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A Bayesian Approach to Automating Argumentation 
Richard McConachy, Kevin B. Korb & Ingrid Zukerman 
Department of Computer Science, Monash University 
Clayton, Victoria 3168, AUSTRALIA 
{ricky, korb, ingrid}~cs .monash. edu. au 
Abstract 
Our argumentation system NAG uses Bayesian 
networks in a user model and in a normative 
model to assemble and assess nice arguments, 
that is arguments which balance persuasive- 
ness with normative correctness. Attentional 
focus is simulated in both models to select 
relevant subnetworks for Bayesian propaga- 
tion. Bayesian propagation in the user model 
is modified to represent some human cognitive 
weaknesses. The subnetworks are expanded in 
an iterative abductive process until argumen- 
tative goals are achieved in both models, when 
the argument is presented to the user. 
1 Introduction 
"The St. Kilda Football Club will probably win the 
grand final in 1997. They are likely to do so be- 
cause they have won at least as many games as 
any other side during the regular season, they have 
scored more points than any other team this year 
so far, and they have few unavailable players." How 
strongly should St. Kilda's good form in the later 
part of the 1997 season be taken as a premiership 
indicator? Is it better to lose narrowly to a strong 
side or narrowly defeat a weak side? Most argu- 
ments, like the St. Kilda example above, must be 
formed using information that is both incomplete 
and uncertain. 
This paper focuses upon the Bayesian underpin- 
nings of our argument generation-analysis system, 
NAG (Nice Argument Generator). The goal of our 
system is to generate nice arguments. A nice ar- 
gument employs normatively strong inferences from 
accepted premises while also being persuasive for the 
target audience. 
The main modules of NAG are shown in Figure 1. 
The Generator (Section 3) uses semantic activation 
to quickly form the initial Argument Graph for an 
argument, or to quickly extend an already existing 
t ,Re-nin  l LAroment 
Generator I Agents Analyzer . Argument 
Goal Analysis .~"~Proposition aalysis~// 
Goal _ I Argument 
Proposition r Strategist 
Argument It User Argument/Inquiry 
USER 
Figure 1: System Architecture 
Argument Graph. An Argument Graph is a net- 
work structure with nodes that represent proposi- 
tions, and connecting links that represent the infer- 
ences that connect these propositions. An Argument 
Graph is fleshed out by consulting several sources of 
information called Reasoning Agents and incorporat- 
ing the relevant inferences and propositions returned 
by these sources into the Argument Graph. This Ar- 
gument Graph is passed to the Strategist. 
The Strategist decides what NAG should do next: 
call the Generator to continue the argument building 
process; call the Analyzer (Section 4) to estimate 
how nice the current Argument Graph is; or present 
an argument based on the current Argument Graph 
to the user for inspection and response. 
The Strategist will pass the current Argument 
Graph to the Analyzer at least once before the argu- 
ment is presented to the user, and often more than 
once. To estimate the persuasive power of an argu- 
ment represented by an Argument Graph, the An- 
alyzer consults a revisable user model that reflects 
the beliefs and cognitive abilities of the audience. 
The Analyzer uses a normative model to gauge the 
normative strength of an argument. Belief updating 
in both the user and the normative model is done 
by a constrained Bayesian propagation scheme (Sec- 
McConachy, Korb and Zukerman 91 A Bayesian Approach to Automating Argumentation 
Richard McConachy, Kevin B. Korb and Ingrid Zukerman (1998) A Bayesian Approach to Automating Argumentation. In 
D.M.W. Powers (ed.) NeMLaP3/CoNLL98: New Methods in Language Processing and Computational Natural Language 
Learning, ACL, pp 91-100. 
tion 4). In the user model, Bayesian updating is ad- 
justed by multiplicative factors which model three 
human cognitive weaknesses (Section 4.1). 
If the Analyzer detects problems with the Argu- 
ment Graph it highlights the weaknesses for the Gen- 
erator to fix. In this way a cycle of alternately cri- 
tiquing and extending the graph is continued until 
a successful Argument Graph is built, or NAG is 
confronted with an event that prevents it from con- 
tinuing, such as the Generator failing to find relevant 
new evidence or the Strategist noticing that the al- 
lowed amount of time has run out. 
2 Related Research 
Charniak and Goldman (1993) describe a Bayesian 
plan recognition system that uses marker passing as 
a method of focusing attention on a manageable por- 
tion of the space of all possible plans. This is similar 
to the way in which NAG uses spreading activation 
to focus on a small portion of the available data when 
generating arguments. 
The approach of "interpretation as abduction" 
used in (Hobbs et al., 1993) aims to recover the 
premises and inferential links which lead to the con- 
clusion of some given argument. This is similar to 
NAG's argument analysis. There are two important 
differences between NAG and the work by Hobbs et 
al.: NAG is a system that reasons under uncertainty, 
and NAG performs both analysis and generation. A 
generative system based on the work of Hobbs et al. 
is described in (Thomason et al., 1996). This sys- 
tem deals with what can be readily inferred, and so 
deleted, during communication, but the generated 
discourse does not present an argument in support of 
a proposition. Two systems that can turn an exist- 
ing fully explicit argument into an enthymematic one 
are described in (Horacek, 1994) and (Mehl, 1994). 
However, both of these systems require a complete 
argument as input, unlike NAG, which constructs 
its own. 
3 Argument Generation 
The Generator receives the following inputs: (1) a 
proposition to be argued for; (2) an initial argument 
context; (3) two target ranges of degrees of belief to 
be achieved (one each for the normative model and 
the user model); and (4) a system attitude param- 
eter, which determines the extent to which the sys- 
tem will take advantage of the user's erroneous be- 
liefs. 1 An argument context is the set of propositions 
1The results in this paper are for a "normal" attitude, 
which allows a small departure from what is normatively 
correct. 
and concepts appearing in the discussion preceding 
the argument or in the current Argument Graph. 
The degrees of belief to be achieved are expressed 
as ranges of probabilities, e.g., \[0.5, 0.6\], in order to 
be able to represent a variety of goals, e.g., inducing 
indifference or assent. 
The Generator produces an Argument Graph 
which starts from admissible premises and ends in 
the goal proposition. Admissible premises are nor- 
matively acceptable propositions that are either al- 
ready believed by NAG and the user (sufficiently 
for the argument to work) or are assented to by 
the user (e.g., sourced from an accepted reference 
work). When constructing an argument, the Gener- 
ator relies on two collections of information: a nor- 
mative model composed of different types of Knowl- 
edge Bases (KBs) and a user model also composed 
of different types of KBs which represent the user's 
presumed beliefs and inferences. A single KB rep- 
resents information in one format, e.g., a semantic 
network (SN), Bayesian network (BN), rule-based 
system, or database. During the argument gener- 
ation process, relevant material from several of the 
KBs may need to be combined into a common rep- 
resentation. We have chosen BNs for this purpose 
because of their ability to represent normatively cor- 
rect reasoning under uncertainty, and because alter- 
ing the normal Bayesian propagation rules allows us 
to model some human cognitive phenomena. 
When assembling an Argument Graph, NAG de- 
velops two BNs: the BN forming one of the KBs 
in the user model, and the BN forming one of the 
KBs in the normative model. As arguments are built 
up, material obtained from other KBs may be con- 
vetted to BN form and added to the appropriate 
BN, e.g., material from a rule-based system in the 
normative model may be added to the normative 
BN (Section 3.4). In order to reduce the amount of 
information NAG must deal with, a focusing mech- 
anism is applied to highlight the portion of the com- 
plete BN in each model needed for the current argu- 
ment (Section 3.2). Hence, both the user model and 
the normative model will contain a single Bayesian 
subnetwork that is under focus. The structural in- 
tersection of these Bayesian subnetworks form the 
Argument Graph. When analyzing the current Ar- 
gurnent Graph, propagation is performed twice, once 
over the Bayesian subnetwork in the user model and 
once over the Bayesian subnetwork in the norma- 
tive mode, each time using probabilistic informa- 
tion sourced from within the model being propa- 
gated (Section 4). Thus, we obtain the strength of 
the same argument in both the user and normative 
models. 
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McConachy, Korb and Zukerman 92 A Bayesian Approach to Automating Argumentation 
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3.1 The Generation-Analysis Algorithm 
As previously described, part of NAG's input is an 
initial argument context, contexto, which is defined 
by the propositions and concepts mentioned in the 
preamble to the argument plus the argument's goal. 
Having established the initial context, NAG acti- 
vates the following algorithm: 
Generation-Analysis Algorithm 
1. i +-- 0. 
2. Clamp any items related to the current con- 
text, contexti, and perform spreading activa- 
tion. This results in an Argument Graph con- 
taining: the clamped nodes, the activated nodes 
(those whose activation exceeds a threshold), 
plus the links connecting the nodes. 
(Section 3.2) 
3. Identify new subgoals in the current Argument 
Graph and tag them for further investigation. 
(Section 3.3) 
4. Pass each of the argument subgoals identified in 
the previous step to the Reasoning Agents, and 
add the new information returned by the Rea- 
soning Agents to the current Argument Graph. 
(Section 3.4) 
5. Pass the current Argument Graph to the Ana- 
lyzer for evaluation. 
(Section 4) 
6. If the Analyzer reports that the current Argu- 
ment Graph is sufficiently nice, then present 
an argument based on the current Argument 
Graph to the user, and wait for a response. 
(Section 5) 
/A~ Higher level ///\ /concepts 
Lower level / / I ~ 'rocks' 
concepts like / / ~/ 
'quartz phenocrysts' / / /~ 
/ ~ -------'-'--~- Semantic \ / ° /' Network 
o 2nd layer 
Semantic / \ ~ ~o/ 1~ ~ ~ Net work--------Tz-~.~/'~ / ~/ 
l~ ~ Z 
1st layer \[\] ~ j o 
/ // . /o / ~q~ /........._Bayesian 
o/~- -''- ~ Network 
Proposition, e.g., \[Porphyry copper deposit exists at Mineral Park\] 
Figure 2: Semantic and Bayesian Networks 
7. i+-i+l. 
8. contexti e-- contexti_l + new nodes connected 
to the goal during the cycle i-1. 
9. Go to Step 2. 
3.2 Focusing the Argument 
Bayesian network propagation (Pearl, 1988), op- 
timized or otherwise (see, for example, Li & 
D'Ambrosio, 1994), is an NP-hard problem in the 
general case (Cooper, 1990). NAG is designed to 
be an interactive system, potentially drawing upon 
very large knowledge bases, so complete propaga- 
tion over large BNs would be too slow. In addition, 
NAG's user model is designed to model human cog- 
nitive abilities, and humans normally cannot absorb 
and analyze all data relevant to a complex prob- 
lem. To cope with both of these limits on complexity 
we emulate the principal means available to humans 
for applying limited cognitive capacity to problem 
solving, namely attention (see, for example, Baars, 
1987). 
NAG uses two hierarchical SNs, one built on top of 
the user model BN and one built on top of the nor- 
mative model BN, to capture connections between 
the items mentioned in the discourse. Figure 2 illus- 
trates one such semantic-Bayesian 'pyramid'. The 
SN (upper levels of the pyramid) and the BN (base 
of the pyramid) are used by NAG to simulate atten- 
tional focus in each model. NAG takes the context in 
which theargnment occurs as providing an initial set 
of salient objects. For example, if the user presents 
an argument to NAG, the concepts occurring in the 
propositions within the argument or in the preceding 
McConachy, Korb and Zukerman 93 A Bayesian Approach to Automating Argumentation 
discussion will be marked as salient. We use acti- 
vation with decay (Anderson, 1983), spreading from 
the salient Objects (which are clamped) to determine 
the focus of attention. All items in the semantic- 
Bayesian networks which achieve a threshold acti- 
vation level during the spreading activation process 
axe brought into the span of attention. The spread- 
ing activation process passes activation through the 
pyramidal semantic-Bayesian networks, each node 
being activated to the degree implied by the activa- 
tion levels of its neighbors, the strength of associa- 
tion to those neighbors, and its immediately prior 
activation level (vitiated by a time-decay factor). 
By these means we have a direct implementation 
of attention which we use to zero-in upon the more 
useful portions of the pyramidal semantic-Bayesian 
networks. This iterative process ceases when an ac- 
tivation cycle fails to activate any new node. 
Determining the more useful portions of the pyra- 
midal semantic-Bayesian networks in this way allows 
NAG to save processing time in two ways: NAG can 
restrict itself to searching for information connected 
with only the most relevant propositions (the ones in 
focus, see Section 3.3), rather than all of the propo- 
sitions known to the system; and similarly, NAG can 
analyze its arguments with respect to just the same 
relevant propositions, saving time in the Bayesian 
propagation procedure (Section 4). 
3.2.1 Focusing Example 
Consider the generation of an argument for the 
proposition "A porphyry copper deposit exists at 
Mineral Park, Arizona," preceded by the preamble 
"A porphyry copper deposit derives its name from a 
porphyritic stock located at the center of the min- 
eral deposit. A stock is a cylindrical igneous mass 
working its way up through the earth's crust. The 
word porphyritic describes the bimodal nature of the 
minerals within the stock: some of these minerals 
axe large and the rest are microscopic. For example, 
porphyritic granite at Mineral Park usually contains 
large crystals (phenocrysts) of feldspar and small 
grains of quartz." (this example is adapted from 
Duda et al., 1978). Initially, the goal proposition 
and the preamble activate any propositions contain- 
ing one or more of the italicized concepts, i.e., nodes 
N1-N4, Ns-Ns, and NI~ in Figure 3 (shown in grey 
boxes). 
After clamping the nodes that correspond to this 
discourse context and performing spreading acti- 
vation, additional nodes become activated in the 
semantic-Bayesian networks. All nodes whose ac- 
tivation level exceeds a threshold are retained and 
added to the Argument Graph. For this example, 
this yields an Argument Graph composed of two 
argument fragments: (1) N1-Ns, Ns, Ns, Ns and 
Nll-Nls; and (2) N4, N7 and Nlo (Figure 3). 
3.3 Choosing Argument Subgoals 
Having used the semantic priming process to add 
items of likely interest to the current Argument 
Graph, NAG must now decide which of these newly 
added items should be set as argument subgoals re- 
quiring further inspection. At present, all nodes con- 
nected to the goal in the current Argument Graph 
that have not been previously passed to the Reason- 
ing Agents axe tagged as subgoals to be investigated 
(Section 3.4). 
We are currently looking at methods for reduc- 
ing the list of current subgoals. One technique for 
achieving this is to choose a subset of the current 
list of subgoals that seems to offer good potential 
for adding new support to the overall argument goal 
with minimal additional effort. A node is deemed 
to have a high potential for support if changes in its 
value would cause a large change in the final proba- 
bility of the goal node after propagation (Section 4), 
and the node has not previously been passed to the 
Reasoning Agents (in which case NAG would have 
already examined the potential contribution of this 
node). This scheme of selecting only some of the 
available options for further inspection by the Rea- 
soning Agents has not yet been implemented. 
3.3.1 Subgoals - Example Continued 
Since none of the nodes in the current Argument 
Graph (Figure 3) have been passed to the Reason- 
ing Agents at this point, all of the nodes connected 
to the goal in the Argument Graph are tagged as 
subgoals. In this example, the nodes N1-Ns, Ns, 
Ns, Ns, Nu and N12 are tagged as subgoals, and 
together with the goal node, NlS, are passed to the 
Reasoning Agents in order to obtain additional in- 
formation (Section 3.4). The nodes that form the 
second fragment shown in Figure 3 - nodes N4, N7 
and N10 - are kept, but are not expanded upon at 
this stage. 
3.4 Extending the Argument Graph 
The initial Argument Graph consists of the subset 
of the BNs which was activated by the attentional 
mechanism. The Generator then activates the Rea- 
soning Agents to collect information relevant to each 
subgoal in the current Argument Graph. During 
the process of adding this new information to the 
Argument Graph, the Generator must determine: 
(1) which of the newly returned inferences should be 
integrated into the Argument Graph; (2) the struc- 
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McConachy, Korb and Zukerman 94 A Bayesian Approach to Automating Argumentation • 
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85 I Favo~ 
groum 
N3 
'no're I I  vo°b'e system in regional 
target area environment 
N4 
~,0 
regional 
environment 
Figure 3: Initial Argument Graph for the Porphyry Copper Deposit Example 
ture of the additions to the Argument Graph repre- 
senting the new inferences; and (3) the parameters 
of the new inferences and propositions. 
Which propositions and inferences to inte- 
grate. New propositions returned by the Reasoning 
Agents are added to the current Argument Graph as 
new nodes. NAG decides whether to introduce new 
inferences returned by the Reasoning Agents into 
the Argument Graph (or to replace existing infer- 
ences with new ones) by applying two simple rules 
designed to ensure that each relationship between 
propositions in the Argument Graph is represented 
only once. The two rules state that: 
1. At most only one inference may directly connect 
any two propositions in the current Bayesian 
subnetworks in each of the user model and the 
normative model. 
2. When selecting from multiple candidate infer- 
ences, preference is given to inferences sourced 
from more expressive representations, where 
expressiveness means how much probabilistic 
information, including joint interactions with 
other factors, can be expressed by the represen- 
tation. 
For example, assume NAG's qualitative rule-based 
system agent finds a rule stating "If D then E is pos- 
sible." If the agent responsible for quantitative rule- 
based systems also finds a rule "If D then E with 
prob = x," which NAG translates into D ev~-~ceE 
with P(EID ) = z (assuming independence from 
other links incident upon node E), then which of 
these inference rules, if any, should be added into the 
Argument Graph? The first rule above states that 
at most one of these two inferences will be incor- 
porated into the current Argument Graph. 2 NAG 
selects which one of the two inferences it will incor- 
porate by applying the second rule. NAG imple- 
ments the second rule via the following preference 
ordering for expressiveness: BNs, quantitative rule- 
based systems, qualitative rule-based systems and 
finally database lookups. The expectation is that 
the representations higher in the list, e.g., BNs and 
quantitative rule-based systems, will usually provide 
more complete and accurate probabilistic informa- 
tion about an inference or proposition than represen- 
tations lower in the list, e.g., qualitative rule-based 
systems. Sometimes this expectation proves false. 
For example, if both a quantitative rule-based sys- 
tem and a BN return a probability estimate for a 
particular proposition being true, it is possible that 
the value returned by the rule-based system will be 
the more accurate one, perhaps because the BN has 
not been fully propagated (and hence the probability 
for the proposition not updated to incorporate all of 
the available information). However, initial testing 
suggests that NAG can often do a good enough job, 
i.e., produce nice enough arguments, using our two 
simple information lossy rules. 
Structural form of the new propositions and 
inferences. The various Reasoning Agents return 
2NAG does not try to merge information gleaned from 
more than one available source since it is unclear how to 
do so. 
McConachy, Korb and Zukerman 95 A Bayesian Approach to Automating Argumentation 
argument fragments which take the form of propo- 
sitions linked by inferences and semantic relations. 
After the two rules mentioned previously in this 
section have been applied to determine which of 
these fragments should be incorporated in the Ar- 
gument Graph, the selected fragments are added to 
the Bayesian subnetwork in the appropriate model, 
e.g., fragments sourced from KBs in the normative 
model will be added to the subnetwork in the nor- 
mative model. Inferences in the fragment which are 
going to replace inferences already in the subnet- 
work (the new inference is from a more expressive 
KB than the one currently in the subnetwork, see 
rule two described previously) are handled in the 
manner described below. 
Adding parameters for the propositions and 
inferences. Incorporating new information about 
the prior probability of a proposition into the Argu- 
ment Graph requires that the information returned 
by a Reasoning Agent be copied to the node in the 
Argument Graph which corresponds to the KB data 
point from which the information was sourced. For 
example, information about priors sourced from a 
KB in the user model is copied to the correspond- 
ing node in the Bayesian subnetwork belonging to 
the user model. Similarly, information about pos- 
sible instantiation values for a proposition are also 
copied to the appropriate proposition in the correct 
model, e.g., \[Fred is a smoker\] may be instantiated 
as TRUE (1.0) or FALSE (0.0). This works so long 
as the new values are filling gaps in the Argument 
Graph. However, if the current Argument Graph 
already contains a prior probability or instantiation 
value for the proposition under consideration, then 
that previous value will be retained and the new in- 
formation ignored. " 
Adding information to the Argument Graph 
about joint conditional probabilities associated with 
new inferences is a harder task. If a Reasoning Agent 
can provide complete conditional probability infor- 
mation for a new inference which takes into account 
other inferences that impinge upon the proposition 
targeted by this inference, then this information is 
added to the conditional probability matrix for the 
node containing this proposition in the Argument 
Graph. However, complete probabilistic information 
is frequently not available to NAG, in which case the 
new information (often a simple conditional proba- 
bility) is assumed to be conditionally independent 
of the other inferences impinging upon the node in 
question. Since assuming conditional independence 
without a good understanding of the domain is dan- 
gerous, NAG reports this assumption to its operator 
interface. This is done so that a human operator can, 
Ng \[ Favourable 
level of 
erosion 
N121 Favourable regional 
, environment 
/ 
N13\[ Porphyry I copper deposit 
at Mineral Park 
Figure 4: Results of node N12 being sent to the Rea- 
soning Agents 
then or later, spot where NAG is most likely to have 
"gone wrong" should one of its arguments appear 
incorrect. The operator can then edit NAG's KBs 
to remove the offending inference or to add extra in- 
formation about the joint conditional probabilities. 
3.4.1 Extending the Argument Graph - 
Example Continued 
The information returned by the Reasoning 
Agents is incorporated into the Argument Graph. 
Some of this information will be included in the 
final Argument Graph presented to the user, e.g., 
the newly found node N9 and the link connecting 
N9 --+ N12 shown in Figure 4 (nodes NI~ and N13 
and the link between them were already contained 
in the current Argument graph). Other fragments 
may also be created during this process, e.g., \[pres- 
ence of igneous rocks\] ev~_~ce \[history of high temperature 
and pressure conditions\], but are eventually excluded 
because of their irrelevance to the goal. 
Node N9 and the link N9 ---r N12 were returned 
when the Reasoning Agents were passed node Nlz 
for inspection (recall that node N12, like all of the 
nodes in the left hand fragment of Figure 3, was pre- 
viously set as a subgoal to be investigated further). 
In this example, node N12 is the only subgoal shown 
in Figure 3 about which NAG could find new infor- 
mation. 
4 Argument Analysis 
The process of computing the anticipated belief in 
a goal proposition as a result of presenting an argu- 
ment starts with the belief in the premises of the 
Argument Graph and ends with a new degree of 
belief in the goal proposition. The Analyzer com- 
putes the new belief in a proposition by combining 
the previous belief in it with the result of applying 
the inferences which precede this proposition in the 
McConachy, Korb and Zukerman 96 A Bayesian Approach to Automating Argumentation 
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Argument Graph. This belief computation process 
is performed by applying propagation procedures to 
the Bayesian subnetwork corresponding to the cur- 
rent Argument Graph in the user model and sepa- 
rately to the subnetwork corresponding to the cur- 
rent Argument Graph in the normative model. 
In propagating only over the subnetworks initially 
seeded by the focusing mechanism (Section 3.2) and 
extended with information returned by the Reason- 
ing Agents (Section 3.4), NAG is ignoring those 
parts of the complete BNs in the user and norma- 
tive models not deemed relevant to the current ar- 
gument. Propagating over the subnetwork corre- 
sponding to the current Argument Graph in each 
of the user model and the normative model is much 
faster than having to perform propagation over the 
complete BN in each model, but the trade off is a 
less accurate estimate of the final belief in the goal 
proposition. Nonetheless, in a system designed to be 
interactive, some such trade off is necessary in view 
of the complexity of Bayesian propagation. 
After propagation, the Analyzer returns two mea- 
sures of an argument's strength: normative strength, 
which is the effect of an argument on the belief in the 
goal proposition in the normative model, and effec- 
tiveness, which is its effect on the user's belief in the 
goal proposition. Of course, the effectiveness of an 
argument presented to a user may be quite different 
from its normative strength. When determining an 
argument's anticipated effect upon a user, NAG cur- 
rently takes into account three cognitive errors that 
humans frequently succumb to: belief bias, overcon- 
fidence and the failure to use base rate information 
(Section 4.1). 
After the Analyzer has evaluated the normative 
strength and effectiveness of the Argument Graph 
it will return an assessment. This assessment may 
point out flaws in the argument structure such as in- 
sufficient support for some propositions within the 
Argument Graph and reasoning loops. At present 
flaws are fixed in the order they are found. The de- 
termination of a preferred ordering in which to ad- 
dress flaws in an argument is left for future research. 
In the case of an insufficiently supported premise, 
the target premise is set as a new argument subgoal. 
This new subgoal is then submitted to the Genera- 
tor with the currently active subnetworks as its con- 
text, in order to generate a new subargnment. After 
integrating the new subargument into the previous 
subnetworks, the now enlarged Argument Graph is 
again sent to the Analyzer for inspection. Hence 
by allowing NAG to complete additional focusing- 
generation-analysis cycles, Argument Graphs that 
are initially unsatisfactory can often be improved. In 
McConachy, Korb and Zukerman 97 
more extreme cases where additional cycles do not 
gather any new evidence, altering the parameters of 
the semantic priming procedure, e.g., increasing the 
initial clamping value or decreasing the rate of de- 
cay, may help NAG identify a new subgoal that can 
be profitably examined by the Reasoning Agents. 
4.1 Modeling Human Weaknesses 
During belief updating in the user model, multiplica- 
tire factors are incorporated into the Bayesian up- 
date formulas (Neapolitan, 1990) to model the hu- 
man cognitive weaknesses of belief bias, overconfi- 
dence and the base rate fallacy (for a fuller descrip- 
tion see Korb et al., 1997). In future we shall model 
additional prominent features of human inference. 
Belief bias is the assessment of an inference as 
being stronger (weaker) than it is normatively be- 
cause it supports (undermines) an existing belief 
(Evans~ 1989). To model this effect we employ a 
function which given the user's prior degree of be- 
lief in a proposition provides a multiplicative factor 
used in any update to that belief. Should the user's 
prior belief be 0.5, then the multiplicative factor is 
1, so that the belief is updated normally. An ex- 
treme prior disbelief on the other hand suppresses 
the impact of supporting evidence via a low multi- 
plier, whereas a strong prior belief enhances that im- 
pact via a factor greater than 1. As a result, NAG 
tends to assume that users will require more and 
better arguments to be persuaded to change their 
strongly held beliefs than should be necessary nor- 
matively. 
Due to overconfidence people tend to exagger- 
ate the probability of very likely events and the im- 
probability of very unlikely events (Lichtenstein et 
aL, 1982). NAG uses this bias to select prior prob- 
abilities.for propositions in the user model when it 
has not been given explicit information about these 
probabilities, but only frequency information also 
known to the user. NAG applies an S-curve to con- 
vert frequencies into user probabilities (Figure 5). 
For example, a very low frequency will be mapped 
into an even smaller prior probability. NAG does 
not use this S-curve directly when the base rate fal- 
lacy applies, since in that case both errors are dealt 
with at once. 
The base rate fallacy is the tendency people 
have to ignore objective prior probabilities based 
on frequency data available to them and to replace 
these probabilities with a uniform probability distri- 
bution. A striking example of this is the cab problem 
described in (Tversky and Kahneman, 1982). 
A cab was involved in a hit and run ac- 
cident at night. Two cab companies, the 
A Bayesian Approach to Automating Argumentation 
1.0 
Belief 
0.5 
0.( .0 0'.5 
Frequency 
Figure 5: Overconfidence Curve 
Green and the Blue, operate in the city. 
You are given the following data: 
• 85% of the cabs in the city are Green 
and 15% are Blue. 
* A witness identified the cab as Blue. 
The court tested the reliability of the 
witness under the same circumstances 
that existed on the night of the acci- 
dent and concluded that the witness 
correctly identified each one of the two 
colors 80% of the time and failed 20% 
of the time. 
By Bayes theorem the probability that the cab was 
Blue is 0.41 based on the evidence given. This is be- 
cause the low prior probability of Blue Cabs (0.15) 
dominates the computation, z Nevertheless, most 
people presented with the story respond that the 
probability that the offending cab was blue is 0.8, a 
response that would be correct if the prior probabil- 
ities were uniformly distributed among the available 
options. This is characteristic of most people's re- 
sponse to many situations involving uncertainty -- 
they flatten all prior probabilities. In order to ac- 
commodate this tendency, NAG computes implicit 
prior probabilities in the user model using a func- 
tion that flattens the middle of the belief-frequency 
graph, thereby reflecting this bias towards uniform 
priors. 
Using the odds-likelihood ratio method (Neapoli- 
tan, 1990) with the additional multiplicative factors 
as described above, we obtain the following update 
formula: 
O(N.,.,IN,,N2,...,N.) = O(N...,) 
tl 
x HAi x belbiasi x overconf~ x baseratei, 
i=l 
where the three biasing factors for each inference 
3The computation being (.8 x .15)/(.8 x .15+ .2 x .85) 
= 0.41. 
are displayed separately, the evidence nodes Ni are 
conditionally independent given the "causal" node 
Nne~, and the likelihood ratio is computed as Ai = 
P(Ni\[Nnew)/P(N~\[-~N~e~). The multiplicative fac- 
tors for each of belbiasl, overconfi and baseratea axe 
either 1.0, if the particular cognitive weakness is not 
active for this inference, or derived as above if the 
weakness is active. 4 The propagation rule for uncer- 
tain evidence and the more general formulae used 
for propagation in singly connected causal networks 
given in (Neapolitan, 1990) are similarly modified 
by means of the three multiplicative factors. 
4.1.1 Analyzing the Example 
The argument that can be built at this stage has 
two main branches: from nodes N1-Nz to node N13 
via Nn (Figure 3); and from node N9 to NI3 via 
N9 --+ N12 -+ N13 (Figure 4). According to the user 
model, the user is believed to attach great strength 
to the inferences N1 --+ N5 ~ Ns and N3 ---> N6 --+ 
Ns, so propagation in the user model leads to an 
anticipated final belief in the goal node within the 
target range. However, the anticipated final belief 
in the goal node in the normative model falls short 
of the desired normative range. 
NAG continues through Steps 7-9 of the 
Generation-Analysis algorithm, putting the newly 
added nodes connected to the goal node in the Argu- 
ment Graph into the current context. On the next 
cycle through the algorithm (Step 2) a new round 
of semantic priming is performed. However, in the 
current example this does not lead to any further 
nodes being connected to the argument goal. As a 
consequence, during Step 3 only one new subgoal is 
tagged, node Ng, which was connected to the goal 
during the last cycle of the algorithm. When node 
N9 is then passed to the Reasoning Agents in Step 4, 
the new link Nlo -~ N9 is found and added to the 
Argument Graph. The resulting Argument Graph 
is returned to the Analyzer again (Step 5), which 
determines that the anticipated belief in the goal is 
now within the target ranges in both models. 
The subgraph corresponding to a complete (non- 
enthymematic) argument generated for this exam- 
ple appears in Figure 6. Node N2 is omitted be- 
cause of its weak contribution to the goal, as ex- 
plained in following section. The focusing and sub- 
goal setting parts of the system managed to find an 
4At present, the activation of a cognitive weakness or 
lack thereof is a tag that accompanies each inference in 
the user model BN. This will support the implementa- 
tion of a user model which determines the activation or 
deactivation of a cognitive weakness depending on fac- 
tors such as a user's expertise in a domain or his/her 
level of alertness. 
McConachy, Korb and Zukerman 98 A Bayesian Approach to Automating Argumentation 
I 
I 
I 
I 
I 
I 
l 
l 
I 
I 
l 
l 
I 
II 
!1 
II 
II 
II 
II 
II 
Ii 
II 
Ii 
II 
II 
acceptable solution to this example problem without 
even having to fully investigate every proposition in 
the Argument Graph (nodes Na, Nr and Nlo were 
never passed to the Reasoning Agents), let alone 
every proposition in the complete BN in the user 
model and the complete BN in the normative model. 
Partial propagation over just the subnetworks cor- 
responding to the Argument Graph in each model 
also ensured that inferences like \[presence of igneous 
rocks\] ev~_~c¢ \[history of high temperature and pressure 
conditions\], which turned out to be irrelevant for this 
argument goal, were not propagated over. 
5 Presentation 
After a successful Argument Graph has been built, 
so that the current Argument Graph now gives an 
anticipated belief in the goal proposition within the 
desired ranges in both the normative and user mod- 
els, then comes the problem of how to present the 
argument to the user. NAG attempts to minimize 
the size of the current Argument Graph by search- 
ing it for the subargument with the fewest nodes 
which still yields a degree of belief in the goal propo- 
sition that falls inside the target ranges in both the 
normative model and the user model. During this 
process, it tries to generate an enthymematic argu- 
ment by iteratively deleting nodes and invoking the 
Analyzer to determine whether the belief in the goal 
proposition in the now smaller Argument Graph still 
suffices. Frequently this process will be able to sim- 
plify the Argument Graph, since upon completion of 
the focusing-generation-analysis cycles, some of the 
propositions in the Argument Graph may be sup- 
ported more strongly than is necessary for the argu- 
ment to work. 
NAG was designed to be a system which gener- 
ates arguments and receives user arguments. At 
present, the front-end of the system is not imple- 
mented. However, a graphical interface is currently 
being constructed which allows the user to build and 
receive arguments in an annotated network form. 
Methods of rendering the system's output in English 
are being investigated. 
6 Conclusion 
NAG uses a series of focusing-generation-analysis cy- 
cles to build two Bayesian networks (one in the nor- 
mative model and another in the user model) that 
contain the information required to construct a nice 
argument. Partial propagation, performed over the 
subnetworks in focus (the current Argument Graph), 
is used to estimate the impact of the resultant argu- 
ment. Modified Bayesian update rules model three 
human cognitive weaknesses. 
Any argumentation system must have access to a 
great deal of domain specific data if it is to gener- 
ate and analyze arguments well. NAG is no excep- 
tion, and consequently setting up a good domain, 
one with sufficient depth and richness to test NAG 
well, is not trivial. By allowing NAG to use existing 
knowledge sources where possible, via small Reason- 
ing Agents written to match the various knowledge 
source types, we have endeavoured to at least par- 
tially mitigate this problem. 
NAG has been tested on five sample scenarios 
which generate BNs containing up to about 50 
nodes. The use of spreading activation to simulate 
attention, and the simplifications NAG employs to 
reduce the time taken to extend and propagate be- 
liefs through the Bayesian subnetworks, lead to a 
significant reduction in argument generation times 
compared to trials run with the same BNs not using 
these techniques. These speed-up methods seem to 
have little effect on the resulting arguments. 
Larger BNs and KBs, which are currently being 
built, will enable us to test more conclusively the 
effects of our modifications on the speed of the gen- 
eration process and the quality of the arguments 
produced. These richer scenarios will also allow us 
to better test the effects of our modeling of human 
cognitive weaknesses. We are currently planning a 
variety of tests to evaluate the performance of our 
system. The graphical interface currently under con- 
struction and an English generator will be used to 
test the effect of arguments generated by NAG on 
users' beliefs. In addition, the English output will 
be used to compare NAG's arguments with those 
generated by people and to test how the order of pre- 
sentation of the points in an argument affects users' 
beliefs. 
Acknowledgments 
This work was supported in part by Australian Re- 
search Council grant A49531227. 

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