Download Argumentation and Dialogue in Artificial Intelligence

Argumentation and Dialogue
in Artificial Intelligence
Syllabus for Tutorial T12, IJCAI 2005
Trevor J.M. Bench-Capon and Paul E. Dunne
Department of Computer Science, University of Liverpool
Liverpool L69 7ZF, U.K.
{tbc,ped}@csc.liv.ac.uk
1. Introduction and Overview
Distinguishing the notions of “proof” and “argument”; practical reasoning examples; concepts of argument status; argument frameworks.
2. Modelling Sets of Arguments
Formal definition of “Argument System”; arguments and attacks; concept of “acceptable argument”; defining “admissible” sets of arguments; overview of assumption based argumentation frameworks.
3. Strengths of Arguments and Audiences
Refining the concept of “successful attack”; Preference-based argument frameworks; Value-based argument frameworks.
4. Dialogue Based on Argumentation Frameworks
Introduction to dialogue in argumentation; dialogue types and protocols; two-party immediate response disputes (tpi) and properties.
5. Structure of Arguments
Argument Schema and their motivation; Toulmin’s argument schema
and developments of this; problems with argument schema.
6. Example Studies
Analysis of some selected legal cases couched in terms of Value-based
argument frameworks.
7. Summary
Argumentation and Dialogue
in Artificial Intelligence
Introduction to Tutorial T12
IJCAI 2005, Edinburgh
Trevor J.M. Bench-Capon and Paul E. Dunne
Department of Computer Science
University of Liverpool
Liverpool L69 7ZF, U.K.
{tbc,ped}@csc.liv.ac.uk
1
Argument and Proof
In Artificial Intelligence reasoning is often modelled on the presentation of a
proof. In some domains and for some topics this is entirely appropriate, but
if we look at the justifications of reasoning offered in practice, they often
fall short of the standards required by proof.
Whereas a proof compels us to accept the conclusion if we accept the
premises, natural language justifications tend to be open to objections: they
may persuade, but they rarely compel. Such justifications are always defeasible: they succeed if the objections that are made are met, but the
process of objection is complete only when the party to whom the justification is presented is content. Such defeasible justifications may be termed
arguments.
Objections can arise from a number of sources:
• arguments tend to leave some premises implicit, presupposing that the
audience will agree with the information. But it may be necessary to
make such premises explicit if these presuppositions are not satisfied.
• arguments tend to use vague, imprecise and open textured terms. All
of these need to be given precise definitions if they are to form part of
a proof.
1
• arguments tend to be “open world”: they typically admit of objections
arising from exceptional cases.
• arguments may be made even when we are uncertain of particular
facts.
So in domains where we have incomplete, uncertain, or imprecise information, or where too much background is presupposed to allow everything to
be explicit we must use arguments rather than proofs.
Arguments can be seen as prima facie justifications, which are acceptable
so long as there is no objection which cannot be met satisfactorily.
These objections themselves take the form of arguments and may attack
a number of points in the original justification:
• we may have an argument for the negation of the conclusion
• we may have an argument for negation of one of the premises
• we may have an argument that the rule is inapplicable.
These attacks apply to an argument with a modus ponens like structure.
There are other structures for arguments each of which have their own characteristic ways of being attacked.
Practical reasoning – reasoning about action – provides an important
area of reasoning in which proof is not possible, and we must rely on arguments. Whereas we cannot choose what we believe, we can choose what
we will try to make the case. Given the scope for choice, there is room for
rational disagreement, and demonstration that an action is correct is not
possible.
Practical reasoning comes with its own distinctive form of argument,
which can be expressed as:
• I wish to bring about some state of affairs S
• I can bring about S by performing A
• Therefore, I should perform A
This can be attacked by arguments which
• show that S is not desirable
• show that A will not bring about S
• declare that S can be brought about in other ways
2
• point to undesirable side effects of A
To use arguments to justify a belief or an action, we must propose an argument, and then defend it against other arguments which attack it. Arguments must therefore be considered in the context of other related arguments.
This issue can be explored using the notion on argumentation framework,
which consists of a set of arguments and the attack relations between them.
Given such a framework, we can then attempt to determine the status of
the arguments within it.
2
Argumentation Frameworks
Dung [25] defines an argumentation framework as follows.
Definition 1 An argumentation framework is a pair hX , Ai where X is a
set of arguments and A is a binary relation on X , i.e. A ⊆ X × X .
For two arguments x and y, the meaning of hx, yi ∈ A is that x represents
an attack on y. We also say that a set of arguments S attacks an argument
y if y is attacked by an argument in S. An argumentation framework is conveniently represented as a directed graph H(X , A) in which the arguments
are vertices and edges represent attacks between arguments. This picture of
underlies much of our discussion.
The key question to ask about such a framework is whether a given
argument, x ∈ X , should be accepted. One reasonable view is that an
argument should be accepted only if every attack on it is rebutted by an
accepted argument. This notion produces the following definitions:
Definition 2 An argument x ∈ X is acceptable with respect to the set of
arguments S, if:
∀y ∈ X hy, xi ∈ A ⇒ ∃z ∈ S such that hz, yi ∈ A
Here we can say that z defends x, and that S defends x, since an element of
S defends x.
Definition 3 A set S of arguments is conflict-free if
∀ x, y ∈ S hx, yi 6∈ A and hy, xi 6∈ A
A conflict-free set of arguments S is admissible if for each x in S, x is
acceptable with respect to S. A set of arguments S in an argumentation
framework H(X , A) is a preferred extension if it is a maximal (with respect
to set inclusion) admissible subset of X .
3
The notion of a preferred extension is interesting because it represents a
consistent position which can defend itself against all attacks and which
cannot be further extended without introducing a conflict. We can now
view a credulous reasoner as one who accepts an argument if it is in at
least one preferred extension, and a sceptical reasoner as one who accepts
an argument only if it is in all preferred extensions.
From Dung [25] we know that a preferred extension always exists, (this,
however, could be the empty set) and that it is not generally true that there
is a unique preferred extension. In the special case where there is a unique
preferred extension we say the dispute is resoluble, since there is only one
set of arguments capable of rational acceptance.
Alternative definitions of acceptability are also possible: instead of the
preferred extension we may use the grounded extension, or the stable extension.
Within such a framework, we can classify the complexity of a number of
problems as has been summarised in Table 1.
Problem
adm(H, S)
pref-ext(H, S)
stab-ext(H, S)
has-stab(H)
ca(H, x)
sa(H, x)
coherent(H)
Description
Is S admissible?
Is S preferred?
Is S stable?
Does H have a stable ext.
Is x accepted credulously
Is x accepted sceptically
Is H coherent
Complexity
p
co-np–complete
p
np–complete
np–complete
Πp2 –complete
Πp2 –complete
Table 1: Complexity of Problems Relating to Argumentation Frameworks
An accessible introduction to complexity classes such as Πp2 is given in
Papadimitriou [51].
To conclude we briefly mention the important assumption-based framework of Bondarenko et.al [13] with which there are close links with Dung’s
formalism. A central idea of the former is to treat “arguments” and “attacks” not as primitive, atomic elements (as they are within [25]), but
rather as constructs derived from a set of assumptions. This view provides a powerful general technique with which default reasoning and various
non-monotonic logics can be modelled.
An assumption-based framework is defined with respect to some formal
deductive system hL, Ri with L the well-formed sentences of some formal
language, e.g. the set of propositional formulae; and R a set of inference
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rules defining how “new” sentences in L may be derived. Given such a
system an assumption-based framework is defined as a triple hT, Ab, i with
T a subset of L describing a given collection of beliefs and Ab ⊂ L a nonempty set of assumptions that are to be used to “extend” T . The component
maps assumptions α into sentences, α of L called the contrary (of α). The
concepts of “conflict-free” and various admissibility semantics are defined
with respect to whether a subset, ∆ of assumptions can extend the starting
belief set T in such a way that the resulting theory T ∪ ∆ does not allow
the derivation of both an assumption α and its contrary α.
The formal deductive system is a significant element in such frameworks:
in particular, as has been shown in Dimopoulos, Nebel, and Toni [19, 20, 21]
the complexity of problems analogous to those given in Table 1 is linked to
the complexity of the “derivability” problem in the supporting logic.
3
Strengths of Arguments and Audiences
In Dung’s framework, an attack of one argument on another is assumed
to succeed. But this is not always appropriate: sometimes we may choose
which argument to accept.
Choice arises in particular when the argument is justifying an action:
then choice may be determined by how we rank social values, attitude to
risk, or other factors. Different people may make different choices: this
means that an argument which is persuasive to one audience may fail to
persuade another audience which makes different choices. The notion of an
audience is explored in the writings of Perelman, e.g. [55].
To accommodate the notion of audience we may extend the standard
argument framework of Dung to include audiences. Two approaches that
have been considered are the Preference Based argumentation frameworks
of Amgoud and Cayrol [2] and the Value Based argumentation frameworks
of Bench-Capon [10].
The preference based scheme of [2] captures a concept of “audience”
through a relationship over arguments. Formally,
Definition 4 A Preference Based argumentation framework (PAF) is a
triple hX , A, P ref i where hX , Ai is an argument framework and P ref ⊂
X × X is a preference relation that is transitive and asymmetric.
Thus hx, yi ∈ P ref is interpreted as “the argument x is preferred to the
argument y”. The key idea is that an attack hx, yi ∈ A may fail not only
because of the presence of a defender for y but also because hy, xi ∈ P ref ,
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i.e. hx, yi ∈ A is a successful attack (in the terminology of [2] x defeats
y) only if hy, xi 6∈ P ref . In such terms the concepts of “conflict-free”,
“acceptable”, and “admissible” are enriched via,
Definition 5 For a PAF hX , A, P ref i, and x, y ∈ X , x defeats y if hx, yi ∈
A and hy, xi 6∈ P ref . A subset S is conflict-free if for each x, y in S if
hx, yi ∈ A then hy, xi ∈ P ref . An argument x is acceptable to S if for
every y ∈ X if y defeats x then there is some z ∈ S such that z defeats
y. A conflict-free set, S, is admissible if every x ∈ S is acceptable to S.
Finally, S, is a preferred extension if it is a maximal (with respect to set
containment) admissible set.
Any preference relation P ref induces a standard argumentation framework
by including only those hx, yi ∈ A for which hy, xi 6∈ P ref , i.e. such that x
defeats y. Now, since P ref is asymmetric this induced framework is acyclic
and its preferred extension (which corresponded to the grounded extension)
is unique, non-empty, and efficiently computable.
While these properties are compelling indicators of the practical efficacy
of “audience related” enhancements to Dung’s schema, there are, however,
a number of issues that PAFs do not address. Thus, Bench-Capon [10]
promotes the view of audiences being captured in the observation that advancing an argument x is not only a statement of “belief” in the argument
itself but also of any “values” endorsed by x.
To record the values associated with arguments we need to add to the
standard argumentation framework a set of values, and a function to map
arguments on to these values.
Definition 6 A value-based argumentation framework (VAF) is a 5-tuple:
V AF = hX , A, V, η, P i, where hX , Ai is an argument framework, V is a
non-empty set of values, η is a function which maps from elements of X
to elements of V and P is the set of possible audiences. We say that an
argument x relates to value v if accepting x promotes or defends v: the value
in question is given by η(x). For every x ∈ X , η(x) ∈ V .
The set P of audiences is introduced because, following Perelman, we want to
be able to make use of the notion of an audience. Audiences are individuated
by their preferences between values. We therefore have potentially as many
audiences as there are orderings on V . We can therefore see the elements of
P as being names for the possible orderings on V . Any given argumentation
will be assessed by an audience in accordance with its preferred values.
We therefore next define an audience specific value based argumentation
framework, AVAF:
6
Definition 7 An audience specific value-based argumentation framework
(AVAF) is a 5-tuple: V AF (α) = hX , A, V, η, α i, where X , A, V and η
are as for a VAF, α is an audience, and α is a value-preference relation
(transitive, irreflexive and asymmetric) over V × V reflecting the value preferences of audience α. We write v1 is preferred to v2 as v1 α v2 . The
AVAF relates to the VAF in that X , A, V and η are identical, α ∈ P and
α is the set of preferences derivable from the ordering α in the VAF.
Our purpose in extending argumentation frameworks was to allow us to
distinguish between one argument attacking another, and that attack succeeding, so that the attacked argument is defeated. We therefore define the
notion of defeat for an audience:
Definition 8 An argument x defeats an argument y for audience α if and
only if both hx, yi ∈ A and ¬(η(y) α η(x)).
It is useful to note the difference between the notion of defeat in PAFs and
that in VAFs. For hx, yi ∈ A, “x defeats y” in PAFs means “the argument y
is not preferred to the argument x”; in VAFs, however, “x defeats y” means
“the value promoted by the argument y is not superior (in the view of the
audience α) to the value promoted by the argument x”
Note that an attack succeeds if both arguments relate to the same value,
or if no preference between the values has been defined. If V contains a
single value, or no preferences are expressed, the AVAF becomes a standard
AF. If each argument can map to a different value, we have a Preference
Based Argument Framework in the sense of Amgoud and Cayrol [2]. In
practice we expect the number of values to be small relative to the number
of arguments. Many disputes can be naturally modelled using only two
values. Note that defeat is only applicable to an AVAF: defeat is always
relative to a particular audience.
Dung [25] introduces the important notions, described in section 2, of
acceptability, conflict free set, admissible set, and preferred extension for
AFs. We next need to define these notions for an AVAF.
Definition 9 An argument x is acceptable to audience α with respect to a
set of arguments S, if: for each y ∈ X if y defeats x for α then there is some
z ∈ S that defeats y for α.
A set S is conflict-free for audience α if
∀x, y ∈ S hx, yi ∈ A ⇒ η(y) α η(x)
A conflict-free for audience α set S is admissible for an audience α if every
x ∈ S is acceptable to audience α with respect to S.
7
A set of arguments S in a value-based argumentation framework is a
preferred extension for audience α if it is a maximal (with respect to set
inclusion) admissible for audience α subset of X .
Now for a given choice of value preferences α we are able to construct an
argument framework equivalent to the AVAF, by removing from the set of
attacks A those attacks which fail because faced with a superior value.
Thus for any AVAF, V AF (α) = hX , A, V, η, α i there is a corresponding
argument framework, AF (α) = hX , Di, such that an element hx, yi ∈ A is
an element of D if and only if x defeats y for α. The preferred extension of
AF (α) will contain the same arguments as V AF (α), the preferred extension
for audience α of the VAF. Note that if V AF (α) does not contain any cycles
in which all arguments pertain to the same value, AF (α) will contain no
cycles, since the cycle will be broken at the point at which the attack is
from an inferior value to a superior one. Hence both AF (α) and V AF (α)
will have a unique, non-empty, preferred extension for such cases.
When we consider a range of audience, we may identify three new categories of acceptability for arguments, according to whether they are acceptable to all audiences (objective acceptance), some audiences (subjective
acceptance) or no audiences (indefensible):
Definition 10 Given a VAF, hX , A, V, η, P i, an argument x ∈ X is objectively acceptable if and only if for all α ∈ P , x is in the preferred extension
for audience α.
An argument x ∈ X is subjectively acceptable if and only if for some
α ∈ P , x is in the preferred extension for audience α.
An argument which is neither objectively nor subjectively acceptable (such
as one attacked by an objectively acceptable argument with the same value)
is said to be indefensible.
Deciding into which of these categories a given argument falls is hard:
• Subjective Acceptance is np-complete.
• Objective Acceptance co-np-complete
• Deciding if a value ordering is critical is harder than either of these.
None the less there are some positive results. For example
• For a given audience, there is a unique, non-empty preferred extension,
and an efficient algorithm to determine it.
• Given S there is an efficient algorithm to discover the class of audiences
for which S is the preferred extension.
8
4
Dialogue
Because argumentation, with its notions of attack and counterattack, is intuitively adversarial in nature, it is natural to relate argumentation to a
dialogue in which two parties attempt to persuade one another. Dialogue
games have been used for sometime (e.g. MacKenzie [46], who used them
to characterise logical fallacies and Gordon [36] who used them to identify
the points of disagreement between parties to a legal case). Dialogue games
have been related to argumentation frameworks also, such as Bench-Capon
et al. [12], which bases the game on the Argument Schema of Toulmin [67]
and Dunne and Bench-Capon [29] in which the game uses Dung’s argumentation framework. Kowalski et al. [42] observe that procedures such
as the TPI dialogue games introduced in Vreeswijk and Prakken [70] and
analysed in [29], as well as variants of this, e.g. Cayrol et al. [15], Doutre
and Mengin [23], may be viewed as “forward-reasoning” proof search mechanisms: they propose an alternative “backward-reasoning” technique within
the assumption-based framework, proving its soundness and completeness
with respect to the credulous admissibility semantics. Other recent work
includes the concept of “graduality” in Cayrol and Lagasquie-Schiex [16];
the dialogue scheme outlined in Doutre et al. [24] for “position analysis”
in Value-based frameworks; and the preliminary study of so-called “Examination Dialogues” (modelling, among other ideas, one of the classical
techniques of Socratic dialogue) presented in Dunne et al. [33].
Typically a dialogue will begin with one party making a claim and proceed with the other party attacking that claim and the original party defending it. The moves available to attack and defend claims will vary according
to the particular dialogue game, and different games will offer more or less
rich sets of moves. Typically the dialogue will terminate with a winner when
one of the parties has no move available to continue the dialogue.
Casting the argument as a formally constrained dialogue allows a number
of issues to be explored, such as: the complexity of the dispute; strategies
for dispute; and the procedures under which disputes may be conducted.
5
Structure of Arguments
So far we have considered arguments as entirely abstract. There are, however, situations in which it is helpful to consider the structure of arguments,
for example if we wish to automate the generation of arguments, or to explore the attack relation in more detail.
9
The most general way to structure arguments is as deductions. Here an
argument will be seen as a sequence of rule applications leading from known
premises or assumptions to a conclusion.
This approach has a number of advantages:
1. It is uniform
2. Any desired logic may be used to guide the inference
3. Generation of arguments is straightforward
4. The notion of derivation is well defined and understood
There are, however, disadvantages. Not all arguments can be put into this
form without some distortion, and the uniformity of the approach can obscure some subtle differences between arguments. To meet these difficulties
a variety of argument schemes have been proposed.
One popular scheme is that proposed by Toulmin [67]. This scheme decomposes arguments into a number of components: claims whose truth we
seek to establish by the argument, data that we appeal to as the grounds for
the claim, and warrants which provide the rules of inference that connect
the data and the claim. Warrants can, in Toulmin’s scheme, bestow varying
degrees of support for the claim, and these degrees of support are indicated
by the use of a modal qualifier, such as “necessarily” or “possibly”. There
may also be exceptional conditions which prevent the claim from being established: these are indicated by the rebuttal which contains circumstances
acknowledged as requiring the authority of the warrant to be put aside.
Warrants also require some justification: this is the role of the backing.
This scheme, although entirely general, has proved popular, and has
some intuitive appeal in that it is able to distinguish different roles played
by various premises, and embodies ideas of defeasibility. It has been used as
the basis of dialogue games in Bench-Capon et al. [12] and Bench-Capon [7].
In addition a number of more specific, special purpose, arguments schemes
have been proposed, by e.g. Perelman and Olbrech-Tyteca [54] and Walton [72]. One classic example is the Argument From Authority:
• X says that P
• X is an authority on matters relating to P
• Therefore, P
10
Such argument schemes have their attractions, in that it is clear that, as
a matter of fact, such arguments are advanced in practice. But there are
problems
• argument schemes often embody fallacious patterns of reasoning
• argument schemes are often ill-defined
For these reasons it is hard to formalise such schemes and to determine what
arguments represent acceptable uses of the schemes.
Despite these difficulties, argument schemes are widely employed in the
analysis of natural argument, and it appears that their understanding is
crucial to realizing the full potential of argument based approaches. We
may therefore expect argument schemes to be receive an increasing degree
of attention in the future.
6
Examples
We conclude with two examples.
One small example is the moral dilemma of a diabetic who loses his insulin and considers taking the insulin of another diabetic in order to preserve
his life. Can he take the insulin? And if he does take the insulin, must he
provide compensation?
The more extended example concerns of body of legal case law. The
particular cases form an example widely used in training law students.
The facts of the chosen cases are:
Keeble v Hickergill (1707). This was an English case in which Keeble
owned a duck pond, to which he lured ducks, which he shot and sold for
consumption. Hickergill, out of malice, scared the ducks away by firing guns.
The court found for Keeble.
Pierson v Post (1805). In this New York case, Post was hunting a fox
with hounds. Pierson intercepted, killed and carried off the fox. The court
found for Pierson.
Young v Hitchens (1844). In this English case, Young was a commercial
fisherman who spread a net of 140 fathoms in open water. When the net was
almost closed, Hitchens went through the gap, spread his net and caught
the trapped fish. The case was decided for Hitchens.
Ghen v Rich (1881). In this Massachusetts case, Ghen was a whale
hunter who harpooned a whale which subsequently was not reeled in, but
was washed ashore. It was found by a man called Ellis, who sold it to Rich.
According to local custom, Ellis should have reported his find, whereupon
11
Ghen would have identified his lance and paid Ellis a fee. The court found
for Ghen.
Conti v ASPCA (1974). In this New York case, Chester, a parrot owned
by the ASPCA, escaped and was recaptured by Conti. The ASPCA found
this out and reclaimed Chester from Conti. The court found that they were
within their rights to do so.
New Mexico vs Morton (1975) and Kleepe vs New Mexico (1976). These
cases concerned the ownership of unbranded burros normally present on
public lands, which had temporarily strayed off them.
These have been represented as a Dung style argumentation framework
in Bench-Capon [8]. In addition the arguments can be associated with their
purposes to instantiate a value based argument framework. The arguments
identified and their associated values are shown in Table 2.
This example shows both how case law can be described as an argumentation framework and how the use of values can explain
• different intuitions and dissenting opinions
• different decisions in different jurisdictions
• different decisions as culture changes
7
Summary
We may summarise as follows:
• Arguments are important when modelling reason, since proof is not
possible in a variety of domains.
• Arguments are defeasible: they are attacked by other arguments and
must defend themselves if they are to be acceptable.
• In consequences, arguments must be considered in the context of related and conflicting arguments.
• Argumentation frameworks give us a means of analysing sets of arguments to determine their status.
• Arguments relating to action often offer a choice between alternatives,
which the audience is free to resolve according to their preferences.
• Argumentation frameworks can be extended to accommodate the notion of audiences.
12
ID
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
Q
S
T
U
V
W
X
Y
Z
Argument
Pursuer had right to animal
Pursuer not in possession
Owns the land so possesses animals
Animals not confined by owner
Effort promising success made
by pursuer
to secure animal
Pursuer has right to pursue livelihood
Interferer was trespassing
Pursuer was trespassing
Pursuit not enough (JUSTINIAN)
Animal was taken (JUSTINIAN)
Animal was mortally wounded (Puffendorf)
Bodily seizure is not necessary (Barbeyrac),
interpreted as animal was brought
within certain control (TOMPKINS)
Mere pursuit is not enough(TOMPKINS)
Justinian is too old
an authority (LIVINGSTON)
Bodily seizure is not necessary (Barbeyrac)
interpreted as reasonable prospect
of capture is enough (LIVINGSTON)
The land was open
Defendant in competition with the plaintiff
Competition was unfair
Not for courts to regulate competition
Attacks
A,T
C
C
B,D
Values
Claim
Clear law
Property
Clear law
Clear law
B
S
F
E
I
I
I
Livelihood
Property
Property
Clear law
Clear law
Clear law
Clear law
E,O
J
Clear law
I,M
Useful
Activity
G,H,C
E,F
S
T
B
Property
Livelihood
Livelihood
Role of
Court
Common
Practice
Property
The iron holds the whale
is an established convention of whaling.
Owners of domesticated animals have
a right to regain possession
Unbranded animals living on land
belong to owner of land
Branding establishes title
Physical presence (straying) insufficient to
confer title on owner
B,U
D
Property
B
C
Property
Clear law
Table 2: Arguments in the Example Cases
13
• Dialogue provides a natural way of modelling the process of argument
between disputing parties.
• We can analyse the structure of arguments using argumentation schemes,
which may range from the entirely general to the very specific.
• We can apply the above notions to quite extensive disputes, such as
an evolving body of legal case law.
14
Annotated Selected Bibliography
It is noted that there is an extensive literature covering topics that are
relevant to the overview presented in this tutorial: reasons of space preclude presentation of a more detailed survey. A number of the articles and
monographs discussed below present excellent comparative surveys of related work, thus providing a valuable source of further reading. Omission
of specific items should not be interpreted as a comment on their merits.
References
[1] A. Aleven. Teaching Case Based Argumentation Through an Example
and Models. PhD Thesis, The University of Pittsburgh. (1997)
This describes CATO, a program designed to teach case based argumentation to law students. It is based in the domain of US Trade Secrets
law, extends the ideas of [3], and represents the factor based approach
to reasoning with legal cases.
[2] L. Amgoud and C. Cayrol. A reasoning model based on the production
of acceptable arguments, Annals of Math. and Artificial Intelligence,
34, 197–215, (2002)
Introduces the model of Preference-Based Argumentation Frameworks
(PAF). These together with the VAF model of [9, 10] are one of the
main mechanisms which seek to extend [25] by accounting for concepts
of attacks which only succeed if the position promoted is not outranked
by the position attacked.
[3] K. Ashley. Modeling Legal Argument: Reasoning with Cases and Hypotheticals. Cambridge, MA: MIT Press, (1990)
Describes the influential HYPO system, developed with Edwina Rissland, which models reasoning with legal cases in the domain of US Trade
Secrets Law. It introduces several important notions, including dimensions for the representation of cases, the three-ply argument scheme for
legal argument, and argument moves using legal cases such as citation,
distinguishing and counter examples.
[4] K. Atkinson, T. Bench-Capon, and P. McBurney. Computational Representation of Persuasive Argument. Technical Report ULCS-04-006,
Department of Computer Science, Univ. of Liverpool, (2004) (submitted)
15
Provides an account of persuasive action over argumentation based on
a argument scheme and associated critical questions.
[5] K. Atkinson, T. Bench-Capon, and P. McBurney. A Dialogue Game
Protocol for Multi-Agent Argument Over Proposals for Action. First
International Workshop on Argumentation in Multi-Agent Systems
(ArgMAS2004), LNAI 3366, Springer-Verlag, pages 149–161, (2004)
(extended version, in press Jnl. of Autonomous Agents and Multi-Agent
Systems
Provides denotational semantics for the account of persuasive argument
given in [4]
[6] T. J. M. Bench-Capon. Argument in Artificial Intelligence and Law
Artificial Intelligence and Law, 5(4):249–61, (1997)
A survey of the uses made of argument in Artificial Intelligence in Law
up to 1996.
[7] T. J. M. Bench-Capon. Specification and Implementation of Toulmin
Dialogue Game. In: J. C. Hage et al. (ed.): Legal Knowledge Based
Systems, pages 5–20. (1998)
A further extension of ideas initiated in [12]. This gives a complete
set of moves for a game based on Toulmin’s schema, together with an
operational semantics for them, and describes an implementation of the
game in Prolog.
[8] T.J.M. Bench-Capon. Representation of Case Law as an Argumentation
Framework. In T. Bench-Capon, Daskalopoulu, A., and Winkels, R.,
(eds) Legal Knowledge and Information Systems, Proceedings of Jurix
2002. IOS Press: Amsterdam. pages 103–112. (2002).
This paper formalises the wild animals cases discussed in the tutorial
as an Argumentation Framework in the style of [25]
[9] T. J. M. Bench-Capon. Agreeing to differ: modelling persuasive dialogue between parties with different values, Informal Logic, 22(3):231–
45 (2003).
Augments the Value Based Argumentation Framework described in
[10], by describing a dialogue game based on the TPI game of [29].
[10] T. J. M. Bench-Capon. Persuasion in Practical Argument Using Value
Based Argumentation Frameworks, Journal of Logic and Computation,
13(3):429–48 (2003).
16
Introduces Value-based Argumentation Frameworks establishing
uniqueness of preferred extension, efficient computational properties,
and defining the ideas of Subjective and Objective Acceptance.
[11] T.J.M. Bench-Capon. Try To See It My Way: Modelling Persuasion in
Legal Discourse. Artificial Intelligence and Law, 11(4):271–87 (2003)
Gives a full account of the wild animals cases discussed in the tutorial.
[12] T. J. M. Bench-Capon, P. E. Dunne, and P. H. Leng. A dialogue game
for dialectical interaction with expert systems. In Proc. 12th Annual
Conf. Expert Systems and their Applications, pages 105–113, (1992).
One of the first formalisations combining dialogue style techniques with
a precisely defined argument scheme - that of Toulmin [67].
[13] A. Bondarenko, P. M. Dung, R. A. Kowalski, and F. Toni. An abstract,
argumentation-theoretic approach to default reasoning, Artificial Intelligence, 93(1–2):63–101, (1997).
Dung’s argument systems described in [25] have concepts of “argument”
and “attack” as atomic concepts. This article takes “assumptions” as
atomic illustrating various approaches to deriving arguments and attacks (in the sense of [25]) from sets of these.
[14] C. Cayrol, S. Doutre, and J. Mengin. Dialectical proof theories for
the credulous preferred semantics of argumentation frameworks. In
Sixth European Conference on Symbolic and Quantitative Approaches to
Reasoning with Uncertainty (ECSQARU-2001), pages 668–679. LNAI,
2143, Springer-Verlag, (2001).
[15] C. Cayrol, S. Doutre, and J. Mengin. On decision problems related
to the preferred semantics for argumentation frameworks. Journal of
Logic and Computation, 13(3):377–403 (2003).
These articles (and [23]) address algorithms for computing preferred
extensions via a dialogue game. This game is couched in terms of the
general classification presented in [41].
[16] C. Cayrol and M.C. Lagasquie-Schiex. Graduality in Argumentation.
Jnl. of A.I. Research, 23:245-297, (2005)
Describes a view of argumentation as based on the exchange and valuation of interacting arguments followed by the selection of the most
acceptable. Introduces “graduality” in the selection of the best arguments to partition the set of the arguments into more than the two usual
17
subsets of “selected” and “non-selected” arguments. Proposes new acceptability classes and a refinement of existing classes taking advantage
of an available “gradual” valuation.
[17] G. Christie. The Notion of an Ideal Audience in Legal Argument.
Kluwer Academic, Dordrecht, (2000).
This applies the idea of an audience proposed in [54] to law, and in
particular provides an account of how and why there are differences
between jurisdictions.
[18] F. Dignum (Editor). Advances in Agent Communication. LNAI, 2922,
Springer-Verlag, 2004
Section IV includes a number of recent papers on dialogue in the setting
of multi-agent system applications. For other multi-agent system based
analyses of dialogue, the articles [47, 48, 49, 50, 52, 53, 61] provide a
good overview of current approaches.
[19] Y. Dimopoulos, B. Nebel, and F. Toni. Preferred arguments are harder
to compute than stable extensions. In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI99), (Ed.,
T. Dean), pages 36–43, San Francisco, Morgan Kaufmann (1999)
See [21].
[20] Y. Dimopoulos, B. Nebel, and F. Toni. Finding admissible and preferred
arguments can be very hard. In KR2000: Principles of Knowledge
Representation and Reasoning, eds., A. G. Cohn, F. Giunchiglia, and
B. Selman, pp. 53–61, San Francisco, (2000). Morgan Kaufmann.
See [21].
[21] Y. Dimopoulos, B. Nebel, and F. Toni. On the compuational complexity of assumption-based argumentation by default reasoning. Artificial
Intelligence, 141, 57–78, (2002).
The basis provided in [13] allows concepts of credulous and sceptical
reasoning, preferred and stable extensions to be developed for a number
of non-classical logics. In studying the complexity of these problems
a significant element is shown to be the complexity of “derivability”
in the associated logic. One consequence is that sceptical reasoning
under some logics can be shown complete for rather higher levels of the
polynomial-time hierarchy.
18
[22] Y. Dimopoulos and A. Torres. Graph theoretical structures in logic
programs and default theories. Theoretical Computer Science, 170,
209–244, (1996).
The results for the decision problems ca, pref-ext, has-stab given in
Table 1 above, all derive from this paper. The terminology differs quite
noticeably from that of [25], however, these are not difficult to relate.
A more detailed discussion of the contribution of [22] expressed in the
terminology of [25] may be found in [28].
[23] S. Doutre and J. Mengin. Preferred extensions of argumentation frameworks: Query answering and computation. In First Intern. Joint
Conf. Automated Reasoning (IJCAR 2001), pages 272–288. LNAI,
2083, Springer-Verlag, June 2001.
See [15]
[24] S. Doutre, T.J.M. Bench-Capon, and P.E. Dunne Explaining preferences with argument positions. Proc. IJCAI05, (to appear)
Presents a “TPI-style” dialogue game for validating that a subset of
arguments within a value-based argument framework has (at least) one
audience for which this set is admissible.
[25] P. M. Dung. On the acceptability of arguments and its fundamental role
in nonmonotonic reasoning, logic programming, and N -person games.
Artificial Intelligence, 77, 321–357, (1995).
Seminal article introducing the concept of argument framework and
acceptability semantics that underpin the ideas and developments presented in this tutorial.
[26] P. E. Dunne. On Concise Encodings of Preferred Extensions. Proc.
9th Non-monotonic Reasoning Workshop (NMR’2002), Toulouse, April
2002, pages 393-398
Complexity-based consideration of whether the set of all preferred extensions of an argument system can be represented by a description
which is both length efficient and admits efficient testing as to whether
a set of arguments is a preferred extension: motivation is to determine
to what extent precomputation of all preferred extensions once is a
feasible approach.
[27] P.E. Dunne. Prevarication in dispute protocols. In Proc. Ninth International Conference on A.I. and Law (ICAIL’03), Edinburgh, June 2003,
ACM Press, pages 12–21
19
Examines to what extent the “loser” of a dispute can exploit dialogue
rules and their opponent’s strategy in order to delay having to concede
defeat.
[28] P.E. Dunne and T.J.M. Bench-Capon. Coherence in finite argument
systems. Artificial Intelligence, 141, 187–203, (2002).
Technical complexity classification proving the problem of deciding if
H is coherent, i.e. every preferred extension is also stable, to be Πp2 complete. A similar classification of sa follows from this result.
[29] P.E. Dunne and T.J.M. Bench-Capon. Two party immediate response
disputes: properties and efficiency. Artificial Intelligence, 149, 221–250,
(2003).
Detailed study and formalisation of the tpi-dispute protocol introduced
in [70]. Introduces the concept of dispute complexity as the number of
moves needed to win an argument. Main technical contribution shows
tpi dialogues establishing an argument is not credulously accepted can
be viewed as a very weak propositional proof calculus and thus may
require exponentially many (in the number of arguments) rounds to
reach a conclusion.
[30] P.E. Dunne and T.J.M. Bench-Capon. Complexity in value-based argument systems. Proc. 9th European Conf. on Logics in Artificial Intelligence. (JELIA’04), LNAI, 3229, Springer-Verlag, pages 360–371,
2004
Classifies the complexity of deciding Subjective and Objective Acceptance that were left open in [10]. Also introduces the problem “critical
pair” concerned with deciding whether a given argument is subjectively
accepted with one specific ordering of a pair of values but indefensible
when this order is reversed. This problem being demonstrated to be
“harder” than deciding Subjective or Objective Acceptance.
[31] P.E. Dunne and T.J.M. Bench-Capon. Identifying Audience Preferences
in Legal and Social Domains. Proc. DEXA’04, LNCS 3180, SpringerVerlag, pages 518–527, 2004
Presents an efficient algorithm by which the set of audiences consistent
with a given S being a preferred extension in a VAF can be recovered.
[32] P.E. Dunne and T.J.M. Bench-Capon (Editors) Argumentation in Artificial Intelligence and Law. Wolf Legal Publishing, (2005), (in press)
20
Collection of papers presenting recent developments in the specific field
of argumentation techniques as applied in legal contexts.
[33] P.E. Dunne, S. Doutre, and T.J.M. Bench-Capon. Discovering inconsistency through examination dialogues. Proc. IJCAI05 (to appear)
Introduces a class of dialogue scheme aimed at modelling question processes seeking to expose inconsistencies in argument.
[34] P.E. Dunne and P.J. McBurney. Optimal Utterances in Dialogue Protocols. Proc. Second International joint Conference on Autonomous
Agents and Multiagent Systems (AAMAS’03), July 2003, ACM Press,
pages 608-615
Considers the question of “move selection” for participants in a dialogue, reviewing notions of what can be said to consitute a “best”
move. Extended version appears in the collection [18].
[35] J. Glazer and A. Rubinstein. Debates and decisions: on a rationale of
argumentation rules. Games and Economic Behavior, 36(2):158–173,
2001.
Good representative article presenting argument and dialogue from the
game-theoretic perspective favoured within economics.
[36] T. F. Gordon. The Pleadings Game: An Artificial Intelligence Model
of Procedural Justice. Dordrecht: Kluwer Academic Publishers. (1995)
An account of how dialogue and argumentation can be used to model
legal process. The idea is that parties use a dialectical exchange to
identify the points of agreement and disagreement between them so
that the issues which need to be decided before a judge can be agreed.
[37] K. Greenwood, T. Bench-Capon, and P. McBurney. Towards a Computational Account of Persuasion in Law. In Proc. of the Ninth International Conf. on AI and Law (ICAIL’03), ACM press, New York, pages
22–31, 2003
An application of the theory of persuasive argument of [4] to legal case
based reasoning, illustrated from the domain of US Trade Secrets Law.
[38] J.C. Hage. Reasoning With Rules. Kluwer Academic Publishers; Dordrecht (1997).
A book describing Hage’s Rule Based Logic, a logic targeted at explaining defeasible argument in Law.
21
[39] A. Hunter. Making argumentation more believable. Proc. of the 19th
American National Conference on Artificial Intelligence (AAAI’2004),
pages 269–274, MIT Press, 2004
[40] A. Hunter. Towards higher impact argumentation. Proc. of the 19th
American National Conference on Artificial Intelligence (AAAI’2004),
pages 275-280, MIT Press, 2004
These two papers give a formal account of audiences, to explain how
different perspectives can affect what people believe.
[41] H. Jakobovits and D. Vermeir. Dialectic semantics for argumentation
frameworks. In Proceedings of the Seventh International Conference on
Artificial Intelligence and Law (ICAIL’99), pages 53–62, N.Y., (June
1999). ACM Press.
Describes a uniform approach to defining dialogue games within argument systems. The schemes presented in [14, 15] are couched in terms
of this approach.
[42] R. Kowalski, P.M. Dung and F. Toni. Dialectic proof procedures for
assumption-based, admissible argumentation (to appear Artificial Intelligence, 2005)
Presents dialogue style proof procedures for credulous reasoning in
assumption-based frameworks, introducing backward reasoning as a
mechanism for guiding the dialogue development.
[43] A. R. Lodder. Dialaw: On legal justification and Dialogue Games.
Ph.D. thesis, Univ.of Maastricht. (1998)
Description of a simple dialogue game based on the Reason Based Logic
of [38].
[44] P. Lorenzen and K. Lorenz. Dialogische Logik. Darmstadt: Wissenschaftliche Buchgesellschaft. 1978
A monograph presenting the view of propositional proof theory as a
dialogue mechanism.
[45] R. P. Loui. Process and Policy: Resource-Bounded Nondemonstrative
Reasoning. COMPINT: Computational Intelligence: An International
Journal 14, 1–38. 1998
This paper investigates the appropriateness of formal dialectics as a basis for nonmonotonic and defeasible reasoning that takes computational
22
limits seriously. Dialectical protocols are shown to be appropriate for
such deliberations when resources are bounded and search is serial.
[46] J. D. MacKenzie. Question-Begging in Non-Cumulative Systems. Journal of Philosophical Logic 8(1), 117–133. 1978
One of the first dialogue games, introducing important notions such as
commitment stores. Based on standard propositional logic, it is particularly intended to explain certain fallacies, especially begging the
question.
[47] P. McBurney and S. Parsons. Representing epistemic uncertainty by
means of dialectical argumentation. Annals of Mathematics and AI,
32(1–4):125–169, 2001.
See comments following Dignum [18].
[48] P. McBurney and S. Parsons. Games that agents play: A formal framework for dialogues between autonomous agents. J. Logic, Language and
Information, 11:315–334, 2002.
See comments following Dignum [18].
[49] P. McBurney and S. Parsons. Chance Discovery using dialectical argumentation. In T. Terano et al., editors, New Frontiers in Artificial
Intelligence, pages 414–424. LNAI, 2253, Springer-Verlag, 2001.
See comments following Dignum [18].
[50] P. McBurney, S. Parsons, and M. J. Wooldridge. Desiderata for agent
argumentation protocols. In Proc. First Intern. Joint Conf. on Autonomous Agents and Multiagent Systems (AAMAS’02), pages 402–
409. ACM Press, 2002.
See comments following Dignum [18].
[51] C. H. Papadimitriou. Computational Complexity. Addison-Wesley:
Reading, MA, 1994.
[52] S. Parsons, C. A. Sierra, and N. R. Jennings. Agents that reason and
negotiate by arguing. J. Logic and Computation, 8(3):261–292, 1998.
See comments following Dignum [18].
[53] S. Parsons, M. J. Wooldridge, and L. Amgoud. An analysis of formal
inter-agent dialogues. In Proc. First Intern. Joint Conf. Autonomous
Agents and Multiagent Systems, pages 394–401. ACM Press, 2002.
23
See comments following Dignum [18].
[54] C. Perelman and L. Olbrechts-Tyteca. The New Rhetoric: A Treatise on
Argumentation. University of Notre Dame Press, Notre Dame (1969).
The definitive presentation of Perelman’s ideas relating to the role of
audience and the role of values in determining the persuasiveness of
arguments. It also contains a systematic exploration of a large number
of argument schemes.
[55] C. Perelman. Justice, Law and Argument. Reidel: Dordrecht, 1980.
A collection of essays providing an accessible introduction to Perelman’s
ideas.
[56] J.L. Pollock. How to reason defeasibly. Artificial Intelligence, 57(1):1–
42. (1992)
This paper describes the construction of a general-purpose defeasible
reasoner that is complete for first-order logic and provably adequate for
Pollock’s argument-based conception of defeasible reasoning.
[57] J.L. Pollock. Defeasible reasoning with variable degrees of justification.
Artificial Intelligence, 133(1–2):233–282. (2001).
Considers how the degree of justification of a belief is determined, where
conclusions are supported by several different arguments, the arguments
typically being defeasible, and there may also be arguments of varying
strengths for defeaters for some of the supporting arguments.
[58] H. Prakken. Logical Tools for Modelling Legal Argument. Kluwer Academic Publishers, 1997.
This book surveys the use of logic in describing conflicts between legal
norms, and discusses logical approaches to resolving such conflicts.
[59] H. Prakken and G. Sartor. A Dialectical Model of Assessing Conflicting
Arguments in Legal Reasoning. Artificial Intelligence and Law, 4(3–
4):331–68 (1996).
Gives a formal description of arguments as deductions and provides a
proof theory based on grounded semantics and expressed as a dialogue
procedure.
[60] H. Prakken and G. Sartor. Argument-Based Extended Logic Programming with Defeasible Priorities. Journal of Applied Non-classical Logics,
7:25–75. 1997
24
This paper discusses non-monotonic reasoning in terms of arguments
represented as logic programs, and in particular offers a formalisation
of how priorities between conflicting arguments can themselves be the
subject of argument.
[61] C. Reed. Dialogue frames in agent communications. In: Y. Demazeau (ed.): Proc. 3rd International Conference on Multi-agent systems (ICMAS-98), pages 246–253. 1998
See comments following Dignum [18].
[62] C. Reed and T. Norman. Argumentation Machines. Kluwer Academic
Publishers: Dordrecht. (2003).
A book surveying argument in AI from a variety of perspectives, including multi-agent systems, decision support, persuasion, law and rhetoric.
[63] C.A. Reed and G.W.A Rowe. Araucaria: Software for Puzzles in Argument Diagramming and XML. Department of Applied Computing,
University of Dundee, Technical Report. (2001).
Describes Araucaria, a program supporting the graphical analysis of
arguments in terms of argument schemes.
[64] J.R. Searle. Rationality in Action. MIT Press, Cambridge Mass., 2001
A recent monograph giving an account of practical reasoning. In particular it addresses the problems with the practical syllogism, and argues
that a deductive theory of practical reason is inappropriate.
[65] G.R. Simari and R.P. Loui. A mathematical treatment of defeasible
reasoning and its implementation. Artificial Intelligence, 53(2–3):125–
157 (1992).
An early and influential presentation of a formal approach to defeasible
reasoning based on argumentation.
[66] D.B. Skalak and E.L. Rissland. Arguments and cases: an inevitable
intertwining. Artificial Intelligence and Law 1:3–44 (1992).
Develops a number of strategies for argument and the moves to realise
in the context of legal case based reasoning.
[67] S. Toulmin. The uses of argument. Cambridge University Press. 1959
This book introduces a popular scheme for the analysis of argument.
25
[68] H.B. Verheij. Automated argument assistance for lawyers. Proceedings
of the Seventh International Conference of Artificial Intelligence and
Law. New York: ACM Press, pages 43–52. (1999).
Describes Argu-Med, which provides a graphical interface to an argumentation framework based on the Reason Based Logic of [38]
[69] G. Vreeswijk. Abstract Argumentation Systems. Artificial Intelligence,
90:225–279, 1997
Presents a theory of argumentation systems modelling these as collections of “defeasible proofs”. The introduction, additionally, provides a
useful comparative survey of formal argumentation systems up to and
including [25].
[70] G. Vreeswijk and H. Prakken. Credulous and sceptical argument games
for preferred semantics. In: Proceedings of JELIA’2000, The 7th European Workshop on Logic for Artificial Intelligence, Berlin, pages 224–
238, 2000
Presents the elements of the Two party immediate response (TPI) dialgoue game studied and analysed in [29], showing this to be sound and
complete for credulous reasoning in any system, and sound and complete for sceptical reasoning in coherent argument systems. Presents
examples of where the sceptical reasoning method may fail in systems
which are not coherent.
[71] D. N. Walton and E. C. W. Krabbe Committment in Dialogue: Basic
Concepts of Interpersonal Reasoning. Univ. of New York Press. 1995
Presents one of the first systematic attempts to construct a taxonomy
of dialogue types and aims.
[72] D.N. Walton, Argumentation Schemes for Presumptive Reasoning. Erbaum: Mahwah, NJ. 1996
An account of presumptive or defeasible argument in the informal logic
tradition. Its approach makes use of argument schemes and critical
questions. It describes some sixteen schemes for presumptive reasoning
and their associated critical questions in detail.
26
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IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
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A1: John should not get sickness benefit (-B)
This is the initial claim
B1: Why?
The first question simply seeks the grounds for the claim, the data in our schema
A2: He is a lazy person (L)
Some grounds are advanced
B2: OK, but so what?
Here two moves are made. The truth of the data is accepted, but its relevance
to the argument is questioned
A3: Lazy people should not get sickness benefit (L -> -B)
A rule which would licence the conclusion is advanced
B3: Is there a law to that effect?
Here a justification for the rule is sought. Note that here we do not seek a justification in terms of a
logical argument for the rule, but rather in terms the authority from which the rule derives - making
use of the backing in our schema. Moreover we seek a legal, not a moral authority
A4: Not as such.
IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
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IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
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B4: So why do you think he should not get the benefit? (-B)
Now there is no reason to think that L is a reason for -B, a different reason is sought.
A5: He is fit for work (F)
Another reason is supplied.
B5: Suppose he is. Why should that matter?
Here player B does not immediately accept the truth of the data, but wishes to defer
consideration of it, while exploring the connection between F and -B
A6: If someone is fit for work, they should not get sickness benefit.
The relevant rule is supplied
B6: Any work at all?
Player B suspects that the rule is not always applicable and seeks the elements of the context which make it applicable to this
case
A7: Work that someone would pay to have done. (P)
The background assumption is given
B7: True, but what's your authority?
Player B accepts that P is true, but now wishes to know the authority for the rule
A8: Social Security Act 1984, section 32(1).
This time player A has an authority, in the form of a statutory provision
B8: Why do you say John is fit for work? (F)
Player B accepts the rule but questions the premise, asking for grounds that support it.
A9: I saw him gardening. (G)
A supplies the grounds
B9: I can accept that. But gardening is unsuitable work for John(G, U -> B)
B accepts the truth of the grounds, and that there is a rule entailing F. On the face of it this would establish -B. But Player B
is aware of an exceptional circumstance which can defeat the argument.
IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
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IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
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A10: What's that got to do with it?
Player A now wishes to know the authority for the rule implicit in B's rebuttal. Note that
it is now B who is the proponent of the claim
B10: Fit for work means fit for suitable work. Toogood, Commisssioner, RS3/58.
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A11: Why do you say gardening is not suitable work?
Player A is forced to accept the rule, but can question the premise
B11: John is a University Lecturer. (J)
B supplies his data for U
A12: OK, OK. John should get the benefit. (B)
Player accepts the truth of J, and that J implies U, and so is constrained to accept that
B
IJCAI 2005 Tutorial: Trevor Bench-Capon and Paul Dunne
15
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