Trust is an important mechanism that describes how credible is the relation between agents in a multi-agent system. In this work, we extend the idea of trust to beliefs of agents, combining not only the provenance of information but also the outdated of such information. The resulting approach allows the agent generate di erent trust values for beliefs, depending on which meta-information is more important for that particular application, the trust in the source or how recent the information is. For this end, we describe some pro les of agents with di erent characteristics, combining the trust on the source and the outdated of information. Furthermore, we discuss how patterns of reasoning like argumentation schemes can play an important role in our approach, considering the expertise of the source of information.
believe; (ii) the meta-information considered in this work is inspired from practical platforms to develop multiagent systems, which makes our work attractive in practical terms; and (iii) we introduce some interesting agent pro les, which are based on various criteria applicable to the meta-information considered. These pro les are interesting for di erent application domains where di erent meta-information may have di erent weights, as discussed in this work.
The remainder of this paper is structured as follows. We rst describe the background of our work, including some interesting features from agent-oriented programming languages for our approach, and trust in multi-agent systems. Next, in Sections 3, 4 and 5, we discuss the application of trust values for beliefs, the possibilities of using time as meta-information, and the trust values combined to meta information such as time, respectively. In Section 6, we show how patterns of reasoning (named argumentation schemes) can play an interesting role in our approach, considering the expertise of the source of information. After that we discuss some related work and, nally, we conclude the paper with some nal remarks. 2 2.1
There are many agent-oriented programming languages, such as Jason, Jadex, Jack, AgentFactory, 2APL, GOAL, Golog, and MetateM, as discussed in [BDDS09], each one with di erent characteristics. In this work, we choose Jason [BHW07]. Jason extends AgentSpeak(L), an abstract logic-based agent-oriented programming language introduced by Rao [Rao96], which is one of the best-known languages inspired by the BDI (Beliefs-DesiresIntentions ) architecture, one of the most studied architectures for cognitive agents.
Jason has some interesting characteristics for our approach and, in this section, we describe some of such features.
Strong negation: Strong negation helps the modelling of systems where uncertainty cannot be avoided, allowing the representation of things that the agent believes to be true, believes to be false, and things that the agent is ignorant about. Therefore, an agent is able to believe that, for example, a particular block is blue, represented by the predicate blue(block), or that the block is not blue, represented by the predicate :blue(block)1. Furthermore, Jason allows agents to have both information in its belief base, with di erent annotation, indicating di erent sources, time-steps, etc. as described below; Belief annotations: One interesting characteristic of Jason is that it automatically generates annotations for all beliefs in the belief base about the source from where the belief was obtained (sensing the environment, communication with another agent, or a mental note created by the agent itself). An annotation has the following format: blue(block)[source(john)], stating that the source of the belief that the block is blue is agent john. In addition to the automatic annotation of the source, the programmer can treat the events of receiving/perceiving any information, including annotation of time and any other meta-information he wants to store.
Speech-act based communication: Jason uses performatives based on speech acts in its communication language, and formal semantics has been given for the changes in mental attitudes caused by the performatives available in the Jason extension of AgentSpeak. The performatives available in Jason can be easily extended, and their e ects over the agent mental state can also be customised. Among such customisations, it is possible to add the annotations mentioned above.
There are other interesting characteristics in Jason, as a series of functions of the interpreter that are customisable, more details can be found in [BHW07]. 2.2
Trust is a useful mechanism for decentralised systems, where autonomous entities deal with uncertain information and have to decide what to believe [PAH+12, PTS+11, TCM+11]. In trust-based approaches, agents can use the level of trust associated with the sources of contradictory information in order to decide about which one to believe. There are many di erent approaches to trust in the literature [PAH+12, PSM12, PTS+11, PSM13, TCM+11, CFP03], but here we will build our de nitions mostly based on the concepts presented in [PTS+11, 1Where, we use the : symbol for representing strong negation. Ag5 0.0
0.8 Ag4
Ag1 TCM+11]. First, in this section, we describe trust simply as a relation between agents, while in Section 3 we expand it, associating trust values for beliefs, which represent how much an agent trusts in that belief based on the sources which it have for it.
Considering trust as a relation between agents and following the de nition presented in [TCM+11], a trust relation can be formalised as:
where the existence of the relation indicates that an agent assigns some level of trust to another agent. For example, (Agi; Agj ) means that agent Agi has at least some trust on agent Agj . It is important to realise that this is not a symmetric relation, so if (Agi; Agj ) holds, this does not imply that (Agj ; Agi) holds too.
A trust network is a directed graph representing a trust relation. It can be de ned as: where Ags is the set of nodes in the graph, representing the agents of the trust network, and is the set of edges, where each edge is a pairwise trust relation between agents of Ags. An example of a trust network can be seen in Figure 1.
In order to measure trust, we follow the de nition given in [PTS+11, TCM+11] where a function tr with the following signature: tr : Ags
Ags 7! R is used. It returns a value between 0 and 1, representing how much an agent trusts another. However, di erently from [PTS+11, TCM+11], we de ne the relation between tr and as: tr (Agi; Agj ) 0 tr (Agi; Agj ) = null , , (Agi; Agj ) 2 (Agi; Agj ) 62 so, in our de nition, a trust level can in fact be zero, represented by tr (Agi; Agj ) = 0, which means that Agi does not trust Agj . This is di erent from cases where Agi has no trust value assigned to Agj , represented by tr (Agi; Agj ) = null. We use (Agi; Agj ) 2= to denote that Agi has no acquaintance with Agj , i.e., it is not able to assess how trustworthy Agj is. Both cases can be seen in Figure 1, where there we have tr (Ag4; Ag5) = 0 and tr (Ag1; Ag4) 2= .
Trust is a transitive relation, so an agent Agi can trust Agj directly or indirectly. Direct trust occurs when agent Agi directly assigns a trust value to Agj . Indirect trust occurs when, continuing the previous example, Agj trusts another agent Agk: in this case we could say that Agi indirectly trusts Agk.
We say there is a path between agents Agi and Agj if it is possible to create sequence of nodes of length n, n 1: so that hAg0; Ag1; Ag2; : : : ; Agn 1; Agni with Ag0 = Agi and Agn = Agj . In order to measure the trust from one particular path from Agi to Agj we need to use an operator to consider all the direct trust values in that path. Following the idea proposed in [PTS+11], a general operator tr can be de ned as follows:
tr (Agi; Agj ) = tr (Ag0; Ag1) tr ::: tr tr (Agn 1; Agn) which will de ne the trust value that Agi has on Agj according to the path Ag0; : : : ; Agn from Agi to Agj , constructed as de ned above. If it happens that there are m di erent paths between Agi and Agj , a rst possible path having a trust value of tr (Agi; Agj )1 and the mth having tr (Agi; Agj )m, following [PTS+11] we can de ne a generic operator tr so that:
tr (Agi; Agj ) = tr (Agi; Agj )1 tr : : : tr tr (Agi; Agj )m For simplicity, in this paper we use those generic operators instantiated as:
tr is the minimum trust value along the path. That is, it is de ned as: tr (Agi; Agj ) = minftr (Ag0; Ag1); : : : ; tr (Agn 1; Agn)g given a path Ag0; : : : ; Agn from Agi to Agj as de ned above.
The tr over trust paths is de ned as:
tr (Agi; Agj ) = maxftr (Agi; Agj )1; : : : ; tr (Agi; Agj )mg where m is the number of di erent possible paths between Agi and Agj .
In practical terms, the trust framework makes the agent explicitly aware of how much the other agents in that multi-agent system are trustworthy, and this info available for the agent by means of predicates such as trust(ag1,0.8), meaning that the trust value that this agent places on ag1 is 0.8. 3
In this section, we introduce an way to calculate trust applied to beliefs, which is based on the trust value applied to the sources of these beliefs. We consider not only other agents as sources of information, but also perception of the environment, artifacts, and \mental notes" (beliefs created by an agent itself). For trust values for information received from other agents, we assume that these values are explicitly asserted in the belief base of agents (but calculated dynamically) based on the approach presented in the previous section. For trust values of information perceived from the environment, these values depend on the application domain, where, for example, multiple sensors could have varying degrees of trustworthiness.
For the purpose of a running example, we use the following trust values:
Source ag1 ag2 ag3 ag4 self percept1 percept2
Trust Value 0.3 0.4 0.5 0.8 1.0 0.9 0.6 tr (Agi; sj )
Therefore, we expand trust to be a relation between an agent and the possible sources of information. So function tr (Agi; Agj ) that returns the trust level of Agi on Agj is generalised to:
where sj represents one of the sources of information for agent Agi. This way, an agent Agi has a trust level on other kinds of sources, percepts or mental notes. This is interesting for cases when, using a similar example to the one presented in [AB14], an agent Agi has a sensor st which is known to have an accuracy of 80%. This way, the trust Agi has on st is de ned as tr (Agi; st) = 0:8, associating the known percentage of accuracy with the trust value on st.
Further, the trust value of a particular sensor could be learned from experience, which seems more appropriate to the concept of trust used in this work.
It is important to emphasise that function tr returns the value of trust an agent has on some source. Now we can de ne a trust value associated to beliefs using function tr.
As a belief ' of an agent Agi can come from multiple sources, in order to know how much Agi trusts ', we must consider the tr value associated with each source of ' for Agi. For this, we introduce the function trbi below:
trbi : ' ! R where trbi(') returns the trust value that Agi has on belief ' based on the trust level Agi has on the sources that asserted information '. The operation that calculates trbi(') varies according to agent pro les, corresponding to di erent attitudes towards one's sources of information.
We introduce two agent pro les for calculating trust values over beliefs. They both may be interesting in di erent domains, depending on whether we are interested in credulous or sceptical agents. De nition 1 (Credulous Agent) A credulous agent considers only the most trustworthy source of information, and does not look for an overall social value.
The formula used by a credulous agent to consider the most trusted source is:
trbi(') = maxftr (Agi; s1); :::; tr (Agi; sn)g where fs1; :::; sng is the set of sources that informed ' to Agi.
De nition 2 (Sceptical Agent) A sceptical agent considers the number of sources from which it has received the information, and the trust value of each such source, in order to have some form of social trust value.
A sceptical agent considers the quantity of sources that the information ' comes from. Therefore, we use a formula that sums the trust values of sources that information ' has been received from by Agi, determining a social trust value as follows: trbi(') =
X tr (Agi; s) s2S'+
jS'+j + jS' j where S'+ = fs1; :::; sng is the set of n di erent sources of ' and S' is the set of sources for '.
For example, considering an agent Agi with the trust values presented in Table 1, if Agi receives an information ' from a set of sources S'+ = fAg1; Ag2; Ag3g and receives ' from S' = fAg4g, then:
A credulous agent will consider only the maximum trust values in S'+ and S' , then it will get trbi(') = 0:5 and trbi(') = 0:8.
A sceptical agent will consider all the various sources. In particular, it will get trbi(') = 0:3+0:4+0:5 = 0:3 4 and trbi(') = 0:8 = 0:2.
4
As another example, when Agi receives an information ' where the sources of ' are S'+ = fpercept1g and receives ' with sources S' = fAg2; Ag3; Ag4g, then:
A credulous agent will have trbi(') = 0:9, and trbi(') = 0:8, having greater trust in ' than in its negation. A sceptical agent however will have trbi(') = 0:9 = 0:2 and trbi(') = 0:4+0:5+0:8 = 0:4, preferring to believe 4 4 ' instead.
There are cases when, for an information ' received by an agent Agi, trbi(') is equal to trbi('). For a credulous agent, it is easy to note that this occurs when the maximum trust value tr (Agi; sv), for a source sv 2 S'+ equals the maximum trust value tr (Agi; sw) for a source sw 2 S' .
Di erently, for sceptical agents, this occurs when Ps2S'+ tr (Agi; s) is equal to Ps2S' tr (Agi; s).
For these cases, we can consider other meta-information such as the time the beliefs were acquired (e.g., giving preference to more recent information) in order to decide what to believe. In next sections, we describe some possibilities for such extra criteria. 3.1
In Section 2.2, we de ned the tr operator, which calculates the trust level that an agent Agi has on another agent Agj when there are n paths between them, as the maximum operator. However, considering the agent pro les, such as the credulous and sceptical pro les presented, a sceptical agent could consider the number n of paths between the two agents Agi and Agj to calculate tr (Agi; Agj ).
For example, consider two agents, Agi and Agj , where, using the max operator, we have tr (Agi; Agj ) = 0:6, while np(Agi; Agj ) = 1 where np is a function returning the number of all di erent paths between Agi and Agj in the trust network. This way we have tr (Agi; Agj ) = tr (Agi; Agj )1. Now consider another agent Agk, where tr (Agi; Agk) = 0:6 is de ned using the max operator too, but np(Agi; Agk) = 4. Then we have tr (Agi; Agk) = tr (Agi; Agk)1 tr ::: tr tr (Agi; Agk)4. This way, it is possible for Agi to consider Agk as more reliable than Agj taking into consideration the various di erent paths between them.
In organisational-based multi-agent systems/societies such as [HSB07], agents could assign trust values to groups of agents (or entire organisations) in the multi-agent system, in order to avoid some undesired bias. For example, consider an agent Ag receiving information from a set of agents Ags = fAg1; Ag2; : : : ; Agng, all belonging to the same organisation B. Then, it might be misleading if Ag considers those agents from Ags as di erent sources, thereby giving a social weight to that information, as those agents could spread some untrue information of interest to organisation B, or be biased in any way simply for belonging to the same organisation. For those cases, there may be a way for agent Ag to keep the information that the agents in Ags represent the same organisation, and this way Ag may not consider them as di erent sources. We will investigate that in future work.
More importantly, in future work we aim to combine our platform with existing trust systems (such as [KSS13]) so that we use realistic forms of update of levels of trust in sources of information while agents interact with each other and the environment, building on the extensive work done in the area of trust and reputation in multi-agent systems [PSM13]. 4
As it was presented in the last section, even using trust the agent can have contradictory information with the same trust values, and for these cases, other meta-information are needed. An example of such meta-information is time. There can exist scenarios where the time a piece of information was acquired can be even more important than the trust on its sources, and this will be explored below, with the de nition of two di erent pro les, which may be interesting in di erent domains.
The rst thing to consider is the way that an agent can maintain the information about time. As it was presented before, in Jason [BHW07], a belief can be annotated with each source that informed it. Besides, annotations can also be easily used for recording the time that the belief was informed by each source.
Considering that an environment is constantly changing, the search for the most recent information is often related to the search for the most accurate information. Sometimes it can be even possible that an agent Agj informs ' to Agi, and some time later, Agj informs '. Considering that the only source of ' and ' is Agj , using time, Agi can easily decide for ', as it is the most recent belief informed and the trust level of the source Agj is the same. This way, it is possible to realise that there exists a timeline of acquired beliefs. For example, consider the discrete time structure of Table 2 representing the instants of time at which beliefs are acquired by an agent Agi:
This way, Agi acquired two beliefs, being ' the latest acquired belief. Considering that the trust level of Ag1 and Ag2 are the same, at time 1 and 2, Agi will believe in ', while at time 3 and 4, Agi will believe in '.
The function that returns the most recent time that a belief ' was received by a source sj is time('; sj ). This way, considering the discrete representation of time in table 2, for the belief ' acquired by Agi from agent Ag1, it is used time('; Ag1) = 1.
Note that an information ' can be received from multiple sources at multiple times. For example, for an agent Agi, if Ag1 inform ' at time 1, and Ag2 inform ' at time 3. This way, it is interesting to realise that each source will be annotated with its own time, for example, as it is in Jason, the belief that a block is blue could be:
blue(block)[source([ag1; ag2]); time([t1; t3])]:
Considering the discrete time structure represented before, we can de ne as outdated time a value acquired from the di erence between the actual time and the time that an information was informed by a source. This di erence, for an information received by an agent Agi, we call Ti.
De nition 3 Considering an agent Agi, Ti('; sj ) is the di erence between the actual time and the time that ' was acquired from source sj .
The formula of Ti could be, considering a belief ' received by an agent Agi from a source sj , and a variable now which represents the actual time:
Ti('; sj ) = now time('; sj )
For a more complex example, it is interesting to note that a belief can come from di erent sources. Consider S(') = fs1; :::; sng and S(') = fs1; :::; smg as the sets of sources for the information ' and ', respectively. In this case, an agent could compare a source sv1 2 S(') with another source sw1 2 S('), where sv1 and sw1 are the sources with the minimal Ti function value from their sets. If Ti is the same for sv1 and sw1, then another source sv2 2 S(') and sw2 2 S(') can be selected, where the time annotated in sv2 is the most recent in the set S(') n fsv1g and the time of sw2 is the most recent in S(') n fsw1g. This could be applied recursively until it nds some svi 2 S(') greater or lower than an swi 2 S('), or if there are no more sources for ' or ' to compare, the agent would remain uncertain about '. 5
To combine trust and time, it is important to realise how one a ects the other. Here trust is the focus, with the time being used to set the trust level adequately, prioritising the most recent information. This way, the older an information is, the less trusted it should be, for the reasons presented in the previous section. So we have: De nition 4 (Outdated Information) Considering a belief ' acquired by an agent Agi from a source sj , the greater the Ti('; sj ) value is, the lower the trust level for this belief ' should be.
Note that naturally the trust level of ' will decrease as time passes, unless some sources keep informing ' by an amount that equalises the ' trust loss.
Considering an agent Agi, we can de ne a function trsi('; sj ) that returns the trust of ' considering just the information received by the source sj at time time('; sj ). Considering S(') = fs1; s2; :::; sng the set of sources that informed ', so Agi may have a di erent trs value for ' associated with each source. Here we use a generic operator trs to relate the trust of the source with the time since the belief was informed by it: trsi('; sj ) = tri(Agi; sj ) trs Ti('; sj )
Now, another function can be de ned. Considering the same set of sources S('), the function trt has just ' as parameter. As in Jason each belief has annotated all the sources that informed this belief, it is not needed to pass as parameter the set of sources of '. We use a generic operator trt, making a relation between all the trs assigned to each source. So we have: trti(') = trsi('; s1) trt ::: trt trsi('; sn) Now there is a generic operator to relate the trust of the sources with the time that they informed a belief.
We de ned two agent pro les in section 3, credulous and sceptical, where each one calculates trbi(') according to it owns attitude. Now we de ne other pro les for calculating trti('), again, they both may be interesting in di erent domains, depending on whether we are interested in meticulous or conservative agents. It is interesting to note that an agent may be credulous meticulous, sceptical meticulous, credulous conservative or sceptical conservative.
De nition 5 (Conservative Agent) A conservative agent uses time just when the trust on con ict beliefs are the same.
For contradictory beliefs, a conservative agent will calculates the trbi(') and trbi('). The way that trbi will be calculated depends on if the agent is credulous or sceptical too. If the trust values of the beliefs are the same, it will calculate the trti(') and trti(') to determinate the trust of each one considering the time they were informed.
De nition 6 (Meticulous Agent) A meticulous agent uses trust just when the time of the con ict beliefs are the same.
Di erently from conservative agents, a meticulous agent Agi will rst calculate the trti(') and trti('), and if it is the same, Agi will consider just the trust, ignoring the time that they were acquired, calculating trbi(') and trbi(').
As example, consider an agent Agi and the beliefs acquired according to the timeline of table 3:
And consider the trust that Agi has in each source according to the table 4:
de nition keeps the idea that how bigger Ti is, less trusted a belief should be. Now, consider the trt operator as a max operator, then we have trti(') = maxftrsi('; s1); :::; trsi('; sn)g, for a set of sources fs1; :::; sng. Then, consider that Agi is a credulous agent and that the actual time in the timeline presented is time 5, so: trs is a fraction operator, then we have trsi('; sj ) = trTii((A'g;is;js)j) . This A credulous conservative agent will consider trbi(') = 0:6 and trbi(') = 0:5, opting to believe in '. A credulous meticulous agent will consider trsi('; Ag1) = 50:61 = 0:15, and trsi('; Ag2) = 50:42 = 0:13. Then, we have trti(') = maxf0:15; 0:13g = 0:15. And for ', we have trsi('; Ag3) = 50:54 = 0:5. This way, trti(') = maxf0:5g = 0:5. So, a meticulous agent will believe in ', as trti(') = 0:15 and trti(') = 0:5.
As it was presented, the trust of a belief depends on the trust of its sources. A natural approach is, when a belief ' is shown to be true or false, the trust of the sources of ' changes, increasing in case of true or decreasing otherwise. Considering time, we can improve this idea. The older an information is, the more time it had to change in the environment. Thus, there can be cases when an information ' is acquired, it is true, but after some time, ' becomes false. Thus, some of ' sources might not have informed something false, but as it had time to change in the environment, it became false. Thus, the idea is, considering an agent Agi, for a belief ' received by a source sj , the longer Ti('; sj ) is, the less trust sj will lose in case of ' shows itself to be false to Agi.
Another interesting criteria to combine, or even to generate trust values for beliefs, is to consider the expertise of the source in regards to speci c kinds of information. For example, when a friend tells you that it is going to rain today, and you watch on television that it is going to be a sunny day, although you have more trust in your friend, it is reasonable to consider that the weatherperson is an expert in that subject (i.e., weather) and it is more reasonable to assume that it will be a sunny day.
A way to consider the expertise of the source is to use patterns of reasoning, for example, the so-called argumentation schemes [WRM08]. In particular, regarding the expertise of the source, Walton [Wal96] introduces the argumentation scheme called Argument from position to know, described below2:
Major Premise: Source a is in a position to know about things in a certain subject domain S containing proposition A.
Minor Premise: a asserts that A (in domain S) is true (or false).
Conclusion: A is true (or false).
The associated critical questions (CQs) for the Argument from position to know are:
Therefore, the pattern of reasoning can be analysed in a dialectical way, where its conclusion is evaluated through the critical questions, due to its defeasible nature, and if the pattern of reasoning is valid, the trust value of that information can be incremented, considering that it comes from an expert source (i.e., someone in a position to know), and there are no reasons to doubt that.
Of course, as we are dealing with a value-based framework, it is necessary to attribute some kind of values for expert sources, including how much critical questions are correctly answered. Again, these values could depend on the application domain, where safety-critical applications such as the ones related to health could give greater consideration to the expertise of the source. For example, it is more reasonable to consider the opinion of a doctor who is expert/specialised on the particular health problem than the opinion of a general practitioner.
On the other hand, in some domains the source expertise may not be so important, for example, in our previous example about the weather: the consequences of taking or not the umbrella are not as strong as in the case of a wrong diagnosis of a serious illness.
We can observe that the argumentation scheme of position to know itself considers how much the source is trustworthy. Further, it considers whether the source is in a position to know such subject, and if it was that same source that provided such information directly.
In order to exemplify these ideas, imagine the following scenario related to the stock market: an agent, named ag2, has informed (to agent ag1) that an expert, named ex1, said that a particular kind of stock, named st1, has a great investment potential. Further, consider the following trust values related to the argumentation scheme for the ag1:
ag2 ex1 expert(ex1; st1)
0.6 0.8 0.9 De nition 7 (Suspicious Agent) A suspicious agent considers only the trust value for the source who provided the information to it, and ignores the trust on the original source who provided the information to that agent who informed the suspicious agent.
In our scenario, the trust value of great invest potential (st1) for a suspicious agent is 0.6. However, the agent that received that information is able to ask directly for the source of that information, in this case the expert ex1, about the investment and, when receiving the information great invest potential (st1) from ex1, the trust value becomes to 0.8.
As observed, for a suspicious agent, even when receiving the information directly from the source, it aggregates the trust it has over the source, and not over the expertise of the source. To consider the expertise rather than the trust over the source can be very useful in some application domains, mainly due to the fact that trust values can be learned from experience, while the expertise of that particular source could be acquired from a reliable newspaper, web-page, etc.
information based on how much the source is an expert in that subject.
Considering our scenario, the trust value for great invest potential (st1) becomes to 0.9. 7
Tang et al., in [TCM+11], combine argumentation and trust, taking into account trust on information used in argument inferences. That work is based on work presented by Parsons et al. [PTS+11], which proposes a formal model for combining trust and argumentation, aiming to nd relationships between these areas.
Our work di ers from [PTS+11, TCM+11] in some points. We introduce an approach for computing trust values for beliefs that di ers from [PTS+11, TCM+11], where trust on a piece of information is assumed to be more directly available to argumentation. Di erent from those approaches, we allow for di erent sources for the same information (which is often the case in Jason agents) a propose ways to combine them into a single trust value for that information. We also de ne some agent pro les to facilitate the development of agents that require di erent social perspectives on the trust values of multiple sources; this is not considered in [PTS+11, TCM+11] either.
Another di erence from [PTS+11, TCM+11] is that we consider other meta-information available in the multiagent system (e.g., time annotation), which is inspired by agent-oriented programming languages that have such meta-information easily available.
Alechina et al., in [ABH+06], introduce a well-motivated and e cient algorithm for belief revision for AgentSpeak. The authors do not use trust or reputation in that work though. Therefore, the main point where our work di ers from [ABH+06] is in the use of trust. We also argue that our approach could be used in order to improve the belief process presented in [ABH+06], as the trust values and the reasoning pattern introduced by us could play an important role in belief revision process too.
Amgoud and Ben-Naim, in [ABN15], propose a new family of argumentation-based logics (built on top of Tarskian logic) for handling inconsistency. An interesting aspect in [ABN15] is that the work de nes an approach in which the arguments are evaluated using a \ranking semantics", which orders the arguments from the most acceptable to the least acceptable ones. The authors argue that, with a total order of arguments, the conclusions that are drawn are ranked with regards to plausibility. Although [ABN15] does not use trust, the proposed approach provides ordered arguments thus avoiding undecided con icts. Our approach follows the same principles, but considering di erent criteria for ranking the information which agents have available in theirs belief bases, considering di erent meta-information available in agent-oriented languages. To use such meta information in argumentation-based approaches is part of our ongoing work [MPB16].
Parsons et al., in [PAH+12], identify ten di erent patterns of argumentation, called schemes, through which an individual/agent can acquire trust on another. Using a set of critical questions, the authors show a way to capture the defeasibility inherent in argumentation schemes and are able to assess whether an argument is good or fallacious. Our approach di ers from [PAH+12] in that we are not interested in agents arguing about the trust they have on each other. We are interested in using such trust values and combining them with other meta-information available in the multi-agent system in order to use trust to resolve con icts between beliefs, what might be interesting in domains where it might be important for the agents to not be undecided about some information.
Similarly we used the reasoning pattern based in an argumentation schemes, we argue that argumentation schemes from [PAH+12] could be used in order to evolve the trust values of di erent sources. In our future work we intend to investigate such integration.
Biga and Casali, in [AB14], present an extension of Jason, called G-Jason, to allow the creation of more exible agents to reason about uncertainty, representing belief degrees and grades using the annotation feature provided by Jason. The authors de ne degOfCert(X), where X is a value between 0 and 1, as a value associated with certainty of a belief and planRelevance(LabelDegree) as a value associated with plans, where the LabelDegree value is based on its context and its triggering event's degOfCert level. Our approach di ers from [AB14] in that we use the notion of trust on agents and sensors in order to infer a level of certainty on beliefs. Further, we consider other meta-information, and we de ne pro les that combine di erent uses of such information, which is not considered in [AB14] . 8
In this work, we described how di erent sources of information available to an agent in a multi-agent system and the trust of each of those sources can be combined to generate trust values for beliefs. Further, considering multi-agent shared environments, which are constantly changing, we combine also the time that information was stored/received by the agent, allowing agents to take into consideration how outdated a piece of information is.
In additional, we discussed how dialectical pattern of reasoning (i.e., argumentation scheme) can play an interesting role in our approach. We showed that argumentation schemes could guide agents in order to consider the expertise of the source instead of only the trust the agent has over that source. This idea seems interesting, considering that the trust values normally are learned from the experience, while the expertise of a particular source can be acquired from, also, reliable sources of information like the speci cation of the multi-agent system.
Finally, considering the di erent weights given to the meta-information discussed in this work, we introduce some agent pro les that can be useful for di erent application domains, as discussed in our brief examples.
In our future work, we intend to evaluate the impact of each pro le introduced in this work for di erent kinds of applications, keeping an open mind for new (or even middle ground ) pro les. This will allow us to identify the best pro les for each application domain, depending on the overall behaviour desired for the multi-agent system.
Furthermore, we also intend to combine the di erent pro les introduced in this work, as well as new proles we will investigate, with practical argumentation-based reasoning mechanisms such as [PMVB14], where trust relations among agents may play an important role in decisions over con icting arguments. Some initial investigation in this direction can be found [MPB16]. [AB14]
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