A dialogue model of belief

This paper offers a definition of the notion of belief and a method for determining whether a proposition is a belief of an agent or not, based on evidence. The method is based on a formal dialogue system for argumentation that enables inferences to be drawn from commitments to beliefs using argumentation schemes (Walton, Reed, and Macagno 2008). Beliefs are defined as commitments that one really thinks hold true, that one is willing to defend against criticisms and objections, and that one uses as assumptions in deciding what to do and what is the case. Arguments are evaluated in a dialogue format using a set of critical questions matching each scheme. A defeasible scheme for inferences to the best explanation is used to infer that an agent believes a proposition judging from its commitments and locutions in a dialogue. The approach offers a middle ground between the two leading artificial intelligence models that have been developed for programming intelligent agents. According to the commitment model, a commitment is a proposition that an agent has gone on record as accepting (Hamblin 1970, 1971). In the belief-desire-intention (BDI) model (Bratman 1987), intention and desire are viewed as the pro-attitudes that drive goal-directed reasoning forward to a proposal to take action. The BDI model is based on the concept of an agent that carries out practical reasoning based on goals that represent its intentions and incoming perceptions that update its set of beliefs as it moves along (Wooldridge 2002). In this paper, practical reasoning is used as an argumentation scheme for judging belief in a dialogue.

As shown in a classic collection of essays (Engel 2000), the proceedings of a conference on acceptance and belief, drawing the distinction between the two closely related notions has proved to be a hard problem to solve. The papers in the volume tried to grapple with this problem by drawing a precise distinction between acceptance and belief in various ways, but their attempts failed to reach agreement, primarily, it could be argued, because there was little or no basic agreement on how to define the notion of belief. As noted by Hinzen (2001, p. 282), writing about the dilemma about what an inquiry into belief should be about, a way out would be to simply define belief as a technical notion. However, there was no agreement in the collections of writings on belief he reviewed on how such a definition should be formulated.

Section 1 introduces the notion of practical reasoning as a form of inference and as an argumentation scheme with a matching set of critical questions. Section 2 is taken up with the project of clarifying the notions of commitment and acceptance. Section 3 offers a pragmatic definition of the notion of belief, derived from the classic paper of Charles S. Peirce, ‘The Fixation of Belief’ (Peirce 1877). In Section 4, three formal dialogue models constructed in the Hamblin style are explained that are used to show how inferences from commitment to belief can be systematically drawn. Section 5 shows how to use the dialogue system and the new definition of belief to derive beliefs from commitments. Section 6 shows how, using this dialogue-based theory, we can build methods for determining, in a given case, whether a proposition is a belief of an agent or not. Section 7 shows how the argumentation scheme for abductive reasoning is used as the tool to infer what an agent's beliefs are, based on eight types of positive evidence and four types of negative evidence. Section 8 presents a pair of defeasible argumentation schemes for an argument from commitment to belief that can be used as additional inferential tools and suggests some projects for future research.

1.Two models of agent rationality

A rational agent of the kind described by Wooldridge (2000a) is an entity that has goals, some (though typically incomplete) knowledge of its circumstances, and the capability of acting in such a way as to seek to alter those circumstances. A rational agent also has the ability to perceive consequences of its actions and to correct them if they move away from realising current goals. An agent can be a person or can be an automated software program of the kind now commonly used on the Internet.1[1] Some such systems are autonomous, while others are tightly programmed in a deterministic way so that the actions lead to the goal by following a strict programme. Autonomous agents have the capability of modifying their goals and the capability of acting with other agents. The central kind of reasoning that agents use to navigate through their environments is called practical reasoning. Practical reasoning, in its basic form, consists of a chaining together of practical inferences of the sort represented by the simplest scheme for instrumental practical reasoning (Walton et al. 2008, p. 323).

Practical reasoning, when deployed in a deliberation dialogue, gives a reason to accept a conclusion for a course of action tentatively, subject to exceptions or counter-arguments that may be advanced by the other side as new circumstances become known. The conclusion has a presumptive status, once reasons to support the proposed action are provided. However, such an argument is cast into doubt if any one of the following critical questions is asked (Walton et al. 2008, p. 293).

Value-based practical reasoning is well explained by Bench-Capon (2003) and Atkinson et al. (2006). The following argumentation scheme for value-based practical reasoning is the one given in Atkinson et al. (2006, pp. 2–3).

But what are goals? Are they intentions in the mind of the agent or are they merely statements that the agent has expressed or formulated, either alone or as part of a group deliberation, and has pledged to carry out, or has publicly expressed commitment to? According to the commitment model, two agents (in the simplest case) interact with each other in a dialogue in which each contributes speech acts (van Eemeren and Grootendorst 1992). Each has a commitment set, and as the one asks questions that the other answers, commitments are inserted into or retracted from each set, depending on the type of move (speech act) each speaker makes. The two participants in the dialogue take turns offering speech acts, like asking a question, making a proposal, or putting forward an argument. Each has a commitment set, and as each move is made, commitments are inserted into or from each set according to commitment rules, depending on the type of move each makes. A commitment is a proposition that an agent has gone on record as accepting (Hamblin 1970, 1971). One type of speech act is the putting forward of an argument. On the commitment-based approach, practical reasoning is modelled in a dialogue format using an argumentation scheme, like the ones above, along with a set of critical questions matching the scheme. The reasoning is supported if the appropriate critical questions are properly answered, or it is otherwise undercut.

The word ‘commitment’ has acquired several different meanings in multi-agent systems (Maudet and Chaib-Draa 2002). Three of these can be noted here. First, a commitment is a persistent intention by an agent to undertake some action. Second, a commitment is a promise made by one agent to another to undertake some action. Third, a commitment is a dialogical obligation incurred by an agent in a dialogue to support some proposition when challenged in the dialogue. The third meaning is the one taken up as central in this paper, and it is the one modelled in dialogue systems like those of Hamblin cited above. The second meaning, of making a promise, is very important, but is beyond the scope of this paper. The first meaning takes us to the consideration of the BDI model.

The second model, called the BDI model, is based on the concept of an agent that carries out practical reasoning based on goals that represent its intentions and incoming perceptions that update its set of beliefs as it moves along (Wooldridge 2002). On the BDI model (Bratman 1987; Bratman, Israel, and Pollack 1988; Paglieri and Castelfranchi 2005), an agent has a set of beliefs that are constantly being updated by sensory input from its environment and a set of desires (wants) that are then evaluated (by desirability and achievability) to form intentions. On this model, the agent's goals in practical reasoning are represented by its intentions, persistent goals that are stable over time and are not easily given up. For example, on Bratman's (1987) version of the BDI model, forming an intention is described as part of adopting a plan that includes the agent's desires (wants) and beliefs.

The most distinctive difference between the commitment model and the BDI model is that desires and beliefs are private psychological notions internal to an agent, while commitments are statements externally and verbally accepted by an agent in a communicative context. The commitment model uses basic practical reasoning for argumentation schemes, expressed in a dialogue format in which two or more agents deliberate to solve a problem. The BDI model uses intentions, beliefs, and desires representing a decision-maker's psychological states that are updated as the agent acquires new data from its perceptions. Despite these clear differences between the two models, many philosophers writing about practical reasoning often appear to blend them together. Searle (2001) ostensibly purports to advocate the BDI model of practical reasoning, but, like others, notably including Bratman (1987) and Levi (1997), very often uses the language of commitment to describe how agents engage in practical reasoning. In an influential paper, Bratman et al. (1988, p. 347) used this language to describe practical reasoning: ‘The fundamental observation of our approach is that a rational agent is committed to doing what she plans’. Such wording here uses the language of commitment, although Bratman, Israel, and Pollack portray themselves as advocating the BDI model.

Both models have been widely employed in artificial intelligence in multi-agent systems. Agent communication languages are used to enable agents to communicate with each other on the basis of conversational policies that are like dialogue rules. The following example of a BDI-based conversational policy states that one agent A can tell a second agent B something only if A believes it also and can establish that B does not believe it. But how is a programmer to implement this requirement? The programmer may be in no position to determine what A believes or what A believes about what B believes. Hence Singh (1998, p. 40) and many other AI researchers in AI have moved to the commitment model.

Argumentation technology of the kind now widely being implemented in new AI systems for multi-agent computing (Wooldridge 2002) has sometimes used the BDI model and sometimes used the commitment model (Dunne and Bench-Capon 2006). Both are useful for evaluating practical reasoning under conditions of uncertainty in changing circumstances leading to commitment where a conclusion is drawn on a basis of tentative acceptance (commitment) on a balance of considerations.

2.Acceptance and commitment

The following four propositions seem fairly similar to each other, and each one might be interchanged with one or more of the others with little or no loss of meaning in everyday conversational argumentation. However, some fine distinctions between them can be drawn to bring out how each might be related to the other.

An example due to Goldstein (Engel 2000, p. 65) was put forward to show not only the difference between belief and acceptance, but also that there can be a conflict between the two notions in a given case: ‘Typically, a person who plays the stock market believes, deep down, that the only person likely to win is the stockbroker, yet, driven by greed, accepts the stockbroker's forecast that he, the punter, will make stupendous financial gains’. Cohen's (1992) pioneering analysis of the distinction between belief and acceptance also showed that acceptance of proposition A is, in principle, compatible with the belief that not-A. Examples of this sort show not only the possibility of drawing a distinction between belief and acceptance, but also the importance of drawing it. As Engel (2000) showed in his introduction to the conference proceedings on belief and acceptance, the distinction, if it could be clarified, would have philosophical power as applied to solving philosophical problems like Moore's paradox. Moore's paradox is the puzzle that the expression ‘P but I don't believe that P’ seems to be an absurd assertion, even though it is not logically inconsistent. An example is the statement, ‘It is raining, but I do not believe it is raining’. It is different from the statement, ‘It is raining, but I am not committed to the proposition that it is raining’. These statements, as will be shown below, need to be treated in different ways as ‘paradoxical’.

Is acceptance the same as commitment? In other words, is the statement ‘Bob accepts A’ always equivalent to the statement ‘Bob is committed to A’? An agent's commitment is defined as applying to any statement that he has gone on record in a dialogue as committing himself to, in virtue of what he said (or did, in the case of action commitments) in the past (Hamblin 1970; Walton and Krabbe 1995). Thus, commitment is a kind of dialogue notion that underlies speech acts. Part of defining any speech act is determined by commitment conditions that apply to the speaker and hearer when this speech act is uttered in a dialogue. This same analysis also appears to partly apply to acceptance. Acceptance, on the one hand, is a kind of speech act. When I say ‘I accept A’, my uttering this speech act can be taken to imply I am now committed to A, possibly subject to later retraction. On the other hand, acceptance is a more general notion that underlies all speech acts and sets requirements on how each speech act is to be defined as a form of dialogue move. In this second sense, it is equivalent to commitment.

Hamblin (1970) looked around for a model of rational argument that could be used as a basis for studying informal fallacies. One might propose epistemological models based on knowledge and belief. For example, a strong rational argument might be one in which the premises are known to be true and logically imply the conclusion. Or a less strong rational argument might be one in which the premises are believed to be true and logically imply the conclusion. Hamblin (1970) rejected such models (chap. 7) because of difficulties in formalising a notion of rational argument based on modal operators of knowledge and belief (p. 238). He was led, for these reasons, to take the alternative route of choosing acceptance, rather than knowledge or belief, as his basic notion on which to build his theory of rational argument. He formulated the following four dialogical criteria for the justifiability of an argument (p. 245).

(D1) The premises must be accepted.

One might ask here, ‘accepted by whom?’ The answer Hamblin gave is that they should be ‘accepted by X’, where X is the name of some person or a group of persons who remain in contact throughout the argument.

(D2) The passage from premises to the conclusion must be of an accepted kind.

This requirement has been expanded by recent developments in argumentation theory, so that it would include not only deductive and inductive forms of argument as warrants, but also argumentation schemes of the presumptive sort.

(D3) Unstated premises must be of a kind that are accepted as omissible.

This criterion requires some analysis of the notion of an enthymeme or argument containing premises (or a conclusion, possibly) not stated in the given text of discourse. Generally, an argument, in the sense of such a set of criteria, is taken as something given, or expressed in a text of discourse. But some premises (or the conclusion) may not be explicitly expressed in the discourse and may have to be inferred as assumptions on which the argument depends.

(D4) The conclusion must be such that, in the absence of the argument, it would not be accepted.

This condition expresses the notion that an argument, as evaluated by the four criteria, is something that gives a reason to accept the conclusion. For the argument to be of worth, it must boost up the evidential weight of the conclusion as a proposition that is to be accepted. Further elaboration of (D4) thus involves the notion of being able to judge the value of the worth of a proposition or argument for acceptance. But Hamblin did not attempt to present any further elaboration of such notions as part of his four dialectical criteria of the worth of an argument.

A key passage in Hamblin's (1970, p. 246) analysis occurs where he asked why he used the word ‘accepted’ in his primary formulation rather than the word ‘believed’. The reason he offered is that the term ‘believed’ is too much of a psychological word, ‘conjuring up pictures of mental states’. In contrast, he saw the term ‘acceptance’ as something that relates to putting on a ‘linguistic performance’. Nowadays that would be called a speech act. His exact wording (p. 257) is interesting:

Belief, although it can sometimes be public, as when we talk about commonly held beliefs, is a more private matter. If belief is an internal psychological matter of what an individual really thinks is true or false, the privacy of belief makes it more difficult to judge what an individual believes. People often lie or conceal their real beliefs. And there is good reason to think that people often do not know what their own beliefs are. If Freud was right, we also have unconscious beliefs that may be quite different from what we profess to be our beliefs. Belief is deeply internal and psychological, and public commitment to a proposition is not necessarily an indication of belief. But perhaps there is a way to infer belief from commitment.

Two forms of an argumentation scheme called argument from commitment are presented in the compendium of schemes in Walton et al. (2008, p. 335).

The first form is the simpler version.

3.A Peircean definition of belief

Why do we need a notion of belief, as opposed to commitment? There are basically three reasons. The first is that western philosophy since the time of Plato has taken the notions of knowledge and belief to be closely connected, and has therefore taken belief to be a fundamental notion of epistemology. Epistemology could even be defined as the philosophical study of knowledge and belief. One could even argue that knowledge implies belief by considering the following statement, a variant on Moore's paradox: I know that the sky is blue but I do not believe it. This statement is arguably self-contradictory, and if so, one could argue that knowledge implies belief. Indeed, philosophy has traditionally defined knowledge as justified true belief, even though counterexamples have shown this definition to be highly problematic, if not untenable. In short, one reason for thinking that we need a notion of belief, as opposed to commitment, is that traditional epistemology, which has strongly influenced models of rational thinking in artificial intelligence, has held belief to be a fundamental notion closely connected to the fundamental notion of knowledge. Mainstream psychology has also accepted this tradition by taking belief to be the most basic type of mental representation and by assuming it is a building block of conscious thought.

The second reason is that it can be plausibly argued that we need the notion of belief in order to connect abstract models of rational thinking to real cases of argumentation (Godden in press). For example, in a persuasion dialogue, the proponent's goal is to persuade the respondent to come to accept some proposition that he did not accept before. Persuasion, on this model, is defined as a change in the respondent's commitments set over a sequence of moves in the dialogue. What has to happen for persuasion to occur is that the respondent was not committed to proposition A before the proponent made her persuasion attempt, but then he became committed to A after the persuasion attempt. This structure defines successful persuasion in the formal model. However, in real life, it might be argued that you have not really persuaded somebody of A successfully unless you have brought about that he believes A. On this approach, the rhetorical persuasion to be successful must achieve not just a change in the respondent's commitment to the target proposition, but must really change the respondent's belief with respect to that proposition . In order to be of any assistance to fields like psychology and rhetoric, that take belief change to be fundamental to the understanding, thinking, and persuading, we need the notion of belief.

Despite widespread acceptance by philosophers that the notion of belief is fundamental to epistemology, there is also been disagreement and controversy (Rudder Baker 1989). Some philosophers hold that beliefs can be modelled as types of sentences and that the common sense understanding of belief is correct. Others have argued that the common sense understanding of belief is wrong and that there is no coherent mental representation of this common sense notion. Some have even argued that the common sense concept of belief is obsolete, much like the notion of phlogiston in the discredited scientific theory of combustion (Churchland 1981; Stitch 1983). If these skeptical views about belief are right, there are significant consequences for science, including not only artificial intelligence generally, but also fields like neuroscience, where belief is taken to be a central concept.

The third reason has to do with negative concepts like insincerity, self-deception and lying, all of which appear to require some notion of belief. For example, the speech act of telling a lie could be defined as putting forward a statement as true when one believes (or even knows) that it is false. These concepts are fundamentally important not only in ethics, but also important in law in the process of examination in trials (including cross-examination), as well as in witness testimony and the crime of perjury. It is one thing to commit yourself in a dialogue to a proposition that you are not really committed to, as judged by your prior commitments in the dialogue. There might be many reasons to explain such an inconsistency of commitments. Perhaps you just forgot, or you can somehow explain the inconsistency. Maybe you just changed your mind, as some new evidence came into the dialogue. But lying is a different thing. To lie, you have to really believe that the statement you made is false. In short, negative notions of a significant kind, like lying, self-deception, and so forth, cannot be fully understood only through applying the notion of commitment, but also require reference to belief. Lying is also closely related to notions like lying by omission, equivocation, deception, and using ambiguity in argumentation, and these notions are in turn related to the study of informal fallacies.

The best place to start working out an analysis of belief is to start with some central characteristics of the notion that are widely accepted. Engel (1998), following the analysis of Bratman (1993), based on the prior analysis of (Kaplan 1981), identified five leading characteristics of belief (summarised by Tuomela (2000, p. 122)).

The second characteristic shows that it makes sense to speak of beliefs as true or false. There is a contrast with commitments here. The proposition one is committed to can be true or false, but commitments are accepted or not. However, to make this characteristic useful for our analysis of belief to follow, we have to define how belief is related to truth or aims at truth. Beliefs should aim at truth, but truth can be hard to find, and therefore the characteristic that beliefs are evidence-related is very important. Note also that if we accept the proposition that beliefs come in degrees (characteristic 5), modelling belief as an either-or property, as done in modal logics of belief, is inappropriate. Degrees of belief are best modelled by a quantitative apparatus, for example, by using real numbers between 0 and 1 to represent a person's degree of belief that a proposition is true.

There is, however, a way in which these five characteristics could be used to orient us to a way of defining the notion of belief in a pragmatic manner that could be useful in artificial intelligence, cognitive science, and other fields of investigation that need to rely on some clear notion of belief. In accord with characteristics 2 and 3, it can be argued that belief should be defined not only as a propositional attitude, but also as an evidence-related notion that tracks the way beliefs are fixed and modified during an investigation in which evidence is being collected in order to prove some ultimate proposition that is in doubt. To say that a proposition is in doubt means that it is unstable in a certain sense: there is insufficient evidence to prove or disprove it, as far as the investigation has proceeded to this point. Therefore, the investigation should be continued and further evidence should be collected in order to overcome this instability and lead to a stable fixation of belief. Looking at belief this way, it needs to be defined not only as a propositional attitude but in a pragmatic context of investigation prompted by doubt or instability, but with the aim of moving towards finding the truth of the matter being investigated. The problem of defining belief can now be recast as a pragmatic problem of the fixation of belief in a single agent or group of agents2[2] conducting an investigation in which evidence is being collected and evaluated.

Peirce (1877), in his classic essay on the fixation of belief, offered some clues on what he took belief to be. Peirce's essay was about what he called the ‘fixation’ of belief, meaning how belief is ‘fixed’, or lodged in place in an agent, and how it is removed or changed. He contrasted the method of authority with the method of science as a way belief is fixed and changed. Peirce did not attempt to define belief, but he did offer a description of what belief is, and how it works, by contrasting it with a characterisation of doubt, and how it works. A quotation from this account shows that his description of how belief works presents several of its leading characteristics.

Careful reading of Peirce's description and accompanying remarks suggests that belief is taken to possess ten defining properties.

Based on these observations, we could set out a Peircean definition of belief by, first of all, stating the implicit assumptions that belief is something that is a property of an agent, and can be said to be held by that agent, and then by adding the properties to this base. An agent can be defined as an entity that can carry out actions based on data that it can receive and that can perceive (to a limited extent) the consequences of its actions. A practical reasoning agent is one that has information about its environment, including ways of carrying out actions, and uses this information in order to attempt to bring about some ultimate goal. An investigating agent is one that has access to evidence, and that collects and evaluates this evidence in order to try to prove or disprove some ultimate proposition. The proposed definition reads as follows:

Now we have offered a definition of the notion of belief that we can work with, the next problem is to find a dialogue framework that could be used to model the operation of one party using the commitments of another to derive conclusions about what the first party believes from his/her commitments.

4.Dialogue systems for explicit and implicit commitment

The solution to the problem is to adapt a formal dialogue system that can model these notions in a limited but very useful way and define commitment and belief in the model. The dialogue system CB3[3] (Walton 1984), a formal system devised after the fashion of formal dialogue systems of Hamblin's earlier systems, has just four locution rules, five commitment rules, and three dialogue rules (Walton 1984, pp. 133–135).

5.Deriving belief from commitment

We now come back to the original problem of trying to show how belief derives from commitment in dialogues, and can be seen to represent a special type of commitment. In the CBV system, the distinction was drawn between a commitment that may have been incurred merely for the sake of argument and may easily be retracted, and a commitment incurred by reason of making a strongly voiced claim of the kind one is obliged to defend. The second type of commitment is more firmly fixed, and one may be more reluctant to give up such a commitment even in the face of reasons for giving up. It could be hypothesised that one difference between the two concerns how each type of commitment represents a state that is stable and firmly fixed and that therefore the second kind of commitment, because it is more stable and firmly fixed, is more closely related to the notion of belief.

It is generally accepted that explicit commitment does not necessarily imply belief, as the comments of Hamblin (1971) make clear. I may go on record as saying something, and thereby commit myself to that proposition, even though I do not believe it. For example, I may be lying or deceiving myself. It would appear that belief does not imply explicit commitment, as I may believe something without ever mentioning it. Nor does belief imply commitment, since someone can believe something without ever indicating the existence of that belief.

If the foregoing remarks are correct, it would appear that there is no logical relationship between commitment and belief. This appearance is misleading, however, once we take implicit commitment into account. What the foregoing remarks show is that there is no connection of deductive logical implication between explicit commitment and belief and vice versa. The possibility remains that there may be a connection in a system like CBV that allows for both explicit and implicit commitments. This connection can be explained as follows. Suppose that you believe a particular proposition A, and A is not in your commitment set, nor is there any subset of propositions within your commitment set that logically implies A. Still, it may be the case that you believe that proposition A is true. What then is the link between your commitment set and your belief that proposition A is true? The link is that I can engage in an examination dialogue with you about proposition A, and about other factual propositions related to A, and judge from the commitments I can extract from you in this dialogue whether you believe proposition A or not. I can even ask you directly whether you believe A or not. Even if you claim not to believe A, I can ask you whether other propositions you have shown yourself to be committed to in the dialogue imply belief in A. So we can say that although there is no link of deductive logical implication between belief and explicit commitment, there can be defeasible links between sets of one's commitments, both implicit and explicit. An agent can be questioned in CBV as to whether his commitments imply a certain belief, and it may even be put to the agent that some set of his explicit and implicit commitments reasonably implies, on the basis of defeasible argumentation schemes, that he believes a particular proposition. The agent may deny that he believes in this proposition, but if what he said has on more than one occasion defeasibly implied belief in this proposition, the case can be made that there is evidence for such a belief, based on dialogue with the agent in which he was questioned about his commitments. Take Moore's paradox as an example. Suppose that agent says ‘P but I don't believe that P’. To confront the apparent inconsistency, we have to examine the agent's commitment set, and see whether there is some proposition P somewhere, and if there is evidence that it is a stable commitment that the agent has often strongly defended. Now we have to ask him why he claims no longer to believe P, given that there is evidence he did before. The agent's assertion ‘P but I don't believe that P’ needs to be handled differently if there is no such evidence. He needs to be asked why he is now saying something that he does not believe. Maybe, for example, he is just conceding it for the sake of argument, even though his grounds for accepting it are not, in his view, strong enough to justify his accepting it. The point is that different responses are required in the CBV system, depending on the circumstances, and the apparently paradoxical statement can be dealt with in appropriate ways.

Now we can understand why stability and reluctance to change a commitment are characteristics of a belief. The reason is that stability and reluctance to give up a proposition indicate a central role for this commitment inferred by one's habit. In the five leading characteristics of belief cited from Tuomela, the characteristic 4 postulates that beliefs are subject to an ideal of integration or agglomeration. This characteristic suggests that a reason for clinging to a belief might be its integration with other beliefs that an agent holds. In other words, consistency could be important. These characteristics could be reasons why an agent is reluctant to give up a proposition that he/she believes.

So if we try to explore the minimal characteristics of belief given in the list of 10 characteristics of belief we attributed to Peirce, we have to start looking into conditions for retractions of belief, and conditions for supporting them by evidence. This takes us into matters of burden of proof, a concept related to speech acts like that of making an assertion, as opposed to saying something without making any claim that it is true and needs to be defended by giving reasons to support it.

It might be added that Peirce's observation that belief can be firmly fixed, as with fanatical believers, should be considered quite important as well. The term ‘belief’ is sometimes associated with fanatical believers whose belief is characterised by an unwillingness to change or retract in the face of evidence to the contrary. Belief of this sort is firmly fixed and highly resistant to rational arguments that raise doubts or present contrary evidence. The pragmatic definition of belief brings out this aspect, which might perhaps be called the irrational nature of belief, quite well.6[6] We might say that belief is sometimes rational and sometimes irrational, and that therefore it would be an error in defining the notion of belief to drift into seeing it as rational belief, excluding the elements that are not influenced by rationality, or even incompatible with the requirements of rationality and evidence. This characteristic ties in with Peirce's description of belief as a calm and satisfactory state. Commitment can be either settled or tentative, whereas belief is a comparatively settled state in which the believer clings to a proposition and is reluctant to give it up. Belief has a characteristic that might be called inertia. Because it is an indication of habit and is a settled state, it tends to be hard to dislodge, even, in many cases, in the presence of evidence to the contrary. This stability can be hardened, and become inflexible in some instances, as in the case of ‘true believers’ of a dogma.

When it comes to defining a notion of belief that could be useful in artificial intelligence and multi-agent systems, the best approach is to characterise a belief as a special type of commitment that is more than just commitment for the sake of argument, and that is characterised by a stable state in an agent that is not easily changed, even though it is a matter of degree. If the agent shows persistence in clinging to a particular commitment over a sequence of deliberative or investigative reasoning, and shows reluctance to give it up, even in the face of doubts that are raised or arguments to the contrary, such indications should be taken as evidence that this commitment is a belief of the agent.

6.General methods for determining belief in CBV

So how can we use ASDV to help bridge the gap between commitment and belief? Believing a proposition is not only acceptance of it, but also an internal attachment to that proposition. A belief is a proposition that an agent has embraced, so to speak, and holds personally. As such, belief is a subjective notion, a private notion, and a deeply psychological notion. What characterises belief is a positive pro-attitude of attachment towards a proposition. To say ‘Amanda believes proposition A’ means that Amanda embraces A as true, in the sense that she is personally attached to A in a way that makes it firmly acceptable for her as a personal commitment.

ASDV is designed to model this notion of belief by providing a basic dialogue structure onto which assumptions of varying strengths can be added. The central epistemological problem about belief posed by using ASDV is how one can devise helpful methods for reasonably judging what an agent's belief is, or is not, from the data given in an instance. In other words, the question is one of how one agent should reasonably draw inferences about whether a given proposition is believed by another agent or not. We can go by what that agent has said or professed, given the evidence of how he or she has argued or acted in the past. The problem is how to infer from commitment to belief.

Hamblin's remark that commitment is a kind of persona of belief suggests an approach to solving this problem. This approach can be sketched out as follows. As a dialogue proceeds, a good deal of evidence may accumulate that may specify an agent's commitment concerning some proposition or issue. The agent may strongly defend a particular proposition or position in several discussions, and she may also make efforts to clarify her own attitude towards it. She might even declare that she believes this proposition, or that she does not believe it. This kind of dialogue would be evidence with respect to not just her commitment, but also her belief. The approach to solving the problem of drawing inferences from commitment to belief can thus be expressed as follows. In a given case, the textual evidence of what has taken place in dialogue exchanges can sometimes take the form of a package that enables an inference from commitment to belief to be reasonably drawn. This package contains not only a consistent set of commitments that tie in together and reinforce each other, but also textual indications that imply that the speaker is personally attached to this proposition and embraces it, as shown by strong and consistent personal declarations of commitment to it. When this kind of evidence is present, we are justified in claiming that not only is the agent committed to A, she also believes A.

What makes a belief inferable from the commitments of a dialogue participant is that it is relatively stable over the dialogue. Stability means that it tends to be (i) a commitment that is consistent with that participant's other commitments, and (ii) a commitment that the participant is reluctant to retract, even under repeated questioning. Stability means that a belief is a commitment that is closely tied in with other commitments that the participant has. For example, if a commitment is identified as a belief of a participant, then another proposition that is an immediate consequence of the proposition contained in that belief will also be highly likely to be a belief of that participant. But it is not necessarily so. Sometimes people are inconsistent in their commitments. This too can be used as a basis for questioning a participant in the CBV system about his belief in a certain proposition.

There are various methods one participant in a dialogue can use to test whether a particular proposition is a belief of the other participant. The first method is that of simply posing a question to ask the other party whether he believes this proposition or not. The second method is to examine what the other participant has gone on record as saying in the previous sequence of dialogue exchanges to see whether there is any evidence indicating that he believes this particular proposition. The third method is to examine actions that can be attributed to the other participant, and to draw inferences from these actions using as premises also the data of what the other participant has gone on record as saying in the previous sequence of dialogue exchanges. The combined use of the latter two techniques is familiar in the literature on the ad hominem fallacy of the circumstantial variety. In such cases, the participant may have gone on record as saying one thing but doing another, where he recommended a particular course of action as something everyone should do, but then an examination of his own personal circumstances reveals that he has failed to act in this way himself in the past, or has acted in a manner that is inconsistent with what he now recommends.

Examination dialogue is a type of dialogue that has two goals (Walton 2006). One is to extract information to provide a body of data that can be used for argumentation in an embedded dialogue, like a persuasion dialogue for example. Examination dialogue can be classified as a species of information-seeking dialogue, and the primary goal is the extraction of information. However, there is also a secondary goal of testing the reliability of the information. Both goals are carried out by asking the respondent questions and then testing the reliability of the answers extracted from him. The formal analysis of the structure of the examination dialogue by Dunne et al. (2005) models this testing function of the examination dialogue. In their model, the proponent wins if she justifies her claim that she has found an inconsistency in the previous replies of the respondent. Otherwise the respondent wins. To implement this testing function, the information initially elicited is compared with other statements or commitments of the respondent, other known facts of the case, and known past actions of the respondent. This process of testing sometimes takes the form of attempts by the questioner to trap the respondent in an inconsistency, or even in using such a contradiction to attack the respondent's ethical character. Such a character attack used in the cross-examination of a respondent can often be used as an ad hominem argument, where for example, the testimony of a witness is impeached by arguing that he has lied in the past, and that therefore what he says now is not reliable as evidence.

So far we have not fully answered the question of which forms of inference are used in ASDV to draw inferences from a participant's commitment-set to a statement judged to be the belief of a participant on the basis of the inference. We have now mentioned two argumentation schemes that might be used for this purpose, the schemes for practical reasoning and the ad hominem argument, in addition to the modus ponens. Recall that CBV only allows for deductive forms of inference whereas ASDV accommodates defeasible argumentation schemes. Many of the most important schemes that would be most useful for this purpose, the scheme for argument from commitment for example, are defeasible. Indeed, we have argued of that an advantage of the methodology for belief proposed above is that it uses the device of critical questions matching an argumentation scheme. In the next section, we discuss how ASDV can be extended with another argumentation schemes of this sort.

7.Determining an agent's beliefs

The traditional problem of other minds in philosophy is that one person has no direct way of determining what another agent's internal states (like beliefs) are. This problem, curiously, is also present in artificial intelligence. Designers of systems of software agents in multi-agent computing are generally not able to access the internal beliefs, motivations or goals of the agents participating in their system, because many of the agents will be designed and created by different design teams. Even if these internal states were observable to a system designer, a sufficiently clever agent designer can always produce an agent able to pass any test of its internal states imposed by the system designer. This situation is called the problem of semantic verification in multi-agent systems (Wooldridge 2000b). It has led researchers in multi-agent systems to concentrate on assessing an agent's states only through externally observable behaviours. The same problem recurs in trying to understand animal behaviour where, for example, researchers on chimp behaviour used the notion of simulation.

The notion of simulation offers a clue into how one agent typically goes about drawing conclusions about what another agent's commitments and beliefs are. The two agents share forms of reasoning, like practical reasoning. The one agent's words and deeds can be used as data furnishing premises from which the other agent can draw inferences. These forms of reasoning, it can be argued, include deductive and inductive forms as well as presumptive schemes like argument from expert opinion that represent a third type of argumentation, plausible reasoning. Explicit commitments are public and social, but implicit commitments are in many instances not directly stated by an agent, and therefore have to be inferred indirectly, based on unstated premises. But it is fairly clear how commitments should generally be determined, given the evidence of an agent's words and deeds in a case. This task requires examining not only what he actually said, or went on record as saying, but looking beneath this to try to fairly determine what this commits him to by drawing inferences from what he said.

Beliefs are derived abductively by one participant in a dialogue from the commitment set of the other participant using evidence collected so far in the dialogue. The theory is based on the notion of simulation, whereby one agent, called the secondary agent, draws an inference in the form of a hypothesis about another agent's belief. The secondary agent draws the hypothesis by looking at the evidence of the primary agent's words and deeds, combined with what it knows about the agent's commitments. In the case of autoepistemic reasoning, the agent can form a hypothesis about what her/his own belief is. This method is based on the ASDV system, according to which an agent's belief is a specially designated proposition that is selected from his/her commitments. According to this theory, a belief is a special type of commitment that has remained stable throughout the course of a deliberation or investigation, and that fits in and agglomerates with other propositions known to be beliefs of that agent. Thus there are three components involved in identifying a belief. The first component is that there needs to be a distinction between the primary agent who possesses the belief and the secondary agent judging that the other agent has that belief or not.7[7] Each plays a different role in the process of determining whether a given proposition represents a belief of the primary agent or not. So you could say that there are always two participants in a dialogue, where each agent has a role as a participant in an investigation or deliberation. The second component is the evidence on which the hypothesis identifying a proposition as a belief is based. The third component is the inference by which the hypothesis is inferred from the evidence. An especially important type of inference is that of abductive reasoning or inference to the best explanation, which proceeds by selecting the best explanation from a given set of data.

The basic argumentation scheme for abductive reasoning (Walton et al. 2008, p. 329) is presented below.

There are two kinds of evidence, positive and negative. Positive evidence, of the following eight types, is evidence supporting the hypothesis that constitutes the explanation of the data. (1) The first kind of positive evidence is explicit or implicit commitment to the proposition in question. (2) If the agent has made strong and emphatic assertions that a particular proposition is true, this would be evidence that he/she believes this proposition. (3) Another kind of evidence is that if under varying circumstances, the agent clings tenaciously to affirming, defending, or acting on that proposition, or behaving in a way that indicates it accepts it as true, it is a belief of that agent. (4) Resistance to attempts to refute the proposition constitutes another kind of evidence. (5) Responding to requests for justification by giving supporting evidence for the proposition, rather than retracting it, is another kind of positive evidence. (6) Another kind of evidence concerns the stability in the way the agent continues to maintain and defend this proposition, especially where that evidence indicates that no doubt is being expressed about whether the proposition is true. (7) Another kind of evidence concerns indications of a habit of defending this belief, accepting it, advocating it, or acting on it. (8) Another kind of evidence concerns the practical reasoning of the agent as it engages in goal-directed actions. If a particular proposition is closely connected to actions used by an agent as means to carry out goals, or closely connected to the goals themselves, that is evidence that the proposition in question is a belief, and not just a commitment of that agent.

Negative evidence concerns alternative explanations that need to be considered, and ruled out in order to establish something as a belief. It includes instances where an agent professes to believe a proposition, but there is also evidence of insincerity, self-deception, hypocrisy, or lying. Evidence of insincerity, or even hypocrisy, can be found in cases where a person claims to accept a particular proposition, but acts in a way that is inconsistent with accepting it. Hypocrisy is closely related to inconsistency of commitments, and based on it, but inconsistency is in some instances itself a type of negative evidence that goes against the hypothesis that an agent holds a belief.

The procedure whereby this evidence is employed to draw a conclusion about an agent's belief by abductive reasoning is shown graphically in Figure 1. As shown in Figure 1, the secondary agent begins with the commitment set of the primary agent, and from the evidence of what the primary agent said and did as known in the circumstances of the case, draws a hypothesis on whether a particular commitment attributed to the primary agent can properly be said to be one of its beliefs.

Figure 1.

Using abduction to derive an agent's belief by inference.

8.Conclusions

This section fits the definition of belief previously formulated in the paper into a more precise formulation in the structure of ASDV and presents an argumentation scheme for arguments from commitment to belief. First, we need to recall the characteristics of belief that emerged from the discussion leading up to the definition. It was emphasised that (1) belief is a settled state (2) that we cling to, (3) sometimes very strongly, (4) it is opposed to doubt, an uneasy or unsettled state, (5) it is shaped by evidence, and (6) it guides our actions and argumentation. It was also stated that (7) belief is a matter of degree. The discussion of these characteristics then led us to a definition of ‘belief’ that can be summarised as follows: belief is a stable state of an agent that is not easily changed, is a matter of degree (held more or less weakly or strongly), and that guides the desires and actions of that agent in goal-directed reasoning in deliberation, or the evidential thinking of that agent in an investigation aimed at removing doubt. Some other characteristics were mentioned as well, like the agglomeration of beliefs into groups.

In the paper, the main thesis argued for was that beliefs can be inferred from commitments, but not in a straightforward manner. The thesis was that we start with the set of an agent's commitments in a dialogue, pick out some of them as potential beliefs of that agent, and then run them through the list of seven characteristics cited above to determine whether they meet the requirements for them. If so, they can be hypothesised to be beliefs of the agent, subject to further evidence that might come in as the dialogue proceeds through the argumentation stage. This analysis is the basis for formulating the following basic defeasible argumentation scheme for an argument from commitment to belief in, where a is an agent taking part in a dialogue D built on the basic structure of ASDV.

The following critical questions match the basic scheme for an argument from belief commitment.

Included in a's commitments are a's goals, actions and professed beliefs.

It is also useful to have a comparative scheme for argument from commitment to belief with the conclusion that a believes A more strongly than B.

The critical questions matching the comparative scheme are the following.

This account of belief uses defeasible argumentation schemes that correspond to the habits of inferring that Peirce took to be fundamental to the notion of belief. Both schemes and their matching critical questions are based on Peirce's view that beliefs are subject to an ideal of integration or agglomeration. They reflect the list of the five widely accepted characteristics of belief set out in Section 3 by incorporating the assumptions that beliefs aim at truth, and that they are shaped by evidence for what is believed. Much more needs to be said about how belief works in different types of dialogues, for example, in examination dialogue and deliberation dialogue. These are left as projects for future research.

As indicated above, finding an agent's actual belief can be very difficult in some instances, even after extensive interrogation and argumentation. Finding conclusive proof that an agent believes a particular proposition is typically not possible. In many instances, there is insufficient evidence to say with a high degree of confidence that an agent believes a particular proposition. Often, it is very hard for us to even know what our own beliefs are, even after considerable introspection and discussion. In this typical kind of situation of lack of direct accessibility to the external evidence, basing the method of determining belief on abductive reasoning is highly suitable, as is the dialogue method. The dialogue method is aided by work on one special type of dialogue called examination (Dunne et al. 2005; Walton 2006). However, to give a general model of belief that can be extended to apply to many more specialised dialogue-like examinations, we used a basic CBV system and extended it to the ASDV, so that various argumentation schemes, especially the ones for practical reasoning and abduction, can be used as rules of inference. The general theory is that each participant in a dialogue can use such schemes to critically question each other's statements and arguments by drawing inferences from each others' commitment sets and then use them to draw out evidence-based conjectures about the beliefs of the other party.