=Paper=
{{Paper
|id=Vol-2050/winks-paper4
|storemode=property
|title=An Approach to Interaction-Based Concept Convergence in Multi-Agent Systems
|pdfUrl=https://ceur-ws.org/Vol-2050/WINKS_paper_4.pdf
|volume=Vol-2050
|authors=Kemo Adrian,Enric Plaza
|dblpUrl=https://dblp.org/rec/conf/jowo/AdrianP17
}}
==An Approach to Interaction-Based Concept Convergence in Multi-Agent Systems==
https://ceur-ws.org/Vol-2050/WINKS_paper_4.pdf
An Approach to Interaction-Based
Concept Convergence in Multi-Agent
Systems
Kemo Adrian a,b Enric Plaza a
a IIIA, Artificial Intelligence Research Institute
CSIC, Spanish Council for Scientific Research,
Campus UAB, 08193 Bellaterra, Catalonia (Spain) enric@iiia.csic.es
b Universitat Autònoma de Barcelona, kemo.adrian@iiia.csic.es
Abstract. The problems that are faced by two communicating systems that have
different knowledge representations can be difficult to formalize due to the different
notations of these different knowledge representation approaches. We present a new
formalism that has been conceived to describe how communicating systems can
argue the meaning of their concepts. This aims to help to develop new methods for
the systems with heterogeneous vocabularies to reach mutual understanding.
Keywords. Multi-Agent Systems, Knowledge-Sharing, Formalism, Interaction-
Based, Semiotics
1. Introduction
“What ya going to have, Mac? Something to eat?”
“Yeah. What kind of sandwiches ya got besides hamburgers and hot dogs?”
“How about a ham’n cheese sandwich?”
“Nah ...I guess I’ll take a hamburger again.”
***
“Hey, that’s no hamburger; that’s a cheeseburger!”
Charles O. Frakes, 1962 [7]
The first requirement for a communication can be seen as the ability for two systems
to send and receive signals. If two systems want to communicate, we assume that they
will need more than sending and receiving random noises. This is where the key notion
of meaning appears. Our two systems will need of course to exchange symbols, but
also to agree that these symbols have – if not equal, at least compatible – meanings. A
global agreement on the symbol-meaning associations from both systems leads to mutual
intelligibility, while disagreements might cause you to eat something different than what
you thought you ordered. How to reach such an agreement is the object of various fields
of research that we can refer to by the term concept convergence.
1.1. Context
Before addressing any issue in communicating systems, there should be a clear definition
for each of the three key elements listed above: the symbol, the meaning and the nature
of their relation.
A definition for the term symbol is given relatively to the notion of sign by Pierce:
there are three kinds of sign – icons, indexes and symbols. A symbol is a sign that “de-
notes its object solely by virtue of the fact that it will be interpreted to do so”: it pos-
sesses an abstract relation with its associated meanings, (for instance the words “poule”,
“pollo” and “chicken” do not share any physical connection with the animal that they
represent). Symbols are the category of sign that we use in computer science.
Conversely, the term meaning is more tricky to define. There is a long story of de-
bate within the field of philosophy of language over the meaning of meaning. However,
Goldstone [8] simplifies them into two major branches: the conceptual web approach
and the externally grounded concepts approach. The former approach considers that the
meaning of a concept is given by its connections to other concepts [3] [6] [11] in a simi-
lar way as the early semiotic theories of Ferdinand De Saussure. In contrast, the last ap-
proach considers that a meaning has to be grounded. The term has been coined by Steven
Harnard and its thought experiment of the Chinese room [9]. The conceptual web ap-
proach finds its foundation in the British empiricist movement and continues to influence
science today, through the embodied cognition theory in cognitive sciences for instance.
With the diversity of approaches to give a definition of meaning, and often in contra-
diction with each other, it can be challenging for researchers to address formally an issue
in communicating systems, especially if the research takes place in an interdisciplinary
context that combine the two approaches. We do not intend to list the advantages and
drawbacks of each approach, we rather intend to create a formalism that can be used in
both.
1.2. Aim of our Formalism
While this formalism does not define the notion of meaning, it defines a set of other
related notions that can help anyone to create a formalization of its custom notion of
meaning – regardless to where this notion falls in the spectrum of possible approaches,
between the conceptual web and the externally grounded concepts. Moreover, even if a
scientific community decides to use a huge set of definitions for the notion of meaning,
as long as they notions are defined in the same formalism it will be possible to compare
them, and their related work.
Researchers from many fields including (but not limited to) Machine Learning, On-
tology Matching or Multi-Agent Systems need to address a broad range of situations
where two communicating systems, that we will refer to as agents from now on, do not
agree on the meaning of their symbols. In order to clarify their problem and solution,
they need a robust and domain independent formalism that provides clear definitions for
notions including meaning, agreement on the meaning, concept etc.
We provide a formalism that defines these notions in a compatible way with respect
to each other. While this formalism has been initially created in the context of symbolic
inductive learning [2], it incorporates elements from semiotics and can be used with
a large set of approaches. The formalism’s inherent flexibility comes from three main
points:
The formalism is designed for an interactive approach In most of ontological ap-
proaches, a third system – the oracle – will solve the disagreements on the meaning be-
tween two other agents by accessing the combined knowledge of both agents [5]. We de-
signed a formalism that is able to work in an interactive way, where the two disagreeing
agents are able to solve their disagreements by interacting with each other, without any
help from a third part. While this allows the formalism to remain compatible with classi-
cal approaches of ontology matching, the growing interest from the research community
in interactive approaches [4] allows this point to be a main feature of our formalism.
The formalism is designed for a lazy approach This formalism is designed to allow a
lazy approach of resolving disagreements on the meaning: a disagreement can be solved
on demand when it arises, without requiring an exhaustive analysis of both agent’s sym-
bols and meanings. For this reason, the formalism can represent a concept as itself, not
only through all its relations with other concepts (external concepts approach). The ex-
haustive approach usually found in ontology matching (conceptual web) can also be for-
malized, due to the notion of contrast set which defines a set of concepts by their respec-
tive relations.
The formalism differentiates symbols and meanings The formalism establishes a strict
distinction between the symbol and what it stands for, allowing the agents to clarify the
notions of symbol, meaning, and these two notions’ relations. This allows researchers
to formalize models where the agents can dynamically modify the symbol of a concept
without modifying the relations that the concept has with other concepts, in the case of a
conceptual web approach.
2. Semiotic Formalism
2.1. Presentation
The formalism uses the three basic components of semiotics from the semiotic triangle
of Odgen and Richards [10], and draw a correspondence between the triangle’s symbol,
thought of reference and referent with respectively the sign, the generalizations and the
examples more commonly used in machine learning (see Figure 1).
These three components are assembled into a concept, and concepts are assembled
among containers. There are two kinds of containers: the contrast sets, that are used for
communication by agents, and the hypotheses, that are not suitable for communication
but useful during the process of building new contrast sets.
2.2. Semiotic Elements
The semiotic element are the components of concepts and containers. The different el-
ements that an agent has perceived in its environment are called examples – real world
observations of objects. For example, a specific chair from an office is an example. They
are noted ei . A context E = {e1 ...en } is a set of examples. An extensional definition on a
context is a set of examples Ei ⊂ E.
The agents are using ψ-terms as their representation language. An agent represents
an example ei using a feature-term. A generalization g j of a set of examples Ei is an other
Intensional definition
Sign Extensional definition
Figure 1. The semiotic triangle representations of a concept to compare the original semiotic elements from
Odgen and Richard (left) to the ones used in our formalism (right).
feature-term that verifies ∀ei ∈ Ei , g j v ei . An intensional definition Ii = {g1 ...gi } is a set
of generalizations.
A sign si is an abstract entity that exists only in the communication between two
agents. A concept Ci = (si , Ii , Ei ) is the triadic relation between a sign1 , an intensional
definition and an extentional definition. The relation should verify: ∀ei ∈ Ei , ∃gi ∈ Ii as
gi v ei . If the concept Ci belongs to an Agent Ak , we note it Cik .
2.3. Containers
Containers are a dyadic relation between a context E and a set of concepts {C1 , ...,Cn }.
A hypothesis H = (E, {C1 , ...,Cn }) is a container such that the set of examples E1 ∪
... ∪ En ⊆ E and where the signs of the concepts are different: ∀Ci ,C j ∈ {C1 , ...,Cn },
i 6= j → si 6= s j . We will note the context of the hypothesis EH .
A contrast set K = {C1 , ...,Cn } is a container such that the context E = E1 ∪ ... ∪ En ,
the concepts are disjoint ∀i, j, Ei ∩ E j = 0/ and the signs of the concepts are different. K
is a partition of E. We will note the context of the contrast set EK .
3. Agreement and Disagreement
In multi-agent systems, agents are using their contrast sets to encode a meaning into a
sign and decode signs into meanings. Understanding the conditions to mutual intelligi-
bility between two agents requires to study the relations between the contrast sets they
are using, A1 .K for agent 1 and A−1 .K for agent 2. Since we aim to grant the agents with
the ability to modify their contrast sets into A1 .K 0 and A−1 .K 0 , the relation between an
initial version Ak .K of a contrast set and its latest version Ak .K 0 needs to be studied as
well.
1 Notice that there is no constraint on the sign, therefore the choice of a sign for a concept is arbitrary. The
arbitrariness of the sign means that all of those signs are symbols from a semiotic point of view.
3.1. Agreement over Meaning
Agents always aim to set the contrast set they are using as intelligible for both of them: we
refer at this aim as mutual intelligibility. Each agent is in charge of evaluating if a contrast
set is intelligible for himself. The different criteria that an agent uses to evaluate whether
or not a contrast set is intelligible from its point of view, are called the agreements.
3.1.1. Synchronic Agreement
The first criterion to the intelligibility, is to share the same signs for concepts with same
extensional definitions, and different signs for concepts with different extensional defi-
nitions. In order to avoid ambiguity, the contrast sets still need to have the extensional
definitions of its concepts disjoint. This criterion is the synchronic agreement, referring
to the sub-field of linguistics that describes language at a specific point of time, by op-
position to diachronic. The synchronic agreement can be formalized as ∀(Cik ,C−k j ) with
k −k k k k k
Ci ∈ Ak .K and C j ∈ A−k .K, (Ei = E j ) ⇔ (si = s j ), (Ei ∩ E j = 0) / ⇔ (si 6= s j ) and
k k k k
(Ei = E j ) Y ((Ei ∩ E j ) = 0)2
/ .
3.1.2. Diachronic Agreement
A second criteria reflects the expected trade-off between generalization and specializa-
tion among a contrast set. We want the agents to have concepts general enough to remain
as far as possible from the extreme scenario of having one different concept by exam-
ple. However at the same time, we want the agents to have concepts specific enough to
remain as far as possible from the extreme scenario of having only one concept for all
examples.
We consider here that agents initially start with contrast sets that were intelligible
from their point-of-view. Therefore, we use there level of trade-off as the baseline for
the expected generality and specialization of any new contrast set’s concepts. However,
if agents need to change their concepts in order to reach mutual intelligibility, they will
have to make concessions either on the generality or the specialization of their concepts.
Therefore, we have to make a choice between having more general or more specific
concepts as the result of the changes.
Since the number of concepts among the contrast set is from far inferior to the num-
ber of examples in its context, the risk of having an over-generalized contrast set is more
constraining than the risk of an over-specialized. For this reason, an agent can only give
its agreement to a contrast set that is more specific than its initial one. It will be the role
of the argumentation to limit the concepts’ specialization. We call this criterion the di-
achronic agreement, in reference to linguistics where diachronic refers to the develop-
ment and evolution of language through time. The diachronic agreement can be formal-
ized as ∀Cik ∈ Ak .K, !∃(Ckj ...Cnk ) ∈ Ak .K 0 such that E j ∩ ... ∩ En = 0/ and E j ∩ ... ∩ En = Ei .
3.2. Disagreements over the Meaning
Within a mutli-agent system, the success of a communication lies on multiple criteria
that we present as agreements. Every contradiction to these criteria are seen as disagree-
2 Y is an infix for “exclusive or”.
Synchronic Agreement Diachronic Agreement
b b b
b
p p p
Agent 1 Agent 2 t t+1
b b
б
b
p p
п
Agent 1 Agent 2 t t+1
Synchronic Disagreement Diachronic Disagreement
Figure 2. A synchronic (left) and diachronic (right) agreement (top) and disagreement (bottom). The syn-
chronicity is related to the concepts’ relations between two different agents’ contrast sets, while the diachronic-
ity is linked to the evolution of one same contrast set over the time.
ments over these criteria. Since the criteria over one agent’s agreement are now clear, it
is possible to express which relations between concepts can contradict them. Since we
have synchronic and diachronic agreements, we refer to their respective contradictions
as synchronic and diachronic disagreements.
First, the synchronic agreement can be contradicted by two kinds of relations: rela-
tions between two concepts’ signs, or relations between two concepts’ extensional defi-
nitions.
The first kind of synchronic disagreement is related to the signs. If two concepts
Cik ∈ Ak .K and C−k j ∈ A−k .K have different signs but their extensional definitions are
the same, situation that is formalized as (si = s j ) ∧ (Ei 6= E j ), the two concepts are in
a relation of homonymy. However, if the two concepts have different sign but the same
extensional definition, formalized as (si 6= s j ) ∧ (Ei = E j ), the concepts are in a relation
of synonymy.
The second kind of synchronic disagreement is independent from the signs, and
lies only on extensional definitions. If one of the two concepts’ extensional definition
is a proper subset of the other concept’s extensional definition such that Ei ⊂ E j , then
the two concepts are in a hypo/hypernymy relation. The other possibility is that the two
extensional definitions are overlapping onto each others such that (Ei ∩ E j 6= 0) / ∧ (Ei ∩
E j 6= 0)
/ ∧ (Ei ∩ E j 6= 0).
/ This relation is referred by as an overlapping relation.
The diacronic agreement can be contradicted in two ways. The first one is by having
at least one concept from a contrast set that does not have its extensional definition in-
cluded in the extensional definition of a concept from an anterior contrast set. The rela-
tion causing the disagreement is referred to as a confusion, and adopting the same nota-
tion as in section 3.1.2 about K and K 0 , we formalize it as ∃Cik ∈ K 0 ∧ @Ckj ∈ K such that
Ei ⊂ E j .
The last contradiction arises when some examples from one contrast set’s context is
not present in a posterior contrast set’s context. This particular case is not caused by a
relation between concepts, but by a relation between contexts. It is noted EK 0 ⊂ EK , and
is referred by as the incompleteness relation.
Set of all cats Set of all (Potatoes) Chips
Set of all
Felis Catus
Synonymy Set of all (Silicon) Homonym
Chips
Set of all Canis Set of all Homeoterms
A (Birds)
Set of all Canis Lupus Set of all Reptilias
Hypo/Hyperonymy Overlap
Figure 3. The different types of synchronic disagreements between two concepts. The concepts’ extensional
definitions are represented as Venn diagrams, using examples from zoology. The disagreement can arise from
the sign of the concept (top) or only the number of examples that their extensional definitions share.
3.3. Overall Relations
The relations behind the diachronic disagreement are easily identifiable by one agent,
since it possesses the two contrast sets with the incriminated relations. However, the
case of the synchronic disagreement is more complicated. Since the relations causing
this disagreement are between examples from different agent, and that agents are not
necessary having the same examples in their contexts, the agents might not individually
identify a disagreement that occurs when you consider the total set of examples present
in both agents. This kind of disagreements is referred to as second order disagreements.
To detect and solve the second order disagreements with the elements of our protocol
listed so far, the agents would need to transfer all their example to each other.
Fortunately, by granting the agents the ability to communicate with each other about
their point-of-view on the relation between two concepts, it is possible to overcome the
requirement of an extensive example transfer. To do so, an agent has to receive all the
pairs of signs and intensional definitions from the other agent’s contrast set. When the
agent Ak received all the pairs from A−k .K, it can build a hypothesis H with the context
EK of its contrast set and a concept Ckj = (s j , I j , E j = {e ∈ E|∃g ∈ I j ∧ g v e}) for each
received pair (s j , I j ).
After building the hypothesis, Ak can examine the relations between the concepts
from its contrast set and the concepts from its hypothesis. These relations are referred
to as the local relations. If Ak has m concepts and A−k has n concepts, each agent has
a set of m ∗ n local relations. In order to standardize the communication, we allow the
agents to express their relations through four different symbols. A relation r between the
concepts Ci and C j takes its value from the set {≡, , , ⊗} depending on the relation
between the concepts’ extensional definitions Ei and E j as follow:
• r = ≡ if Ei is equivalent to E j .
Set of all cats Set of all dogs
Set of all
cats
Equivalence Set of all cats Exclusion
Set of all Mammals Set of all Homeoterms
A (Birds)
Set of all dogs Set of all Reptilias
Inclusion Overlap
Figure 4. An illustration of the different possible relations between concepts with examples from zoology. A
concept is always equivalent to itself, and have different relations according to the number of examples that it
shares with another concept.
• r= if Ei and E j are disjoint.
• r= if Ei ⊂ E j or E j ⊂ Ei .
/ Ei ∩ E j 6= 0/ and Ei ∩ E j 6= 0.
• r = ⊗ if Ei ∩ E j 6= 0, /
Ak knows the local relation between each pair of concepts (Cik ∈ Ak .K, Ckj ∈ Ak .H).
Since A−k behave similarly, Ak knows that there exists two concepts Ci−k ∈ A−k .H and
C−k −k −k
j ∈ A−k .K. By getting the local relation between Ci and C j , Ak can infer the overall
k −k
relation between Ci and C j according to the following rule:
• case 0: if the two local relations are the same, the overall relation is also the same.
• case 1: if the local relations are Cik Ckj and Ci−k C−k
j , the overall relation is
Cik ⊗C−k
j .
• case 2: if the local relations are Cik Ckj and Ci−k ≡ C−k
j , the overall relation is
Cik C−k
j .
• case 3: if the local relations are Cik ≡ Ckj and Ci−k C−k
j , the overall relation is
Cik ⊗C−k
j .
• case 4: if the local relations are Cik ⊗Ckj and Ci−k C−k −k
j , Ci C−k −k −k
j or Ci ≡ C j ,
the overall relation is Cik ⊗C−k
j .
Since these relations are symmetrical, this set of rules covers any possible combi-
nation of relations. The overall relation is the relation that the two concepts Cik and C−k
j
would have in an overall context E = EAk .K ∪ EA−k .K .
Case 1 Case 2
Ak : ⌘ A k: ↵ Ak : A k: ↵
Overall : ⌦ Overall : ⌦
Case 3 Case 4
Ak : ⌘ A k: Ak : ⌘ ↵ A k: ⌦
Overall : Overall : ⌦
Ei Ej E i [ Ej
Figure 5. The four cases where the two local relations are not matching, and their associated overall relations.
3.4. Hierarchy
The overall relation does not provide enough information yet to decide an agreement in
all cases. The relation does not specify which concept includes the other in the overall
relation. In order to resolve this ambiguity, the agents have to decide on a hierarchy
between the concepts.
If we look at the vocabulary from section 3.2, we see that the case of a concept’s
extensional definition having the extensional definition of another concept as a subset
is referred to as a hypo/hypernymy. This name comes from the field of linguistic: a
hyponym shares a type-of relation with its hypernym, where the most general concept is
the hypernym and the most specific is the hyponym. An example is the color navy-blue,
that is a hyponym of blue. Deciding a hierarchy, in our case, means deciding which of
the two concepts of the overall relation is the hyponym, and which one is the hypernym.
The hierarchy among the overall relation is deciding according to the following
rules. There are five possibilities that leads to the relation as the overall relation be-
tween two concepts Cik and C−k j . In three of these possibilities, both local relations were
already a relation:
• if Ei ⊂ E j and E j ⊂ Ei , or E j ⊂ Ei0 and Ei ⊂ E j , the overall relation is in fact
Cik ⊗C−k
j .
• if E 0j ⊂ Ei and E j ⊂ Ei , C−k k
j is the hyponym and Ci the hypernym.
• if Ei ⊂ E j and Ei ⊂ E j , Cik is the hyponym and C−k
j the hypernym.
What Agent 1 sees : What Agent 2 sees :
Set of all Homeotherms Set of all Homeotherms
Set of all (Birds) (Snakes) (Mammals)
Reptilias Vs.
Synonymy Set of all Reptilias Exclusion
(Disagreement) (No disagreement)
Mammals
Set of all Reptilias (Snakes) (Birds) Set of all Homeoterms
Overlap
(Disagreement)
Figure 6. In some situations, the relation between two concepts might be seen differently depending on which
agent observes it. This is due to the different contexts of their contrast set. In the Figure, the two agent are
seeing the relation between two concepts as equivalence and disjoint (top) while the reality is a third relation
of overlap (bottom)
.
In the last two possibilities, one of the local relation was not but ≡, as in case 2
of section 3.3:
• if Ei ⊂ E j and Ei ≡ E j , or Ei ≡ E j and Ei ⊂ E j , Cik is the hyponym and C−k
j the
hypernym.
• if E j ⊂ Ei and E j ≡ Ei , or E j ≡ Ei and E j ⊂ Ei , C−k k
j is the hyponym and Ci the
hypernym.
3.5. Complements
These additions are not part of the core formalism, but can be still useful for researchers
that face particular situations.
Ambiguity of the Sign: Since sometimes the concepts Cik from Ak .K and C−k j from
A−k .K will be in a situation where i = j. In this situation, the concept Ci from AK and
the concept C j from Ak .H can be both noted Cik or Ckj . In order to remove this ambiguity,
we will note Ckj0 the concept that belongs to Ak .H. This way, the apostrophe marks the
belonging to a hypothesis. In the situation where i 6= j, the absence of ambiguity allows
us to not put the apostrophe.
Co-hyponymy: In this Section, four notions from semiotics have been introduced to
describe the semantic relation3 between two concepts. These notions are: hyponymy,
hypernymy, synonymy and homonymy. We add now a fifth notion, the co-hyponymy.
A set of concepts Ch1 , ...,Chn are co-hyponyms of a common hypernym CH if the co-
3 We are not referring there to the local and overall relations, which do not belong to the field of semantic but
only to the field of set theory.
hyponyms’ extensional definitions Eh1 , ..., Ehn are a partition of the extensional definition
of the hypernym’s extensional definition EH .
4. Discussion
The formalism is versatile and can be used in many of the fields cited in the introduction
(Ontology Matching, Symbolic Inductive Learning, Semiotic ...). However, the real in-
terest of the formalism lies in its compatibility with works that belong to a combination
of these fields. The main feature of the formalism is its ability to formalize concepts of
our language that we use to talk about language itself. This function of language, the re-
flexive function, can be confusing sometimes. Expressions like meaning of the meaning,
or concept of concept are often useful to use in a research paper from one of the previ-
ously cited field, but confuses the reader. This problem is exacerbated in the case of in-
terdisciplinary texts, where making a reference to which instance of a notion like concept
is used may degrade the clarity of the text even more. By formalizing each of these terms
together with their relations, we aim to improve the clarity of interdisciplinary research
reports: for instance C refers to the formal notion of a concept while concept refers to the
notion of concept in its broad meaning. The concept of concept is now noted Cconcept .
We do not provide a definition for the meaning. Since this notion is subjective and
defined in different ways among different approaches, we prefer to let each user of the
formalism choose the way that he/she considers the most appropriate to define the notion
of meaning. Different ways to formalize the meaning of a concept Ci include (but are not
limited to):
• its intensional definition Ii (dualism)
• its extensional definition Ei (materialism)
• the concept Ci itself, as the tuple {si , Ii , Ei } (externally grounded concepts)
• the relation r of the concept Ci with another concept C j (conceptual web)
The formalism has been used in an experiment where a pair of agents resolves simple
scenarios of disagreements by arguing over the meaning of their concepts [1].
5. Conclusion
We presented an original formalism that can fit, but is not limited to, interdisciplinary
approaches of communication. This formalism presents the basic elements sign, exten-
sional definition and intensional definition, how their interaction forms a concept, how
concepts are organized to partition a linguistic context, and finally how these organiza-
tions can cause disagreements on the meaning, what is the typology of these disagree-
ments and how we can evaluate a good organization that results in an agreement, even
from the point of view of an agent that has only partial information on the linguistic con-
text of its interlocutor. We are looking forward to see how the research community will
use this formalism to disambiguate abstract notions of our language.
Acknowledgements This paper has been partially supported by projects ESSENCE:
Evolution of Shared Semantics in Computational Environments (ITN 607062).
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