STUDIES IN LOGIC, GRAMMAR AND RHETORIC 23 (36) 2011

Floris Bex and Chris Reed
University of Dundee

SCHEMES OF INFERENCE, CONFLICT,AND PREFERENCE IN A COMPUTATIONAL MODEL
OF ARGUMENT

Abstract: Argumentation demands that various non-deductive patterns of reasoning are accounted for from a strong theoretical foundation. The theory ofargumentation schemes has provided such a theoretical foundation, and has led
to a significant programme of research not only in epistemological and metaphysical philosophy but also in knowledge representation and multi-agent systems in
artificial intelligence. More recently, work on computational models of argument
has posited that not only inference, but also conflict, might be governed by moresophisticated relationships that just propositional negation. And finally, workon developing a standard computational ontology for handling argument hassuggested that preference too demands such schematization. This paper shows
how schematic templates can be designed to capture these stereotypical patterns of inferring, conflicting and preferring, and furthermore, demonstrates thestrong representational and constitutive similarities between these apparently
very different phenomena.
Keywords: argumentation schemes, Argument Interchange Format, inference,
conflict, preference

1. Introduction
The theory of argument is a rich, interdisciplinary area with insightsfrom diverse disciplines such as philosophy, law, psychology, communication
studies and artificial intelligence. This paper explores the ways in whichparts of arguments can be connected together.
Recent research in philosophy has shown that the broad range of ways inwhich inference is performed in natural texts can be understood by taxonomizing and classifying ‘argumentation schemes’, which capture stereotypical
patterns of reasoning (Walton 1996; Walton et al. 2008). These argumentation schemes have been demonstrated to be not only powerful tools forscholarly investigation of argument, but also of practical use both in pedagogy and in computational settings (Reed and Walton, 2005). In addition toinference, however, argument makes fundamental use of two further types
ISBN 978–83–7431–***–*ISSN 0860-150X

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Floris Bex and Chris Reedof relation: conflict and preference. Conflict acts as a driver for argumentative discourse, and for many authors is a defining feature of such linguistic
behaviour. Preference, in turn, is the key to resolving conflict, particularly
where (as is very common) the conflict is rooted not just in propositional
disagreement, but in mismatches in values.
This paper argues for an approach that tackles inference, conflict andpreference as genera of a more abstract class of schematic relationships. This
allows the three types of relationship to be treated in more or less the sameway, meaning that the logical and semantic machinery required for handlingthem is greatly simplified. The context of the work is a method for representing argument structures which aims simultaneously to provide a languagethat is rich enough to talk about the enormous variety of naturally occurring
argument, whilst at the same time enforcing a level of specificity and claritythat allows for computational interpretation. This context is the Argument
Interchange Format, AIF, which serves as an interlingua between various
software tools and systems in the burgeoning community in computationalmodels of argument (Chesñevar et al., 2006).
The rest of this paper is organised as follows. In section 2 we provide
a brief and very general introduction to the most important concepts inargumentation theory. Section 3 introduces the language of the AIF; 3.1 discusses the basic concepts and 3.2 concentrates on the various schematic
relations. Section 4–6 discuss inference, conflict and preference schemes,
respectively. These sections start with a short introduction to the representation of inference, conflict and preference in models of computational
argument. After this, the modelling of these concepts in the language of the
AIF is presented. Section 7 concludes the paper.

2. Argumentation
In an argument, a defeasible inference leads from premises to a conclusion; associated with a defeasible inference is a generalization, usually ina conditional form, which justifies or warrants the inference link between
premises and conclusion. Generalizations are generalized statements about
how we think the world around us works; they can express generally accepted patterns (e.g. (“If a witness testifies that ‘P’ then P is the case”) or they
can be more case-specific (e.g. “Chris is usually at work before 8 o’ clock”).
Very often, generalizations are left implicit in natural argument, but explicitly expressing the generalization can help in determining the relevanceand force of the inference. Take, as a simple example the argument for the2Schemes of Inference, Conflict, and Preference in a Computational Model...
conclusion that Harry was in Dundee based on Bob’s testimony, visualised
as a diagram in the style of Toulmin (2003):

Figure 1: a Toulmin-style argument for the claim that Harry was in Dundee

Generalizations that occur often in natural argument have been studied
in the form of argumentation schemes (Walton et al. 2008), stereotypical
patterns of reasoning.1 As an example, take the scheme for “argument fromappeal to witness testimony”, which is similar to the above generalization(adapted from Bex et al. 2003):
Witness W asserts that P is true (false).
Therefore, P may plausibly be taken to be true (false).

Associated with each argumentation scheme are critical questions thatpoint to standard sources of doubt. Standard sources of doubt with regards
to witness testimony are, for example, the witness’ bias, whether he is lying
or whether he correctly remembers what he observed; critical questions forthe argumentation scheme are hence, for example, ‘Is the witness biased?’or ‘Is there a chance that the witness misremembers?’.
Most everyday arguments are defeasible, in that new information cancast doubt on information previously taken to be true. For example, ‘witness
Peter testifies that Harry was in Amsterdam’ is a reason for the fact that
Harry was in Amsterdam. This provides a counterargument to the original
conclusion that Harry was in Dundee. In addition to attacking conclusions(called rebuttal in the literature, see Pollock 1994, Prakken 2010), we may
also attack the defeasible inference (this type of attack is often called undercutting). Recall that the generalizations or schemes that justify inferences

1 As Prakken (2010) has shown, argumentation schemes are often (but not always)
generalized rules of inference.

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Floris Bex and Chris Reed
express a stereotypical pattern of everyday reasoning: normally we expectthat people bear witness only to events they actually observed. However,
it is not unthinkable that in any particular case the witness misremembers
or lies (cf. the critical questions for the argument from witness testimony).
In such a case we are dealing with an exception to the general rule. Suchan exception does not deny the premise or conclusion of the argument but
attacks the inference from premise to conclusion: if, in the example, the witness is lying, this does not mean that Harry was not in Dundee; it just showsthat this particular witness testimony is not a good reason for believing thisconclusion.
Undercutting and rebutting are just ways to express conflict in argumentation. Conflict is just as important as inference in argumentation: thedialectical process is essentially a process of argument and counterargument.
However, while some of the mathematical properties of conflict have been
extensively studied,2 (context-)specific types of conflict have not received
much attention in (computational) argumentation theory.3
Inference and conflict allow us to build arguments and provide counterarguments. In many contexts, a choice then needs to be made as to whichof the arguments one decides to believe or, in other words, which of thearguments is preferred. This preference is naturally tied to the applicable“rules” of the discussion (e.g. a judge or jury cannot decide for an argument
on inadmissible evidence, even if she prefers this argument). In general, however, this preference is intimately tied to the beliefs of the person doing
the evaluation. For example, we can only accept that Harry was in Dundee
if we believe that Bob (who stated Harry was in Dundee) is a more trustworthy witness than Peter (who stated that Harry was in Amsterdam).
Formal models of argumentation have long enjoyed rich, mature models ofpreference and priority. Bench-Capon (2003), for example, has shown how
one’s values might influence the choice of beliefs and Modgil (2009) has
extended Dung’s (1995) abstract argumentation frameworks with reasoning
about preferences. However, as with conflict, more context-specific patterns
of preference (outside the value orderings of Bench-Capon) have not been
widely examined in (computational) argumentation theory.

2 See the large body of work on argumentation theoretic semantics in the style of(Dung 1995), e.g. (Caminada 2006, Dunne 2009).
3 However, some argumentation schemes, such as the scheme for ad hominem arguments, seem to have more to do with conflict rather than inference.

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Schemes of Inference, Conflict, and Preference in a Computational Model...
3. The Argument Interchange Format
Argumentation is a large and diverse field stretching from analyticalphilosophy to communication theory and social psychology. The computational investigation of the space has multiplied that spectrum by a diversityof its own in semantics, logics and inferential systems. One of the problems
associated with the diversity and productivity of the field, however, is fragmentation. With many researchers from various backgrounds focusing on
different aspects of argumentation, it is increasingly difficult to reintegrate
results into a coherent whole; for the plethora of methods, processes andtools for argumentation, there are just as many individual languages forargumentation, ranging from logical to visual to natural language. Thisfragmentation makes it difficult to present new ideas which can be adapted
across the board and difficult for new research to build upon old. To tackle this problem, the computational argument community has initiated aneffort aimed at building a common ontology for argument: the Argument
Interchange Format (AIF).
The AIF is a communal project which aims to consolidate some of thedefining work on (computational) argumentation (Chesñevar et al. 2006).
The AIF project aims to present a common vision and consensus on theconcepts and technologies in the field, thus promoting research and development of new argumentation tools and techniques. A main aspiration of
the AIF is to facilitate data interchange among various tools and methods
for argument analysis, manipulation and visualization. To this end, the AIF
project aims to develop a commonly agreed-upon core ontology that specifies the basic concepts used to express argumentative information andrelations. The purpose of this ontology is not to replace other languages
for expressing argument but rather to serve as an abstract interlingua thatacts as the centrepiece to multiple individual languages. These argument
languages may be, for example, logical languages (e.g. ASPIC, see Prakken
2010), visual diagramming languages (e.g. Araucaria, see Reed and Rowe2004) or natural languages (e.g. pragma-dialectics, see van Eemeren and
Grootendorst 2004). The idea is that an interlingua drastically reduces thenumber of translation functions that are needed for the different argumentation languages to engage with each other; only translation functions to
the AIF core ontology have to be defined (i.e., n instead of n2 functions forn argumentation languages).
3.1. The AIF core ontology
In the AIF ontology, arguments and their mutual relations are described
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Floris Bex and Chris Reedby conceiving of them as a an argument graph. The ontology falls into twonatural halves: the Upper Ontology and the Forms Ontology. The Upper
Ontology, introduced in (Chesñevar et al. 2006), describes the languageof different types of nodes and edges with which argument graphs can bebuilt. The Forms Ontology, introduced by (Rahwan et al. 2007), allows forthe conceptual definition of the elements of the graphs, that is, it describes
the argumentative concepts instantiated by the specific nodes in a graph.
Figure 2 visually renders part of the ontological structure of the AIF; theexplanation of the different elements is below Figure 2. Note that here, only
a part of the ontology is shown; as we will show in this paper, for example,
conflict schemes also have descriptions of the elements that are in conflict.
For readability, however, only the elements connected to the defeasible anddeductive inference schemes are shown.

Figure 2: The AIF core ontology

The Upper Ontology places at its core a distinction between information, such as propositions and sentences, and schemes, general patterns ofreasoning such as inference or conflict, which are used to relate pieces of information (I-nodes) to each other. Accordingly, there are two types of nodes
for building argument graphs: information nodes, I-nodes, and scheme nodes, S-nodes. Individual nodes can have various attributes (e.g. “creator”,“date”). In a graph, I-nodes can only be connected to other I-nodes via
S-nodes, that is, there must be a specific scheme application that expresses
the rationale behind the relation between I-nodes. In the basic AIF ontology, scheme nodes can be rule application nodes (RA-nodes), which denotespecific inference relations, conflict application nodes (CA-nodes), which denote specific conflict relations, and preference application nodes (PA-nodes),which denote specific preference relations. Different S-nodes can be connected to each other; for example, we can express that two preference applications are in conflict with each other (e.g., x > y and y > x) by connecting
the two PA-nodes through a CA-node.
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Schemes of Inference, Conflict, and Preference in a Computational Model...
3.2. Scheme application in the AIF
The Upper Ontology defines the basic building blocks of argumentgraphs (in a sense, it defines the “syntax” for our abstract language). In
contrast, the Forms Ontology defines what these individual nodes mean inargumentative terms It defines the forms of the schemes that are used inreasoning, that is, the inference schemes, conflict schemes and preference
schemes. Informally, inference schemes are criteria for inferring (deductively, inductively or presumptively), conflict schemes are criteria (declarative specifications) defining conflict (which may be logical or non-logical)
and preference schemes express (possibly abstract) criteria of preference.
These main scheme types can be further classified. For example, inference
schemes can be deductive or defeasible. Defeasible inference schemes canbe further subdivided into more specific argumentation schemes, such as
Expert Opinion, Practical Reasoning and so on (see, for example, Walton
et al. 2008).4 Accordingly, the AIF ontology has a Schemes Ontology, which
is a sub-ontology of the Forms Ontology. This Schemes Ontology contains
specific inference schemes and may vary from very simple (containing only
the basic deductive and defeasible schemes) to extensive (containing a large
number of specific deductive and defeasible argumentation schemes).
As can be seen in Figure 2, the Forms Ontology and the Upper Ontology
are intimately connected because a specific applications of schemes (denoted
by RA-, CA- and PA-nodes) are instantiations of general (inference-, conflict- and preference-) schemes; in other words, the S-nodes fulfil the schemes
expressed in the Forms Ontology. Like argument-graphs from the abstract
language of the AIF, schemes can also be translated into a more concrete
language; for example, Rahwan et al. (2010) define schemes as combinationsof classes of statements in Description Logic, with object level arguments
then being instances of those classes. In this paper, like in (Rahwan et al.
2007), we will represent the Forms Ontology and the schemes contained in
it as graphs.5
RA-, CA- and PA-nodes capture the passage or the process of inferring,
conflicting and preferring, respectively, whilst the inference schemes, conflict
schemes and preference schemes embody the general principles expressing
how it is that A is inferable to B, A is contrastable to B (‘conflictable’ is too
4 It is important to note that the AIF ontology does not (and should not) legislate
as to which schemes or forms are the correct ones; different schemes are each plausible
according to particular theoretical assumptions.
5 Note that these graphs simply express concepts (i.e. Forms) and the ontologicalrelations between them; they are not AIF argument graphs, which exist at the object
level.

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Floris Bex and Chris Reedcumbersome a term), and A is preferable to B, respectively. RA-nodes thus
correspond mostly closely to what a traditional system of formal logic would
regard as entailment, i.e. where ϕ is a premise for an RA to a conclusion ψ,
the RA corresponds to ϕ ⊢ ψ. In contrast, conditionals such as ϕ → ψ areavailable as I-nodes – in instances of (defeasible) modus ponens, for example.
Of course it is possible to formulate – in natural language – a proposition
corresponding to the fact that ϕ ⊢ ψ, so in principle we can also represent
such a proposition as an I-node. But this I-node can be handled as a special
type of ‘calculated property’ (Reed 2010): a propositional result of runningsome (arbitrary) process over an AIF structure. This proposition could use
the RA itself as a basis for establishing the entailment proposition, but as
Bex et al. (2010) have argued, this exact connection between an AIF graphand the properties calculated on the basis of the graph cannot be captured
in the core AIF ontology itself (and nor should they be, for otherwise the
AIF would swell to some general purpose programming language).
This contrast between propositions expressing implicative relationships
and propositions expressing entailment relationships is important because
for inference, we have strong intuitions and mature theory to guide the way
in which the AIF should handle them. For conflict and preference, we needto develop strong analogues to inferential components. If we say then thatϕ → ψ expresses that ψ is inferable from ϕ, we might similarly say thatϕ ≻ ψ expresses that ϕ is preferable to ψ, and ϕ –× ψ expresses that ϕ iscontrastable with ψ. These could all be captured by I-nodes and could allserve as foundations for RA-, CA- and PA-nodes respectively. In contrast,ϕ ⊢ ψ captures that ψ is (in fact) inferred from ϕ, and so similarly we might
say that ϕ |≻ ψ corresponds to the fact that ϕ is (in fact) preferred to ψ,
and that ϕ |× ψ corresponds to the fact that ϕ does (in fact) conflict with ψ.
Again, these can all be captured by I-nodes, but their connection to RA-,CA- and PA-nodes is tenuous and is governed by the process which determines these calculated properties, and not by the AIF per se. These strong
analogies between the three schematic classes are very useful in developing
accounts of scheme usage through the AIF as a whole.

4. Schemes of Inference
One of the main issues of argumentation discussed in section 2 concerns
the generalizations warranting the defeasible inferences. In a logic, conditional generalizations of the form ‘if ϕ then ψ’ (or‘ϕ therefore ψ’) can bemodelled both as an object-level rule (ϕ implies ψ, formally represented as8Schemes of Inference, Conflict, and Preference in a Computational Model...
ϕ → ψ) or as a metalinguistic rule of inference (ϕ entails ψ, formally represented as ϕ ⊢ ψ). The various argumentation logics (see Chesñevar et al.
2000, Prakken and Vreeswijk 2002 for overviews) have different stances on
how these generalizations should be modelled. For example, Prakken (2010)
and Pollock (1994) model them as rules of inference, whereas (Bondarenko
et al. 1997) and Verheij (2003) model them as (defeasible) implications in
the object language and have a (defeasible) modus ponens inference rule forreasoning with these implications. The most important difference between
the two ways of modelling them is that conditionals in the object language
can be reasoned about in a natural way; they can, for example, be denied byarguing that “¬(ϕ → ψ)” or they can serve as the conclusions of arguments.
A problem for the argumentation logics that model generalizations as inferences is that it is often unclear how statements like ϕ ⊢ ψ can be renderedin the object language and what, in the object language, their relation to
ϕ → ψ is. In the AIF ontology, the fact that in the AIF ϕ ⊢ ψ is represented
by its own RA-node in the object language and ϕ → ψ is represented by its
own I-node in the object language disambiguates this relationship between
the two.
Now, as was argued above conditional generalizations can be modelled either in the object language (as an I-node) or in the metalanguage, asa Scheme in the Forms Ontology. Figure 3a models the conditional expressing the generalization as a premise (I-node) and connects this premise together with another premise (I-node) representing the antecedent of theconditional to the conclusion by way of a (defeasible) modus ponens inference (RA-node).

Figure 3: Two ways of modelling defeasible inference

The inference rule that is applied is explicitly shown in the AIF structure. In the case of the argument in Figure 3a, the generalization justifying
the inference (“If a witness testifies that ‘P’ then P”) is made explicit as an
9Floris Bex and Chris Reed
I-node and can be questioned. However, no further information about thegeneralization is provided; if an arguer or an analyst wishes to critique theinference step (e.g. by undercutting it), it remains for them to introduce
sufficient contextual knowledge to form an attack. One of the advantagesof the scheme-based approach advocated by, among others, Walton et al.
(2008) is that it provides a theoretically principled way of structuring thiscontextual knowledge. So the Argument Scheme from Witness Testimony
provides not just a characterisation of the minor premise and conclusion,
but also a raft of implicit premises (presumptions) which may be taken to
hold, and exceptions, which may be taken not to hold. These presumptions
and exceptions are part of the Scheme Ontology. A scheme-based analysis(Figure 3b) shows that the premise and conclusion are connected by thisspecific type of Witness Scheme inference. The general form of this scheme
gives the implicit premises and exceptions are part of the scheme and which
can be used to critique the scheme. Figure 4 shows both the abstract Defeasible Modus Ponens (a) and the specific Witness Testimony Scheme (b).
Notice that the Witness Testimony scheme shows the (implicit) presumptions and exceptions; exactly how these can be used to attack an argumentthat uses the scheme will be discussed below in section 5.

Figure 4: The Defeasible Modus Ponens and Witness Testimony schemes
as represented in the AIF

So modelling generalizations as conditional premises as in Figure 4aallows for a lot of flexibility, whereas modelling them as schemes as in Figure 4b provides a firm grounding to the rules of inference that are being
used in our reasoning. This can be seen in the case of Toulmin’s characterisation of backing, a reason for why we should believe the warranting
generalization. In at least some of Toulmin’s examples, backing serves tojustify a general rule, rather than its specific application. This is possible in10

Schemes of Inference, Conflict, and Preference in a Computational Model...
the case of the argument in Figure 3a: reasons can be given for the conditional premise that expresses the generalization. In the case of the argumentin Figure 3b, a backing can only be given if it is explicitly encoded in theForms Ontology (i.e. if the scheme for Witness Testimony has a Backing description). It is not possible to give a backing in an object-level argument,
as this would require Scheme Forms from the Scheme Ontology to be able
to stand as the conclusions of arguments.
It is important to note that AIF ontology does not (and should not)legislate as to which analysis in Figure 3 is correct. They are each plausible
according to particular theoretical assumptions. Similarly, the AIF ontology does not (and should not) legislate as to which schemes or forms are
the correct ones; different schemes are each plausible according to particular theoretical assumptions. Argument analysis needs, like many techniquesapplicable to naturally occurring language, to be flexible, and to admit ofalternative views. AIF’s job is to make such alternative analyses clear andunambiguous in a common language.

5. Schemes of Conflict
Conflict is a central notion in dialectical argumentation and it can takemany forms. For example, two claims may be in conflict because they express
opposing points of view or because they were uttered by people from different political parties. In logical models of argument, conflict is often equated with logical conflict, i.e., the contradiction between ϕ and ¬ϕ. Some
frameworks for formal argumentation (e.g. Bondarenko et al. 1997, Prakken
2010) generalize this to a contrariness relation, where ϕ is in conflict with
its contrary ϕ̄. Thus, other non-logical conflict relations can be expressed.
An important concept in logical models of argument, which is closely
related to conflict, is that of attack. Attack expresses that one argument issomehow a counterargument to another.6 However, conflict is not the sameas attack. First, the fact that two propositions are in conflict does not mean
they attack each other, as this depends on one’s definition of attack. For
example, in the ASPIC framework (Prakken 2010) a proposition ϕ onlyattacks another proposition ¬ϕ if ¬ϕ is not a necessary premise. If this is

6 Not to be confused with “defeat”. Attack and defeat are different concepts: attacking
your enemy does not guarantee their defeat, only a successful attack defeats. So attack
expresses that one argument is a counterargument to another, whilst defeat says that anargument is a counterargument and is preferred (Garcia and Simari 2004).

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Floris Bex and Chris Reedthe case, ϕ is in conflict with ¬ϕ but it does not attack it. Here, attack isbased on conflict, it is a calculated property. Second, attack is often definedover arguments, where conflict is usually only defined over propositions and,in some cases, inference applications (Figure 7).
In the AIF ontology, conflict is expressed using conflict schemes in theForms Ontology and applications of these schemes in the object layer, conflict application or CA-nodes. Conflict schemes are similar to (but certainly
not analogous to) inference schemes, in that they are patterns of reasoning
which are often used in argumentation. Like inference schemes, conflict schemes may denote abstract, logical patterns (e.g. logical conflict) as well as
more concrete patterns of conflict dependent on, for example, legal or linguistic conventions (e.g. a bachelor is not married, a man is not a woman).
Like inference schemes, conflict schemes can be strict (no exceptions to thescheme; e.g., ϕ and ¬ϕ are always in conflict) or defeasible (there are exceptions to the scheme; e.g. a man is not a woman unless (s)he is androgynous).
Like inference, conflict is often expressed as a generalization; for instance, “people cannot be in two places at the same time” or “it is impossible
for both the Tories and Labour to both be in government”. Where generalizations that warrant inference are often rephrased as conditionals of theform “if ϕ then ψ”, generalizations that express conflict can be rephrased
as “ϕ conflicts with ψ”. These conflict generalizations can be represented
as information (I-nodes) in the object layer, or in the layer of the Schemes Ontology, as conflict schemes. Take, for example, the conflict between
the British Labour Party and the British Conservative Party (“the Tories”)
being in government. Generally, the two parties are not in the same government (the last time was during the Second World War). Now, we can makethe generalization (Figure 5a), or we can model the conflict generalizationa separate conflict scheme (Figure 5b and Figure 6b).

Figure 5: Two ways of modelling conflict generalizations
Figure 5 shows an important difference between conflict and inference,
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Schemes of Inference, Conflict, and Preference in a Computational Model...
namely that often (but not always), conflict is a symmetrical relation, whilst
inference is certainly not. That is, if ϕ is in conflict with ψ, then ψ is also
in conflict with ϕ. For inference, this is not the case. One of the reasonsfor this is that with inference, we can gain new information (e.g. we haveinformation that a witness testified that Harry was in Dundee, so we caninfer the new information that Harry was in Dundee). Conflict schemes
have no such generative function, as they only allow us to represent conflict
between existing propositions.
In Figure 5, two conflict schemes are used, a general and a specific one.
These two schemes are rendered in Figure 6. The general conflict scheme(Figure 6a) takes a generalization from an I-node and uses this generalization to warrant the application of a conflict. In this sense, it can be likened
to the inference scheme for (Defeasible) Modus Ponens (Figure 4a), which
warrants the inference application with a generalization from an I-node.

Figure 6: Conflict schemes in the AIF Forms Ontology

An advantage of modelling conflict generalizations as I-nodes is thatthey can be reasoned about. For example, we can give reasons for why, in
general, Labour and Tories cannot be in the same government, having the
I-node that contains this generalization in Figure 5 as the conclusion ofan RA-node. When conflict generalizations are modelled as schemes in theForms Ontology, it is not possible to provide them with a “backing” in thisway. However, representing a conflict generalization as a scheme allows us
to specify implicit presumptions and exceptions to the scheme. For instance,
an exception to the generalization that Labour and Conservatives are notin the same government is that there is a coalition government, as was thecase during the Second World War (the exception basically says that theelements 1 and 2 are in conflict unless there is a coalition government ofparty X and Y). Thus, the implicit presumptions and exceptions to conflict
relations can be incorporated in a principled way.
Conflict does not just exist between I-nodes. There are cases in which,for example, some information is in conflict with an inference or a preference, or two inferences or preferences are in conflict. Take the example in13

Floris Bex and Chris Reed
Figure 7. Here, the information that Bob is biased conflicts with the application of the Witness Testimony inference scheme. This type of conflict,called undercutting by Pollock (1994), is quite common in argumentation.
It allows us to attack the way in which some information has been derived
rather than the information itself (that is, we attack ϕ ⊢ ψ). In the example,
knowing that Bob is biased is not a reason for the opposite conclusion, that
Harry was not in Dundee, but rather it is a reason to believe that we might not be justified in inferring Harry’s whereabouts from Bob’s testimony.
Figure 7b shows the conflict scheme used in the argument. Note how thisconflict scheme connects an inference scheme with one of its exceptions.

Figure 7: Conflict between an I-node and an RA-node

6. Preference Schemes in Argumentation
In addition to inference and conflict, the we treat preference as a basic
concept of argumentation. Inference and conflict allow us to build arguments
and provide counterarguments. In many contexts, a choice then needs tobe made as to which of the arguments one decides to believe. Based on
the arguments for the prosecution and the defence, does the jury rule thesuspect to be guilty or innocent? After a long election campaign, who do we
decide to vote for? After comparing the pros and cons, which car (if any) do
we buy? The thought that one argument (or set of arguments) is consideredbetter or stronger than another can be expressed using preferences. For
example, the jury can argue that the witnesses for the prosecution weremore convincing than those for the defence. Which argument we believe may
depend on personal preferences; for instance, someone who prefers equality
to enterprise and red to blue will generally vote social democrats and buy
red cars.
Formal models of argumentation have long enjoyed rich, mature mo14

Schemes of Inference, Conflict, and Preference in a Computational Model...
dels of preference and priority. For example, (Amgoud and Cayrol 2002,
Garcia and Simari 2004) define in, for example, systems of preference-based
argumentation, where preferences are used to determine whether an argument that attacks another argument actually defeats the attacked argument.
Bench-Capon (2003) further extends this by basing the preferences between
arguments on value orderings. Modgil (2009) has proposed Extended Argumentation Frameworks in the style of Dung (1995), where preferences aremodelled as attacks on attacks: if an argument A is preferred to anotherargument B, any attack from B on A is itself attacked. Recently, Prakken (2010) has incorporated preferences in his framework for structured
argumentation. Here, the preferences are not between arguments but rather between premises or inference rules. If desired, preferences between
arguments can be calculated on the basis of these preferences (Modgil andPrakken 2010).
In line with the now-familiar pattern, the AIF ontology expresses preferences by using preference schemes and applications of these schemes in
the object layer, preference application or PA-nodes. Like conflict schemes,
preference schemes are similar to inference schemes, again with some important differences, which will be highlighted below. Like inference schemes,
preference schemes are patterns of reasoning which are often used in argumentation, which may be abstract, logical patterns as well as more concreteand context-dependent patterns. Preference schemes can also be strict (noexceptions to the scheme) or defeasible (there are exceptions to the scheme).
In argumentation (as in most everyday language use), the preferences
themselves can be expressed as generalizations of the form “ϕ is preferredto ψ”. As with inference and conflict, these generalizations (which can besaid to warrant a particular preference) can be explicitly rendered in theobject layer, that is, as I-nodes, or they can be modelled as a concrete preference scheme in the Schemes Ontology. So, for example, say that we havea generalization that, in general, government policies that promote equality are preferred over policies that promote enterprise. Figure 8a shows
this generalization as an I-node that warrants the application of a general preference scheme and Figure 8b shows this generalization as a specificpreference scheme. The preference schemes used in Figure 8 are shown in Figure 9.
Note the similarities with conflict and inference: while modelling thegeneralization as in Figure 8a allows us to further reason about this generalization, incorporating it as a scheme allows us to provide possible exceptions
to this generalization. One example of reasoning about preference generalizations is to base them on one’s ideals, one’s values (Bench-Capon 2003).
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Floris Bex and Chris Reed

Figure 8: Two ways of modelling preference generalizations

Figure 9: Preference schemes in the AIF Forms Ontology

Figure 10 shows how this can be done. The scheme that corresponds toRA74 is not rendered, but will be something along the lines of “if one
prefers value A to value B, one should amend one’s policies accordingly”.

Figure 10: Two ways of modelling preference generalizations

As was already discussed in section 4, it is of course possible to provide
such a “backing” for the policy preference scheme in the Forms Ontology. As
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Schemes of Inference, Conflict, and Preference in a Computational Model...
for inference generalizations, rendering them as I-nodes provides flexibility,
as the generalization can easily be denied or argued for. Rendering a generalization as a scheme, however, is that it structures contextual knowledge
in a principled way. Whilst argumentation schemes for inference are a subject of much study, conflict and preference schemes have not yet been fully
developed. Hence, the examples in this paper of such schemes (Figure 6b
and Figure 9b) might seem somewhat far-fetched. More intuitive examples
the sorts of contextual knowledge preference schemes in the Forms Ontology can express are perhaps the irreflexivity and antisymmetry propertiesof a particular preference relation. Take, for example, the preference relation ≻ as described by (Prakken 2010). A scheme for this relation can beincorporated in the Forms Ontology (Figure 11).

Figure 11: The ASPIC preference relation as a scheme
in the Forms Ontology

Here, the properties of irreflexivity and antisymmetry have been incorporated into the scheme as implicit presumptions.

7. Concluding remarks
In this paper, we have shown how the apparently very different relationships of inference, conflict and preference can be captured analogously in
a common language. The approach provides an ontologically parsimonious
way of handling a diverse and sophisticated range of argumentation components. Schematising all of these relationships offers particular advantages
in terms of explicit characterisation of the constitution of different forms
of inference, conflict and preference; spelling out missing or implicit parts(such as assumptions and presumptions), and capturing stereotypical waysof evaluating and critiquing.
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Floris Bex and Chris Reed
We have also shown for the first time how scheme instances can interact
with propositional statements that capture expressions of inference, preference and conflict, by virtue of the distinction between, on the one hand,
the inferring/preferring/conflicting relation captured by RA/PA/CA-nodes
and on the other hand, the inferability/preferability/contrastability captured by I-nodes. Whereas in the current logics for argumentation the distinction between ϕ → ψ and ϕ ⊢ ψ is fairly well developed, these distinctions
are often not explicitly made for preference (i.e. between ϕ ≻ ψ and ϕ |≻ ψ)or for conflict (i.e. between ϕ –× ψ and ϕ |× ψ).7 As an increasing numberof research groups and systems start to take advantage of what the AIF has
to offer, and thereby, what other teams have already achieved, it becomesvital that a thorough understanding of schematic argument relations andtheir inter-connections is established, and it is this that the current paper
has laid out.

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Floris Bex
Argumentation Research Group
School of Computing
University of Dundee
Dundee DD1 4HN Scotland, UK
florisbex@computing.dundee.ac.uk
Chris Reed
Argumentation Research Group
School of Computing
University of Dundee
Dundee DD1 4HN Scotland, UK
chris@computing.dundee.ac.uk
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