Abstract
We propose a formal approach to the argumentative theory of reason, combining argumentation theory and modal logic in a novel way. We show that the resulting framework can be used to model important mechanisms identified by the theory, including how confirmation bias and other problematic modes of reasoning may in fact serve an important argumentative purpose that can give rise to classically sound conclusions through the process of social deliberation. We go on to suggest that the argumentative theory is based on an understanding of intelligent reasoning and rationality that sees these notions as irreducibly social, and that the argumentative theory itself provides a possible starting point in the search for new theoretical foundations based on this understanding. Moreover, we suggest that formal logic can aid in the investigation of foundational issues, and we sketch the development of an axiomatic approach to the study of rational deliberation.
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Notes
- 1.
This perspective has long been influential in political philosophy, sociology and social psychology, particularly in research traditions going back to the work of George Herbert Mead and the Chicago school (Mead 1967). But to many other fields, particularly those based on formal methods or rational actor models, it represents an important recent trend, a move away from methodological individualism towards more holistic approaches. Important work has also been devoted to attempting to unite the two paradigms, such as List and Dryzek (2003) which presents a deliberative approach to social choice theory.
- 2.
This does not mean that the various intelligence-as-optimization theories that have been proposed (see e.g., Russell 1997) are mistaken. On the contrary, we agree that such theories can be highly informative. However, they are also inherently incomplete. Therefore, they should be complemented by models that allow us to investigate other aspects, such as reflexive reasoning about what it means for an agent to optimize its behavior. If we ever succeed in creating a truly intelligent agent, such an agent might well take issue with our explanation of what exactly it is that makes it intelligent. Indeed, such an ability would in itself be a mark of intelligence, perhaps the best we can hope for.
- 3.
The connection between various branches of social science and formal logic and computer science has received much attention in recent years and it has led to a surge of interest in interdisciplinary research (Parikh 2002; van Benthem 2008; Verbrugge 2009). However, while much recent work in applied logic has been devoted to modeling agency and interaction, the usual starting point is still that agents reason in adherence to some given standards of correctness, which remain fixed even in models that are designed specifically to model changes in the environment of the agents. In particular, most formal work is based on an individualistic and highly normative view on what it means to reason correctly about a state-of-affairs, a view we will challenge in this paper.
- 4.
This stands in contrast to most formal work on rationality and interaction, which tends to be based on the assumption that agents are individually rational in some appropriate sense, for instance because they seek to maximize given utility functions. Here, we will argue that in order to provide adequate formal foundations for rational interaction we must depart from the approach of trying to reduce it to individual attempts at utility-maximizing. Instead, we propose an approach based on an enactive view of reasoning as an argumentative process, where we model argumentative deliberation as it unfolds along a temporal structure in response to agents’ deliberative actions. We mention that models of agents acting in an environment have received much attention from the formal logic community recently, see e.g., Broersen (2011), Alur et al. (2002), Ågotnes and van Ditmarsch (2011), and Hoek et al. (2007). By drawing on argumentation theory, we believe it is possible to develop this work in a direction that will make it even more relevant to the task of modeling situated social interaction.
- 5.
Some argumentation scholars have criticized this approach, by pointing out that negotiations over meaning is a key aspect of argumentation that most theories developed in the normative tradition seem incapable of accounting for in an appropriate manner, see e.g. Kock (2007) and Wohlrapp (1998). To some, the challenge lies with the inherent subjectivity of argumentation, which calls for a shift of focus towards rhetoric (Kock 2009). However, others have stressed how argumentation gives rise to important mechanisms whereby people may change their positions and collectively develop novel (and normatively sound) views on the matter under consideration (Wohlrapp 1998). In our opinion, this is the crucial insight, which is also important in relation to the results reported in Mercier and Sperber (2011). In particular, we think it serves as a link between the descriptive and normative content of this theory, as well as with previous work on argumentation.
- 6.
The theory of argumentation frameworks has been influential in the context of artificial intelligence (Rahwan and Simari 2009). It is capable of capturing many different semantic notions, including semantics for multi-valued and non-monotonic logics, logic programs and games (Dung 1995; Dyrkolbotn and Walicki 2014). The work of Brewka et al. (2011), on the other hand, shows how argumentation frameworks can be used to provide a faithful (and computationally efficient) representation also of semantics that are formulated with respect to the more fine-grained formalism of abstract dialectical frameworks (Brewka and Gordon 2010). It is also important to note that much recent work focuses on providing logical foundations for the theory, work we can draw on when we develop multi-agent extensions (Grossi 2010; Arieli and Caminada 2013; Caminada and Gabbay 2009).
- 7.
In terms of each individual agent, using terminology from cognitive science, this means that we employ argumentation frameworks to describe (parts of) the informational level of cognitive processing, see Stenning and van Lambalgen (2008, p. 348) for an informal definition of this term. Previous work has demonstrated that logical tools can have a particularly crucial role to play in facilitating exploration at this level, also serving to shed new light on established truths arrived at through empirical work, see Stenning and van Lambalgen (2008, pp. 348–360), and Stenning and van Lambalgen (2005) for a concrete example. We note that our use of argumentation frameworks to model information-processing and representation makes good sense with respect to the argumentative theory; since agents reason to win arguments, it is natural to assume that they tend to represent semantic information in argumentative terms.
- 8.
There is strong formal evidence supporting the claim that classical reasoning about AFs is captured by the stable semantics, in particular the result that AFs under the stable semantics provide a normal form for theories of propositional logic (Bezem et al. 2012).
- 9.
This result was also rediscovered in Dung (1995), but kernel theory offers many additional results and techniques, see for instance Galeana-Sánchez and Neumann-Lara (1984). These results can be understood as providing conditions which ensure the possibility of imposing classical standards of reasoning on agents’ interpretations of the world, establishing an interesting link between the formalism in this paper and an established subfield of graph theory.
- 10.
In a perfect world, this might not matter, since all debate might eventually be settled conclusively by brute empirical fact, such as observing actual rain as opposed to consulting weather reports and puddles. However, in such a world, deliberation would not be very interesting and luckily, deliberation is hardly ever conclusive in the real one. Rather, a debate involves crucially a search for common ground, and common ground depends crucially on how agents perceive the statements made by others, as they reflect on the totality of the debate. This is why we need to be explicit about subjective views and ask for a representation of how each individual agent interprets the semantic meaning of all those claims that are relevant to the scenario at hand.
- 11.
There has recently been work done on merging of multiple argumentation frameworks, where different agents typically endorse different frameworks, see Coste-Marquis et al. (2007), Gabbay and Rodrigues (2014), and Dunne et al. (2012). This is related to the work we present in this paper. However, merging has so far been studied as an aggregation problem, the goal being to describe principles of aggregation that are “fair” and/or “rational” in lieu of social choice theory (for a list of possible principles, formulated for argumentation scenarios, see Dunne et al. 2012). In our opinion, normative approaches of this kind fail to do justice to the subtle interaction games that take place when agents negotiate about meaning. Therefore, we suggest a different approach, based on branching-time descriptive models of deliberative processes (which may, but need not, result in a merging of different viewpoints), drawing on insights from work done on temporal and strategic logics.
- 12.
Interestingly, this does not mean that a possible unanimity regarding the semantic status of an argument is necessarily reflected in the view aggregated by deliberation, not even when all agents reason according to the same semantics. If the agents differ in their account of why an argument should be accepted, deliberation might lead to its rejection. We will formalize a scenario like this in Sect. 19.3.1, Example 19.3.
- 13.
In this paper we only sketch a framework that permits us to logically examine spaces of possible outcomes, such as those identified by (Q, R). We remark, however, that a natural next step is to try to investigate which one of these would actually result from cooperation, given some assumptions about the faculties of the agents involved, and depending on how arbitration takes place inside coalitions.
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Dyrkolbotn, S.K., Pedersen, T. (2016). Arguably Argumentative: A Formal Approach to the Argumentative Theory of Reason. In: Müller, V.C. (eds) Fundamental Issues of Artificial Intelligence. Synthese Library, vol 376. Springer, Cham. https://doi.org/10.1007/978-3-319-26485-1_19
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