=Paper=
{{Paper
|id=Vol-1283/paper1
|storemode=property
|title=Trust and Agency in the Context of
Communication
|pdfUrl=https://ceur-ws.org/Vol-1283/paper_2.pdf
|volume=Vol-1283
|dblpUrl=https://dblp.org/rec/conf/ecsi/Demolombe14
}}
==Trust and Agency in the Context of
Communication==
https://ceur-ws.org/Vol-1283/paper_2.pdf
Trust and Agency in the context of
Communication
Robert Demolombe1
Institut de Recherche en Informatique de Toulouse
France
robert.demolombe@orange.fr
Abstract. The communication process is analyzed on the basis of the
notions of trust and agency. The aim of the paper is to clarify the role
played by causality on one hand and the role played by logical conse-
quences of assumptions about trust in information sources on the other
hand. The first part is informal and the second part refers to the logical
framework of modal logic though it requires a quite limited background
in this area.
1 Introduction
The communication process may involve two different concepts: agency and
trust. Agency explains some causal consequences of an informing action and
trust explains some logical consequences about what an agent believes. However,
it is not easy to make a clear distinction between these two kinds of consequences
because they may be imbricated.
Let’s consider, for instance, a situation in an airport where John is waiting
the arrival of the flight AF001. In the arrival hall there is a screen where it is
indicated that this flight should arrive at 11.30. At 11.20 a speaker announces
that the flight is delayed of 15 minutes. It may be that John has heard this
announcement. In that case John believes that the speaker has said: ”the flight
number AF001 is delayed of fifteen minutes ”. It may also be that John believes
that the speaker has said: ”the flight number AF001 is delayed of fifty minutes ”
and it may also be that at this moment John was talking with some friend and
that he has heard nothing.
We can also imagine another similar situation where at 11.20 there is the text
”DELAYED 15 mn” that appears in the screen. If John is looking at the screen
he believes that someone in the airport has run a program which has modified
the line of the flight AF001 on the screen.
In both cases, oral announcement or screen modification, it may be assumed
that John believes that the meaning of the transmitted message is that the flight
should arrive at 11.45.
If, in addition, it is assumed that John trusts the person who has performed
the informing action1 in his reliability, it can logically be inferred that John
believes that the flight shall arrive at 11.45.
If, in a similar situation, at 11.20 or at some further moment no informing
action about the fact that this flight is delayed has been performed, and John
trusts the information source who is in charge to announce a flight delay in the
property of announcing a flight delay if there is a flight delay, then John believes
that the flight AF001 is not delayed. It is worth noting that in that case what is
derived by John is the logical consequence of the fact that an informing action
has not been performed.
The aim of this paper is to clarify the roles played by causal effects of inform-
ing actions and by logical consequences of trust in the communication process.
Since there are several variants in the definitions of causality and agency and
in the definitions in trust, in the first part of the paper are given semi-formal
definitions of these concepts. In the second part are presented in a more formal
way how these concepts interacts in the communication process. Then, it will be
shown that we could accept a variant of the notion of agency which takes into
account the different kinds of trust.
Most of the content of the paper is intended to be read by people who have
a limited familiarity with formal logic. Then, people who have this background
could find that some formal details are missing.
2 Informal section
2.1 Causality and Agency
Surveys about the most significant approaches of causality can be found in [21,
1]. In this section are briefly presented some of the most significant definitions
of this concept. We have slightly changed authors’ notations for the sake of
homogeneity of the presentation.
G.H. von Wright in his paper [22] defines causality with respect to three
states of the world: w the state of the world where the agent starts to act, w′
the state of the world where the agent ends to act and w′′ the state of the world
where we would be if the agent had not been active, that is where the only
changes are due to the laws of nature. In the following this world is called the
”counterfactual world” (see [17]).
Then, the action performed by an agent has caused that a property repre-
sented by p is obtained iff p is not the case in w, p is the case in w′ and p is
not the case in w′′ . In that situation we say that in w′ the agent has brought it
about that p. See figure 1.
For instance, if p means that the door is open, the agent has caused that the
door is open iff in w the door is not open, in w′ the door is open and in w′′ the
door is not open.
1
In most cases this kind of trust is implicitly adopted by the users. Nevertheless, it
is necessary to draw the following consequences.
p
w’
¬p
w
¬p
w’’
Fig. 1. To bring it about that p.
In von Wright definitions it is assumed that agent’s action leads to a unique
state of the world. That means that what is called an action should be interpreted
has a specific occurrence of an action.
In another definition proposed by I. Pörn in [19] an agent brings it about
that p iff the action he does necessarily leads to a situation where p holds and
it might be that p does not hold if this action is not performed in a situation
which is the same as the current situation, except that this particular action
is not performed. This second condition is called the ”counteraction condition”.
Here the notion of necessitation is defined with respect to the set of hypothetical
situations where the agent does at least the action he does in the actual situation.
A significant difference with regard to von Wright’s definition is that Pörn
does not make explicit reference to the world where the action starts and the
world where the action ends.
R. Hilpinen in [11] has proposed a definition of agency which has similarities
with von Wright’s definition since he also considers three worlds, and similarities
with Pörn since his definition is based on some notion of necessity. Nevertheless,
the Hilpinen’s necessity condition refers to the set of all the possible performances
of a given action type a instead of the set of situations where the agent may do
any actions in addition to the action he actually does.
For example, Hilpinen might consider the set of possible instances of the
action type ”to close the door”, while Pörn might consider the set of situations
where the agent closes the door and also smokes a cigarette or closes the door
and also speaks to someone else ... etc ... The counteraction condition given by
Hilpinen is more precise. It is defined with respect to the performance of an
instance of an action type.
The definition of agency we have adopted in this paper takes inspiration
from the three authors we have presented before. It is based on the definition
presented in [10]. Instead of the notion of ”action” it is based on the notion of
”act”2 .
An act is a pair made of an actor i (an agent) and an action type a. This
pair is denoted by i : a. An actor can perform an action type in many different
ways and a relation is defined between three worlds: the world w where the
action starts, the world w′ where a given instance of the action type has been
performed and the world w′′ which is the counterfactual world of this particular
instance of the action type.
It may be that in w′ other acts than i : a have been performed in parallel.
The set of all the acts performed in w′ (including the acts performed by other
agents than i) is called all. Then, the set of acts performed in w′′ is denoted by:
all − {i : a}.
In this definition we say that the act act is going to bring it about that p in
w when the set of acts performed in parallel is all iff
1. for all the worlds w′ where the set of acts all ends it is the case that p holds,
and
2. there exists a world w′′ where only all − {i : a} are performed and where p
does not hold.
2.2 Trust
There are many definitions of trust (see [2]). However, most of them agree on the
fact that trust is a form of the truster’s belief in some trustee’s property. In [5,
6, 18] we have proposed several kinds of trustee’s properties which are relevant
in the context of communication. They are first presented by examples.
Let’s consider a situation where Peter is a consultant in the field of finance
and John is looking for advices about buying or selling stocks of the company
XYZ. In particular John is interested in the truth value of the proposition p:
”the value of the stock of company XYZ is going to strongly decrease”.
The properties of the information source Peter are defined in terms of the
relations between the fact that Peter has informed John about p, the fact that
Peter believes that p is true and the the fact that p is true. These relations
have the form of conditionals. For example Peter’s sincerity means that IF Peter
informs John about the fact that p is true, THEN Peter believes that p is true.
Then, John trusts Peter in his sincerity about p means that John believes that
Peter is sincere with regard to John about p.
The different kinds of properties of an information source are defined in this
example as follows.
Sincerity. Peter is sincere with regard to John about p iff IF Peter informs
John about the fact that p is true, THEN Peter believes that p is true.
Competence. Peter is competent about p iff IF Peter believes that p is true,
THEN it is the case that p is true.
2
In [10] agency is defined for joint acts that cause some effects. Here, for simplification,
the definition is restricted to the effects which are caused by a unique act.
Validity. Peter is valid with regard to John about p iff IF Peter informs
John about the fact that p is true, THEN it is the case that p is true.
It is worth noting that these properties are not logically independent. Indeed,
validity can be derived from sincerity and competence.
From each property of the form ”IF A, THEN B” we can define a dual
property of the form ”IF B, THEN A”. That leads to the following properties.
Cooperativity. Peter is cooperative with regard to John about p iff IF Peter
believes that p is true, THEN Peter informs John about the fact that p is true.
Vigilance. Peter is vigilant about p iff IF it is the case that p is true, THEN
Peter believes that p is true.
Completeness. Peter is complete with regard to John about p iff IF it is
the case that p is true, THEN Peter informs John about the fact that p is true.
These properties can be generalized to any truster i, any trustee j and any
proposition p 3 .
They are represented in the figure 2 where the edges can be seen as implica-
tion operators and the labels of the edges as the name of the properties.
j Informs i about p
COOPERATIVITY SINCERITY
VALIDITY COMPLETENESS
p is true VIGILANCE j Believes p
COMPETENCE
Fig. 2. Relationships between believing, informing and truth.
2.3 Communication
In this section we analyze the communication process on the basis of the notions
of agency and trust we informally adopted before.
3
A. J. I. Jones in [14–16] has defined the properties of reliability and sincerity which
respectively correspond to what we call validity and sincerity. However, the other
properties like competence or completeness (the dual of validity) are not mentioned
in these works.
The first step in this process is the performance of an informing action at the
physical level. As we have seen in the above examples at this level an agent j
does some physical action the effect of which is that a message (we could also say
a ”signal”) is produced. It may be a sound in the case of an oral announcement
in an airport or it may be a text that appears on a screen or any kind of physical
support. This physical message is denoted by ”p”.
At the end of this step, on the basis of the definition of agency we have
adopted, we can clearly check whether it is the case that some effect has been
caused by an action performed by agent j.
In a second step, it may be that an another agent i has perceived the message
”p”. To be more precise we must say that i believes that the message ”p” has
been produced by j. Indeed, it may be, if the communication process does not
work well, that i believes that ”p” has been produced while it is another message
”q” which has been produced.
It can be assumed in a third step that agent i assigns some meaning to the
message ”p”. This meaning is that a proposition denoted by p is true. Then, on
the basis of this assumption, the logical consequence of what i has perceived is
that i believes that j has performed an informing action the effect of which is
that a message has been produced and that this message means that p is true4 .
Can we say that what i believes at this step has been caused by the informing
action? To answer this question we have to check whether i already had this belief
or not before j performs the informing action.
If it is assumed, in addition, that, for example, i trusts j in is validity about
p and that i has some reasoning capacities, then it can be inferred that i believes
that p is true.
At this level we can ask a similar question: does the fact that i believes that
p is true has been caused by the informing action performed by j? The answer
is ”yes” if it is the case that before performance of this action i did not believe
that p is true and i would not believe that p is true in a counterfactual situation.
Let’s consider now another scenario where i trusts j in his completeness
about p. From the definition of completeness, if we can apply the contraposition
rule to the IF A, THEN B proposition, we can infer IF ¬B, THEN ¬A. Then,
from i’s trust in completeness we can infer that i believes that IF j does not
inform i about p, THEN it is not the case that p is true.
The same kind of reasoning which has been shown for trust in validity could
lead to the conclusion that if j has not informed i about p, then i believes that
it is not the case that p is true. However, there is a significant difference which
can be understood if we consider the two concrete examples we have seen above.
Indeed, in the case of the arrival time of the flight AF001, if John trusts
the airport speaker about his completeness he cannot infer that the flight is not
delayed at any time before 11.30. For instance, if no announcement has been done
4
The distinction between the action of sending a message and the informing action is
similar as the distinction between a locutionary act and an illocutionary act in the
J. Searle’s Speech Act Theory [20]. See also J. I. I. Jones in [14, 15].
at 10.00 that does not guarantee that a delay announcement will not happen
further, for instance at 11.15.
In the example of the finance consulting it is the same. Even if John trusts
Peter in his completeness about p he can infer that the value of the stock of
XYZ is not going to decrease only in some well defined circumstances.
We can imagine a third example where these circumstances are easier to
define. Let’s consider a speaker who is announcing the list of students who have
succeeded at a given exam. If John is such a student and he trusts the speaker in
his completeness about the set of students who have succeeded, after the speaker
has ended to announce the list, if the name of John has not been announced,
John infers that he has not succeeded. Because he believes that the list was
complete.
These examples show that the properties assigned by the truster to the
trustee are properties that holds only if some specific conditions about the con-
text are satisfied. In semi formal terms, these properties must have the form: IF
C, THEN (IF A, THEN B), where C his a proposition that characterizes this
context.
3 Formal section
To represent more formally the notions of agency and trust and the derivations
involved in the communication process we need first to briefly introduce the
formal language.
Language: The language is a First Order Modal Language (see [3]). It is
+
defined as usual and its modal operators are: Beli (p), Brall,i:a (p), Inf ormi,j (p).
The intuitive meaning of these operators is:
Beli (p): agent i believes that the proposition represented by p is true.
+
Brall,i:a (p): agent i is going to bring it about that p by doing an action of
type a in a context where the set of acts performed in parallel is all5 .
N ec+
all,i:a (p): p is true after any instance of the set of acts all has been
performed (notice that all includes the act i : a).
The operator N ec+ all,i:a (p) is intended to represent the fact that a proposition
p is true after performance of a set of acts even if its truth has not been caused
by these acts. That is the case for instance for laws of nature (for example, the
proposition: time is flying holds whatever the agents do).
Inf ormi,j (p): agent i has transmitted to agent j a message the meaning of
which is that a proposition represented by p is true.
Axiomatics. The axiomatics of these modalities is briefly defined below.
Beli is a normal modality which obeys the system (KD).
+
Brall,i:a : is a classical modality which only obeys the following inference rule.
+ +
(REB) If ⊢ φ ↔ ψ, then ⊢ Brall,i:a (φ) ↔ Brall,i:a (ψ)
Inf ormi,j : is a classical modality which only obeys the inference rule:
5 +
In Brall,i:a (p) the + is used to make the distinction with Brall,i:a (p) which means
+
that agent i has brought it about that p. Brall,i:a (p) can be defined from Brall,i:a (p).
(REI) If ⊢ φ ↔ ψ, then ⊢ Inf ormi,j (φ) ↔ Inf ormi,j (ψ)
Frame.
A frame is a tuple which has the following components:
– A domain D for the interpretation of the terms of the language.
– A set of possible worlds W .
– A set of relations Ri defined on W ×W for the interpretation of the operators
Beli .
– A set of relations Rall,i:a defined on W × W × W for the interpretation of
+
the operators Brall,i:a .
– A set of functions Ii,j defined from W to W W for the interpretation of the
operators Inf ormi,j .
The intuitive meaning of Rall,i:a (w, w′ , w′′ ) is that the set of acts all which
have started in w have ended in w′ and w′′ is a counterfactual world of w′ where
all the acts in all have been performed except the act i : a.
Model. A model M is a frame which validates the axiom schemas and in-
ference rules of the above operators and of Classical First Order Logic. The fact
that a formula φ is true at the world w of the model M is denoted as usual by:
M, w |= φ and the fact that φ is a valid formula is denoted by: |= φ.
Satisfiability. The satisfiability conditions are defined below.
We have M, w |= Beli (φ) iff for every world w′ such that Ri (w, w′ ) we have
M, w′ |= φ.
+
We have M, w |= Brall,i:a (φ) iff
1) we have M, w |= ¬φ and
2) for every world w′ and for every world w′′ such that Rall,i:a (w, w′ , w′′ ) we
have M, w′ |= φ and
3) there exist a world w1′ and a world w1′′ such that Rall,i:a (w, w1′ , w1′′ ) and
M, w1′′ |= ¬φ.
+
The satisfiability conditions of the operator Brall,i:a assigns a more precise
meaning to the notion of agency.
We have M, w |= N ec+ all,i:a (φ) iff
for every world w′ and for every world w′′ such that Rall,i:a (w, w′ , w′′ ) we have
M, w′ |= φ.
We have M, w |= Inf ormi,j (φ) iff the set of worlds Ii,j (w) is the set of worlds
w′ such that M, w′ |= φ.
Now, we can give formal definitions to the different kinds of trust.
Trust in sincerity.
def
T rustSinci,j (p) = Beli (ctxt → (Inf ormj,i (p) → Belj (p)))
Trust in competence.
def
T rustCompi,j (p) = Beli (ctxt → (Belj (p) → p))
Trust in validity.
def
T rustV ali,j (p) = Beli (ctxt → (Inf ormj,i (p) → p))
Trust in cooperativity.
def
T rustCoopi,j (p) = Beli (ctxt → (Belj (p) → Inf ormj,i (p)))
Trust in vigilance.
def
T rustV igi,j (p) = Beli (ctxt → (p → Belj (p)))
Trust in completeness.
def
T rustComplti,j (p) = Beli (ctxt → (p → Inf ormj,i (p)))
ctxt is a proposition which restricts the circumstances where the truster trusts
the trustee.
Now, we can formally define some terms and predicates which are relevant
in the context of communication.
Informing act. i : infj,”p” is an informing act where i does an action of the
type: infj,”p” . The meaning of this action type is to transmit to j the signal ”p”.
Predicate T ransmitted. The predicate T ransmittedi,j (”p”) means that i
has transmitted to j the message ”p” (”p” is a constant).
We present now a derivation which formally shows the derivation process.
This derivation shows the point of view of a logician who is reasoning about
what the agents do and believe.
Let’s assume first that in the world w agent j is going to bring it about that
T ransmittedj,i (”p”) is true by doing an action of the type infi,”p” . Then, we
have:
+
(1) M, w |= Brall,j:inf i,”p”
(T ransmittedj,i (”p”))
+
From (1) and the satisfiability conditions of the operator Brall,j:inf i,”p”
, for
every world w′ such that Rall,j:infi,”p” (w, w′ , w′′ ) we have:
(2) M, w′ |= T ransmittedj,i (”p”)
Let’s assume now that in the world w agent i pays attention to the fact that
j transmits ”p” to him. This assumption is formally represented by:
(3) M, w |= N ec+ all,j:infi,”p” (T ransmittedj,i (”p”) → Beli (T ransmittedj,i (”p”)))
From (3) and the satisfiability conditions of the operator N ec+ all,j:infi,”p” in
′
w we have:
(4) M, w′ |= T ransmittedj,i (”p”) → Beli (T ransmittedj,i (”p”))
From (2) and (4) we have:
(5) M, w′ |= Beli (T ransmittedi,i (”p”))
Let’s assume that in w, when agent j has performed any instance of the act
j : infi,”p” , agent i assigns to the message ”p” the meaning that p is true. Then,
we have:
(6) M, w |= N ec+ all,j:infi,”p” (Beli (T ransmittedj,i (”p”) → Inf ormj,i (p)))
From the satisfiability conditions of the operator N ec+ all,j:infi,”p” , in w we
′
have:
(7) M, w′ |= Beli (T ransmittedj,i (”p”) → Inf ormj,i (p))
From (5) and (7) we have:
(8) M, w′ |= Beli (Inf ormj,i (p))
Let’s assume now that in w agent i trusts agent j in his validity about p
when agent j has performed any instance of the act j : infi,”p” . Then, we have:
(9) M, w |= N ec+ all,j:infi,”p” (T rustV ali,j (p))
From the satisfiability conditions of the operator N ec+ all,j:infi,”p” in w we
′
have:
(10) M, w′ |= T rustV ali,j (p)
Then, from T rustV al definition we have:
(11) M, w′ |= Beli (ctxt → (Inf ormj,i (p) → p))
From (8) and (11) we have:
(12) M, w′ |= Beli (ctxt → p)
Let’s assume that in all the worlds like w′ i believes that proposition ctxt
holds. Then, we have:
(13) M, w′ |= Beli (ctxt)
From (12) and (13) we have:
(14) M, w′ |= Beli (p)
The fact that we have (14) in every world w′ where j has performed the act
j : infi,”p” is not enough to conclude that in w j is going to bring about that i
believes that p is true. We also need to satisfy the conditions 1) and 3) in the
satisfiability conditions of the operator Br+ .
The condition 1) requires to have:
(15) M, w |= ¬Beli (p)
The condition 3) requires that there exist a world w1′ and a world w1′′ such
that we have Rall,i:a (w, w1′ , w1′′ ) and:
(16) M, w1′′ |= ¬Beli (p)
If (15) and (16) hold, and the assumptions that allow to infer (14) hold, we
have:
+
(17) M, w |= Brall,j:inf i,”p”
(Beli (p)) (see figure 3).
w′
Beli (p)
Rall,j:infi,”p”
+
Brall,j:inf i,”p”
(p)
w ′′
w ¬Beli (p)
¬Beli (p)
Fig. 3. Agent j is going to bring it about that agent i believes p.
(17) intuitively means that in the world w agent j is going to bring it about
that agent i believes that p is true by doing the act j : infi,”p” , in a context
where the set of performed acts is all.
This derivation exhibits the assumptions that allow to infer (17). These as-
sumptions are: (3) the message sent by j is received by i
(6) i assigns the meaning p to this message
(9) i trusts j in his validity about p
(13) i believes that he is in a context where he can trust j
(15) before j sends the message i does not believe p
(16) if j had not send the message, i would not believe p; that is, the other acts
in all do not inform i about p.
A similar kind of derivation allows to characterize the assumptions that lead
to the conclusion that j is going to bring it about that agent i believes that j
believes that p is true, if i trusts j in his sincerity.
The situation where in the world w agent j has not informed agent i about
p cannot be analyzed on the basis of a trivial duality between trust in validity
and trust in completeness.
Let’s assume that in w agent i trusts j in his completeness about p. We have:
(1’) M, w |= T rustCompi,j (p)
From the definition of trust in completeness we have:
(2’) M, w |= Beli (ctxt → (p → Inf ormj,i (p)))
Let’s assume that i believes that in w the context ctxt holds. We have:
(3’) M, w |= Beli (ctxt)
From(2’) and (3’) we have:
(4’) M, w |= Beli (p → Inf ormj,i (p))
By contraposition, from (4’) we have:
(5’) M, w |= Beli (¬Inf ormj,i (p) → ¬p)
Let’s assume that in w i believes that j has not informed i. Then, we have:
(6’) M, w |= Beli (¬Inf ormj,i (p))
From (5’) and (6’) we have:
(7’) M, w |= Beli (¬p)
(7’) is a logical consequence of the above assumptions. Now, we can ask the
question: ”is it the case that agent j has brought it about that i believes that p
is false in the world w”?
Answering this question deserves further researches, but we are inclined to
think that the answer is ”no”. Our argument to support this answer is that if (6’)
holds, that is, if i believes that j has not informed i in w, then, it does not exist
a world w0 and a world w0′′ such that we have: Rall,j:infi,”p” (w0 , w, w0′′ ). Since
the notion of agency has been defined for an action which has been performed
we cannot infer that (7’) has been caused by some informing action performed
by j.
The definition of agency is usually defined as a relationship between an action
and a proposition that holds after the action been preformed. However, one
could say that we just need to modify the definition of agency in order to accept
statements of the kind: ”i believes that p is false because it is not the case that i
has been informed by some agent who is trusted by i in his completeness about
p”. Nevertheless, in this approach we would need to define a counteraction world
with respect to an action which has not been performed. That is certainly a non
trivial issue.
4 Conclusion
Formal logic has been used to give clear definitions of several kinds of trust in
information sources and to help to understand the roles played by causality and
agency in the process of information communication. It has been shown that if
some assumptions are accepted communication can be interpreted as a causal
process in the case where an informing action has been performed. In the cases
where the informing action has not been performed the question of viewing the
communication as a causal process is an open question.
There are still many other open issues to be investigated. We just mention
some of them below.
The definition of agency is more complex when several agents are acting
together (see [10]) and the extension of the notion of trust to a group of agent
should deserves further researches. Also, the notion of trust must be refined when
several agents are involved in the communication process. That raises the issue
of trust transitivity (see [9]).
The notions of causality and agency could be refined depending on the type
of agents we are interested in. They may be human agents, software agents or
institutional agents (like a bank) (see [8]). The basic differences are that in the
case of software agents the causal relationship is only determined by the laws of
nature, in the case of human agents the notion of free choice plays a significant
role (see [12, 13]) and in the case of institutional agent causality is indirectly
determined by institutional norms which define who are the human agent who
are acting on the behalf of an institution (see [4]).
Another non trivial issue is to define the notion of agency in the case where
we move to graded trust which is defined for several qualitative levels like in [7].
Acknowledgements. We would like to thank a reviewer who has pointed
out some mistakes.
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