Ontology
Workshops 2019 (JOWO 2019), CEUR-WS.org, Graz, Autriche, 2019, pp. 1–9.
[3] C. Khnaisser, L. Lavoie, B. Fraikin, A. Barton, S. Dussault, A. Burgun, et al., Using an ontology
to derive a sharable and interoperable relational data model for heterogeneous healthcare data and
various applications, Methods of Information in Medicine 61 (2022), e73–e88.
[4] A. Barton, F. Toyoshima, L. Vieu, P. Fabry, J.-F. Ethier, The Mereological Structure of
Informational Entities, in: B. Broadaric, F. Neuhaus (Eds.), Formal Ontology in Information
Systems. Proceedings of the 11th International Conference (FOIS 2020), IOS Press, Bolzano, Italy,
2020, pp. 201–215.
[5] A. Barton, C. Tarbouriech, L. Vieu, J.-F. Ethier, A Mereological System for Informational
Templates, in: T.P. Sales, M. Hedblom, T. He (Eds.), Proceedings of the Joint Ontology
Workshops 2022 (JOWO 2022), CEUR Workshop Proceedings, Jönköping, Sweden, 2022, pp. 1–
12.
[6] B. Smith, W. Ceusters, Aboutness: Towards foundations for the information artifact ontology, in:
Proceedings of the 6th International Conference on Biomedical Ontology, CEUR-WS.org, Lisbon,
Portugal, 2015, pp. 1–5.
[7] R. Arp, B. Smith, A.D. Spear, Building Ontologies with Basic Formal Ontology, The MIT Press,
2015.
[8] M. Heidegger, Introduction to metaphysics, Yale University Press, 2014.
[9] D. Lewis, On the plurality of worlds, Blackwell, Oxford, 1986.
[10] The Editors of Encyclopaedia Britannica, Sunyata, Encyclopaedia Britannica, 1998.
[11] R. Casati, A.C. Varzi, Holes and other superficialities, MIT Press, 1994.
[12] T. Hahmann, B. Brodaric, The void in hydro ontology, in: Formal Ontology in Information
Systems, IOS Press, 2012, pp. 45–58.
[13] S. Betz, Linguistic Considerations on the Awkward Silence, in: Silence and Its Derivatives:
Conversations Across Disciplines, Springer, 2022, pp. 43–62.
[14] G. Apollinaire, Calligrammes: Poèmes de la paix et de la guerre (1913-1916), Mercure de France,
1918.
[15] Y. Reza, Art, Actes Sud, 1994.
[16] M.N. Parent, Yohaku, JAANUS (Japanese Architecture and Art Net Users System), 2003.
[17] S. Davies, John Cage’s 4′ 33 ″: Is it music?, Australasian Journal of Philosophy 75 (1997), 448–
462.
[18] O. Jaeggli, K.J. Safir, The null subject parameter and parametric theory, The Null Subject
Parameter (1989), 1–44.
[19] E.M. Sanfilippo, Ontologies for information entities: State of the art and open challenges, Applied
Ontology 16 (2021), 111–135.
[20] International Organization for Standardization, ISO/IEC 21838-2:2021 Information technology
— Top-level ontologies (TLO) — Part 2: Basic Formal Ontology (BFO),
https://www.iso.org/standard/74572.html, 2021.
[21] A. Barton, F. Toyoshima, J.-F. Ethier, Clinical Documents and Their Parts, in: J. Hastings, F.
Loebe (Eds.), ICBO|ODLS 2020 International Conference on Biomedical Ontologies 2020,
CEUR-WS.org, Bolzano, Italy, 2020, p. A.1-11.
[22] S. Borgo, R. Ferrario, A. Gangemi, N. Guarino, C. Masolo, D. Porello, et al., DOLCE: A
descriptive ontology for linguistic and cognitive engineering, Applied Ontology 17 (2022), 45–69.
[23] Whitespace character, Wikipedia, the Free Encyclopedia (n.d.),
https://en.wikipedia.org/w/index.php?title=Whitespace_character&oldid=1146154369.
[24] A. Barton, L. Vieu, J.-F. Ethier, Directing Actions, in: A. Barton, S. Seppälä, D. Porello (Eds.),
Proceedings of the Joint Ontology Workshops 2019 (JOWO 2019), CEUR-WS.org, Graz,
Autriche, 2019, pp. 1–10.
[25] F. Toyoshima, A. Barton, O. Grenier, Foundations for an ontology of belief, desire and intention,
in: B. Broadaric, F. Neuhaus (Eds.), Formal Ontology in Information Systems. Proceedings of the
11th International Conference (FOIS 2020), IOS Press, Bolzano, Italy, 2020, pp. 140–154.
[26] C. Zaniolo, Database relations with null values, in: Proceedings of the 1st ACM SIGACT-
SIGMOD Symposium on Principles of Database Systems, 1982, pp. 27–33.
[27] K. Baclawski, The Meaning of Null in Databases and Programming Languages,
https://arxiv.org/html/1606.00740, 2016.
[28] A. Varzi, Mereology, in: E.N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy, Spring 2019,
Metaphysics Research Lab, Stanford University, 2019.
[29] C. Tarbouriech, A. Barton, L. Vieu, J.-F. Ethier, The Counting Problem of Slot Mereology, in:
T.P. Sales, E. Sanfilippo (Eds.), Proceedings of the Joint Ontology Workshops 2021 (JOWO 2021),
CEUR Workshop Proceedings, Bolzano, Italy, 2021, pp. 1–15.