We study how using argumentation as an alternative foundation for logic gives a framework in which we can reconcile human and automated reasoning. We analyse this reconciliation between human and automated reasoning at three levels: (1) at the level of classical, strict reasoning on which, till today, automated reasoning and computing are based, (2) at the level of natural or ordinary human level reasoning as studied in cognitive psychology and which arti cial intelligence, albeit in its early stages, is endeavouring to automate, and (3) at the level of the recently emerged cognitive computing paradigm where systems are required to be cognitively compatible with human reasoning based on common sense or expert knowledge, machine-learned from unstructured data in corpora over the web or other sources.
The ever increasing demand for smart machines with ordinary human-level
intelligence, attuned to every-day common sense reasoning and simple problem
solving, has reignited the debate on the logical nature of human reasoning and
how this can be appropriately formalized and automated (e.g. see [
For over half a century now it has been known that the classical view of logic
from mathematics is at odds with the nature of human reasoning, as identi ed
in many empirical behaviour studies of cognitive psychology (e.g. see [
In this paper, we rst re-consider the foundations of logic from an
argumentation perspective, in the spirit of the approach of [
Before analysing how argumentation can be used to reconcile human and
automated reasoning, we note that argumentation has been at the heart of logic
ever since its inception with Aristotle4: logical reasoning according to Aristotle
was to follow certain accepted patterns of inference, called complete deductions,
that were a-priori justi ed, to nd other forms of valid patterns (syllogisms) for
drawing conclusions. Syllogisms, which in modern logic correspond to derivations
in proof theory, are in e ect arguments for supporting the conclusions that they
draw. Moreover, complex arguments can be built from simpler, basic arguments
and indeed Aristotle had attempted to show that all valid arguments can be
reduced to his basic forms of arguments. This reduction task is not easy [
We also note that dialectical argumentation forms a wider context that embraces the conception of logic in Aristotle5. A process of dialectic argumentation is based on common beliefs or reputable views from which arguments are built to support conclusions. The important di erence with simply demonstrating that a conclusion follows through an argument, is the (extra-logical) additional requirement that the process aims to convince or persuade. When logic is formalised as argumentation, both views of logic (as validity and as dialectics aiming at persuading) play an important role, as we discuss in Section 2 below. 2
From the point of view of argumentation, reasoning can be seen as a double process: constructing arguments linking premises and conclusions that we want to draw as well as defend these arguments against (possible or proposed) counterarguments generated from an attack relation between arguments.
Arguments are built from constituent parts (e.g. private or common beliefs or reputable views) that are combined in some way to form a structure supporting desired positions. In a logical setting the process of constructing an argument for a desired position can be associated to a logical proof for the position. Hence, given some language, L, for logical sentences together with a notion of deduction, `, drawn from some set of inference rules, an argument can be constructed by choosing some set, , of sentences in L | the argument's premises | that under the application of (some of the) inference rules deduce, via `, a conclusion that is identi ed with the desired position. Arguments may also draw intermediate conclusions (combined, as dictated by the inference rules of `, to give the main conclusion) and thus combine sub-arguments within a single argument structure.
A logical language would typically also contain some notion of contradiction
or inconsistency (denoted by ?), which can be used, in conjunction with the
inference rules, to provide the notion of counter-argument/the attack relation
4 A concise introduction to Aristotle and logic can be found in [
Several methods have been proposed in the literature on argumentation in
arti cial intelligence (e.g. see [
For the illustration, let us consider a simple example, where we take as the underlying language L a standard language of classical PL allowing to represent the following rules (and all other knowledge/beliefs presented later in this section): { \normally, a seller who delivers on time is trustworthy"; { \normally, a seller who delivers the wrong merchandize is not trustworthy".
These rules can be represented6 in PL by the following sentences (for some seller in the ( nite) domain of discourse): (1) (2) (4) timely delivery ! trusted wrong delivery ! :trusted
Given additional information about a delivery by the seller we can build arguments for and against trusting the seller. For example if we observe that the seller delivers on time timely delivery (3) then we can build argument A1 with premises the sentences (1) and (3) and conclusion that the seller should be trusted. Moreover, if the seller has made a wrong delivery
wrong delivery 6 As we will discuss later, under the argumentation-based reformulation of PL the implication connective used here does not need to be interpreted as classical material implication. Rather, an implication A ! B may be interpreted, informally, as \given A we have an argument for B". then we can build argument A2 with premises the sentences (2) and (4) and conclusion that the seller should not be trusted. These two arguments are counterarguments against (or attack) each other when indeed we have both pieces of information (3) and (4). Furthermore, if we also have the additional rule { \if the seller is trusted then one can place large orders", represented as trusted ! large orders (5) then we can build argument A3 with premises (3), (1) and (5) and conclusion that large orders can be placed with the seller in question. Note that argument A2 is still a counter-argument against A3, despite the fact that the ( nal) conclusions that they support are not contradictory, as A2 undercuts A3 on trusted on which A3 depends. In other words, A2 attacks A3 because it attacks a subargument of A3, namely the sub-argument A1.
Given arguments and attacks between them, we can determine which
arguments are (dialectically) acceptable, e.g. in the spirit of admissibility in abstract
argumentation [
A1 and A2 are both acceptable; { neither trusted nor :trusted are sceptically entailed by T , since their (respective) negation is credulously entailed by T .
Note that it may be useful in some cases to use hypotheses as premises of arguments whose conclusions are credulously entailed if the hypotheses are dialectically legitimate and the arguments using them as premises are acceptable. For example, it may be desirable to hypothesize :large orders (6) to form an argument A4 with premises the sentences (2) and (4) from the given theory and hypothesis (6) to support the conclusion :large orders while also including, within the premises of the argument, its defences against attacks. The argument A4 is acceptable because it can defend against all attacks. For example, the attacks against A4 by argument A1 and by argument A3 are both defended against by A4 since they are defended against by the sub-argument A2 of A4. This is depicted in gure 1 below, showing the dialectic nature of the argumentation semantics of acceptability. Here, A3 disputes the hypothesis :large orders in A4, and the sub-argument A1 of A3 disputes the conclusion
A1 (trusted) SK
A3 (large orders; trusted) SK
would be credulously entailed by the above theory.
:trusted of sub-argument A2 of A4. Notice that the defence by A2 against A3
does not come simply from the symmetric incompatibility of :large orders on
A3. This can be justi ed via an implicit priority of premises from the given theory
over hypotheses: arguments solely supported by the given theory are stronger
than those supported by hypotheses. Notice that priorities on premises can also
be given explicitly [
It is easy to see that credulous entailment of a sentence corresponds to a form
of satis ability, i.e. if a sentence is credulously entailed then there exists a
maximal consistent sub-theory of T with which the sentence is also consistent. More
signi cantly, for appropriate de nitions of arguments, attack and defence [
When working with classically inconsistent theories, PL can use the RAA
inference rule (or proof by contradiction) to derive, by means of an indirect
proof, any sentence based on a subset of contradictory premises in the theory.
For this reason, most works in logic-based argumentation, e.g. [
Separating out the RAA rule and excluding this from being one of the
primary means to construct arguments gives rise to (a form of) Argumentation
Logic (AL) [
In AL, the notions of acceptability and non-acceptability of arguments are de ned dialectically in terms of notions of attack and defence amongst arguments, where defence is de ned as a restricted type of attack, ensuring asymmetry (as discussed earlier).
Acceptability is de ned as a relative notion between arguments, i.e. that an argument a is acceptable with respect to another argument a0, informally meaning that if we a-priori accept a0 then a is an acceptable argument. The argument a0 helps to render a acceptable. For example, when we want to adopt an argument this could be used in its defence against counter-arguments and analogously an argument could render itself non-acceptable by rendering one of its counter-arguments acceptable. The informal de nition of this acceptability notion of \a is acceptable with respect to a0" is that for every argument, b, attacking a there is an argument, d, that defends against b and this defending argument\d is acceptable with respect to a [ a0". The defending argument d in e ect renders the attacking argument non-acceptable. Then, non-acceptability is de ned as the classical negative dual of acceptability. Finally, a sentence (seen as an argument) is (sceptically) entailed from a theory if it is acceptable with respect to the empty argument and its negation (seen again as an argument) is not acceptable with respect to the empty argument. To illustrate this let us consider the additional statement:
{ \normally, a seller that delivers late is not trustworthy", represented as :timely delivery ! :trusted (7) and, further, assume that we have also learned (by analyzing our sale records) that, for our particular seller,
{ \normally, when the delivery is on time the wrong item is delivered", timely delivery ! wrong delivery (8) Consider now the theory T consisting of sentences (1), (2), (7) and (8). This is classically consistent and it classically entails :trusted. Let us see how in AL we would derive that trusted is non-acceptable, that is needed for AL to the dialectical process of argumentation depicted in gure 2.8 (sceptically) entail :trusted. The non-acceptability of trusted can be determined by considering the argument B1 with premises T and hypotheses ftrustedg, and
SK O
attack : T [ftrustedg[f:timely deliveryg`DD? defence by opposing the hypothesis of B2 attack : T [ftimely deliveryg[ftrustedg`DD? gument, given T = f(1); (2); (7); (8)g, in order to determine classical entailment of trusted from T . All arguments have T as their premises and hypotheses as indicated in brackets.
The
gure shows that there is an attacking argument (B2) for which there is no acceptable defence as the only possible defence (B3) against this attack is attacked by the proposed argument (B1): the defence is rendered non-acceptable by the proposed argument and hence the proposed argument is not acceptable.
Note that the example theory T is classically consistent and the above
dialectic proof of the non-acceptability of trusted can be shown [
The following results of AL [
But perhaps the most important property of AL, shared by most
argumentation frameworks proposed in AI over the last 25 years, is its dialectic nature
of reasoning that gives a natural form of bounded reasoning by considering
incrementally di erent attacking arguments as they arise in the case of reasoning
at hand through new (evidential) information that is brought in the theory or
to the attention of the reasoner: a form of on-demand reasoning which, as we
will see in the next section, is supported by psychological evidence [
Reconciliation - level 1: Given the above results on AL we have reached our rst level of reconciliation of human and automated reasoning. Assuming that argumentation and argumentative dialectic reasoning is closer to human reasoning than strict classical logic and thus human reasoning can be automated through argumentation, it is important to know that an argumentation perspective is not a radical deviation of the status quo in automated reasoning. Indeed, the whole notion of computation and its formalization and automation rests on the foundation of PL, Boolean algebra and von Neumann computer architectures. Adopting the new foundation of argumentation for logic and reasoning does not abandon the existing frameworks of automated reasoning but co-exists with the foundation of computation through classical logic as the \calculus of computer science".
From now on we will use the term AL to refer, generically, to the re-formulation of logical reasoning via argumentation. 3
The aim of this section is to present some of the main features of human reasoning coming out from empirical studies in the Psychology of Logic (Reasoning) and to examine how formal argumentation in AI, and in particular AL, conforms with these features. We will also overview some recent work from Psychology that gives direct evidence for argumentation in human reasoning. Putting these results together with the previous section we will argue that human reasoning can be formalized well through argumentation in a way that facilitates its automation for building arti cial intelligent systems.
Over the last century, a large amount of research has been carried out in
the area of Psychology of Reasoning with the results suggesting that human
reasoning is failing, in comparison with strict mathematical or classical logic, at
simple logical tasks, committing mistakes in probabilistic reasoning and being
subject to irrational biases in decision making [
Humans do well when using Modus Ponens with implications. But they do
not fair well in using Modus Tollens, which also indicates that they have di
culty in reasoning by contradiction (i.e. in applying the classical RAA rule). On
the other hand, humans recognize that the falsi cation of an implication comes
through a case where the condition (antecedent) of an implication holds yet the
conclusion of the implication does not hold [
Most work in the Psychology of Reasoning then points to the observation
that human reasoning di ers from reasoning in classical logic and di erent
interpretations and theories on the nature of human reasoning have been proposed.
On the one hand, there are proposals that stay very close to the mathematical
and strict form of logical reasoning, such as the proposal of \The Psychology of
Proof" theory [
Importantly, the study of the Psychology of Syllogisms [
But building mental models can be seen as building arguments from the
available evidence currently at hand and general premises of common sense
knowledge that people have acquired. Then, as argued also in [
Summarizing, the work in the Psychology of Reasoning has exposed the following salient features of human reasoning given here from a modern view of computational logic in Arti cial Intelligence: { Human reasoning is able to handle contradictory information without trivializing. There is no inconsistent state of the human mind that would make it incapable of drawing any inference. { Human reasoning is defeasible. Conclusions drawn can be retracted in the face of new information. Knowledge on which human reasoning is based is not absolute. { An implication (or a rule) expresses only an association between its conditions and conclusion, not a necessity. Other properties of an implication that are implicit in the classical logical interpretation are not prominent in human reasoning.
Finally, we separate out some recent work from the Psychology of
Reasoning which provides explicit evidence for the argumentative nature of human
reasoning. In [
What characterizes the process of reasoning proper is the awareness, not just of a conclusion, but of an argument that justi es accepting that conclusion. To validate their argumentation theory for reasoning, the psychologists have carried out experiments to test how humans form, evaluate and use arguments. One important conclusion of their study is the fact that humans will come up with \solid" arguments when they are in an environment where they are motivated to do so, i.e. in an environment where their position is challenged. Otherwise, if not challenged the arguments produced could be rather naive. But once counterarguments or opposing positions are put forward people will produce better and well justi ed arguments for their position by nding counter-arguments (i.e. defences) to the challengers. For example, in experiments where mock jurors were asked to reach a verdict and then were presented with an alternative one it was observed that almost all of them were able to nd counter arguments against the alternative verdict (very quickly) strengthening the arguments for their original verdict.
This indicates that automating human reasoning through argumentation can follow a model of computation that has an \on-demand" incremental nature. This will be well suited in a resource bounded problem environment and more generally for cognitive systems that we will consider in the next section. 3.1
Human Reasoning and Argumentation in AI
The Psychology of Reasoning had in uenced AI in its e ort to automate human
reasoning. From the early stages of AI an approach based on production rules was
developed, in uenced by the psychological ndings on the nature of implications
in human reasoning. Cognitive architectures [
To address these shortcomings but also independently motivated by the
desire to have a clear formal semantics of intelligent computation in AI, new formal
logical frameworks, beyond classical logic, were proposed (starting with the
seminal works [
Nevertheless, with the introduction of formal argumentation in the early
1990s, to capture in particular the non-monotonic reasoning of negation as
failure in Logic Programming [
All these studies of argumentation in AI show that argumentation has the capacity to address the salient features of human reasoning that the empirical studies of psychology have pointed out. Argumentative reasoning is a natural form of reasoning with contradictory information by supporting arguments for con icting conclusions, such that conclusions are withdrawn when new stronger arguments come into play. Argumentation gives a form of reasoning in an intended mental model, the model corresponding to the conclusions that are supported by the stronger arguments available, which is naturally defeasible as this model can change in the face of new information. 3.2
Argumentation for Story Comprehension The argumentative nature of human reasoning is quite pronounced in the central task of comprehension of a given situation or narrative. Humans try to comprehend situations they are faced with through a mental model constructed by inferring information that is not explicitly present in the situation, yet it follows from it, explaining why things happened as they did, linking seemingly unconnected events, and predicting how things will further evolve, by developing arguments in each case. To construct such an intended comprehension model it is necessary to be able to draw inferences relating to how information changes over time (e.g. the story line) whether these are about the state of the physical or mental (e.g. intentions of protagonists in a story) world in the narrative.
Several works [
Recently, combining this argumentation approach to reasoning about actions
and change with empirical knowhow and theoretical models from Cognitive
Psychology, it was possible to show that argumentation can successfully capture
many of the salient features of narrative text comprehension by human readers,
as exposed through many years of empirical and subsequent theoretical studies
from Cognitive Psychology. In particular, the mental comprehension model that
is built by human readers of stories corresponds to the grounded extension of a
corresponding argumentation framework whose arguments are grounded on the
explicit information in the story [
Consider, for example, a scenario where we hear Alice saying to her colleague: \Bob delivered the rst car we ordered on time, but he brought us the wrong model. This is a big problem. We should cancel the other order with Bob.". Upon hearing Alice, we seek to bridge her utterances. We may reason that Alice might be invoking the following premises timely delivery ! trusted and wrong delivery ! :trusted to build arguments for and against trusting Bob. From Alice's second sentence, that there is a problem, we might infer that the second premise and argument built from it is stronger for Alice, and that despite the con icting inferences of the two arguments, Alice is led to infer that Bob is not trusted. We may further consider that Bob's trustworthiness related to the cancelling of the second order through the premise :trusted ! :large order, and thus we make sense of the situation. We would as easily make sense of the situation had Alice said \This is a minor problem. We should keep the other order with Bob.", realizing that the preference on Alice's premises and arguments built from them are reversed. For more information the reader is referred to the web site of the STAR system for Story Comprehension through Argumentation at http://cognition.ouc.ac.cy/star.
Despite the fact that further work is needed to address fully the important problems of coherence and abstraction in narrative text comprehension the fact remains that argumentation can provide a basis on which to build further these important features of the comprehension model.
Reconciliation - level 2: Argumentation logic and argumentative dialectic reasoning is closer to human reasoning than strict classical logic capturing well the features that crucially characterize and distinguish human level natural intelligence from mathematical and scienti c reasoning. Argumentation treats all human knowledge as inherently defeasible building from these arguments to support conclusions. Argumentation is able to reconcile all approaches to date in AI for automating human reasoning under one umbrella that conforms to the empirical observations on the nature of human reasoning in Psychology. As such Argumentation Logic and argumentation in general provides a solid foundation for automating human reasoning in AI able to accommodate reasoning with inconsistent premises and revision of conclusions. 4
We now present how argumentation can form a foundational basis for the new paradigm of Cognitive Computing and for the development of cognitive systems, which, as we have argued in the Introduction, forms the renewed impetus for the need to automate human reasoning.
Cognitive systems, as studied for example in [
In e ect, what we are asking is for these systems to be able to reason like humans and to interact with humans in the form of a dialectic argumentative dialogue. Given the discussion of the previous sections where we have argued that human reasoning can be formalized in terms of argumentation and that formal argumentation from AI captures well the human dialectic process of argumentation, we believe that argumentation can form the basis for the Reasoning API of cognitive systems.
But argumentation can have a much deeper role in the development of the eld of Cognitive Computing. This new paradigm needs a new foundational notion of computation that classical logic cannot provide but which formal argumentation is well suited for. This is linked to the second main characteristic of cognitive systems, the fact that these systems depend and operate on knowledge acquired from unstructured data normally through some form of machine learning, again analogously to the situation that we have in humans who learn over time the knowledge on which they base their reasoning. For example, cognitive home or work assistants, analogous to personal assistants, need to have common sense knowledge so that they can humanly comprehend their environment, which would normally also include human users, from the explicit (but sparse) information that this gives to them, which is su cient for a human to comprehend the environment. This is much like story comprehension where this needs the integration of the explicit information in the narrative with common sense background world knowledge.
How is then common sense knowledge to be acquired? The eld of cognitive
computing implicitly assumes that this, or any other form of expert knowledge
whether this is \data science" knowledge, or knowledge from \data analytics",
or even \mined arguments", on which a cognitive system will be built, would
be obtained incrementally through a process of (largely) autonomous learning
from unstructured data. Learning frameworks that integrate symbolic learning
and reasoning have shown that this can be done in a manner that the learned
knowledge is guaranteed to draw inferences that are probably approximately
correct [
Such learned knowledge cannot form strict absolute knowledge as it could in a
didactic supervised form of learning. It would be defeasible knowledge that holds
for the most part. It expresses typical not absolute relationships between
concepts, where these links are dependent on the various contexts and sub-contexts
of the problem domain. Hence the form of such knowledge can be naturally
associated to argumentation: learned knowledge from unstructured data forms the
basis, the premises, for building arguments. In philosophical terms, the inductive
syllogism, as Aristotle calls this process of acquiring rst principles from
empirical experience, cannot produce absolute knowledge: an inductively produced
implication A ! B does not formally express the \necessity" of B when A is
known to hold but an argument for B thus making B \probable" in the current
case, as the philosopher David Hume [
We note that this formalization of such learned knowledge in terms of argumentation does not apply only to common sense knowledge but also to expert knowledge acquired from unstructured data. Hence when IBM Watson is applied to oncology in health applications the scienti c knowledge learned provides the basis for acceptable arguments that the machine can build in its task to give medical recommendations. These arguments provide a way for the Watson machine to explain the structure and quality of its recommendation to the human doctor as one human doctor would do to another doctor.
Reconciliation - level 3: The new foundation for logic and reasoning of argumentation can provide the basis for a more exible paradigm of computing on which to build systems that are cognitively compatible to humans. Such cognitive systems are built by exploiting common sense knowledge or expert knowledge learned from unstructured data whose formal understanding can naturally be captured by argumentation logic. 5
Drawing from past and recent work in Psychology and AI, we have argued that an alternative view of logic as a framework for argumentation is closer to natural human reasoning than classical logic. As such an argumentation-based formulation of logical reasoning o ers a way to reconcile and bridge human and automated reasoning.
Within argumentation the notion of classical logical entailment can be formulated in a way that conforms with an open ended dialectic process of argumentation o ering new possibilities and features that are attuned to human reasoning. Important such features included handling con icting information and a form of bounded rationality of \on-demand" reasoning where arguments are defended against counter-arguments that are grounded on the evidential information of the case at hand rather than on hypothetical situations that might possibly arise.
Argumentation Logic allows us to give a di erent interpretation to symbolic knowledge that on the one hand has the exibility of human reasoning while at the same time o ers a suitable target language for learning from unstructured data. This makes argumentation a suitable logical foundation for the emerging paradigm of Cognitive Computing. In this new paradigm the abstract notion of computation can be formalized as the construction of acceptable arguments supporting solutions of the problems. These solutions are not necessarily globally and objectively optimal but rather solutions that are locally convincing and persuasive, according to the expectation of the human user, both for the case where the problem is a common sense task or a task in an expert domain.
To some extent our proposal constitutes a return back to early AI where cognitive psychology had a strong in uence on the eld. The crucial di erence is that now we are advocating argumentation as a new logical foundation for this human-level AI, away from the, albeit many times implicit, assumption that classical logic can form the basis for automating human reasoning, as it does for all other conventional computing problems within the realm of scienti c and engineering problems. In fact, AI, by insisting on a classical logic foundation for intelligence, took a turn towards problems that fell in this engineering realm with an emphasis on \super intelligence" beyond the level of common sense intelligence one would nd ordinarily in humans. But for cognitive systems where knowledge is typically incomplete and inconsistent from a classical logic perspective, a radical change in the formal foundations of intelligent computation is needed. We have argued that this can be given through a reformulation of logic through argumentation as the primary notion of logical reasoning.
Given the need for a new logical foundation for cognitive computation one might ask whether this would also need its own architecture of computers on which to be realized, in the same way that the Von Neumann architecture is linked to classical (Boolean) logic. What would such an architecture be? Could it be a connectionist architecture where the threshold activation of signal propagation is linked to argument construction under inputs for and against the argument, thus giving argumentation a nal reconciliation role between symbolic and connectionist approaches to automating human reasoning?