Strategies for efficient agent dialogues

1
Strategies for efficient agent dialogues
2
Contents of talk

• Agents and belief representation
• Arguments, their representation, attacks and
  defeats
• Evaluating arguments
• Dialectical argumentation in dialogues
• Dialogue example
• Properties of dialogue strategies

3
Agent P
Set of beliefs about the world
4
Agent P
Set of beliefs
The patient Mrs Brown is 52. The patient Mrs
Brown is post menopausal. There are two free
beds in the oncology ward. If a patient has a
breast lump and is aged over 40 then she
should be referred urgently.
5
Agent P
State beliefs
The patient Mrs Brown is 52. The patient Mrs
Brown is post menopausal. There are two free
beds in the oncology ward. If a patient has a
breast lump and is aged over 40 then she
should be referred urgently.
Domain beliefs
6
Representation of beliefs

• Propositional Logic a ? b ? c, (? ? ?) ? ?
• propsitions a,b,c etc. ?, ?, ? etc.
• normal logic symbols ? ? ? ?

Mrs B has a lump AND Mrs B is over 40 IMPLIES Mrs
B should be referred urgently
?
?
7
Problem
Propositional logic is not expressive enough. For
example, does not allow us to say something like
For all patients, if that patient has a breast
lump and that patient is aged over 40 then that
patient should be referred urgently.
First order logic ?X, patient(X) ? hasBrLump(X)
? age(X,Y) ? gt(Y,40) ? refer(X, urgent)
But we have to start somewhere. Using first order
logic would add much complexity to an already
very complex system.
8
Restricted propositional logic
Set of literals a, a, b, b, c, c etc
(Literal is either a
proposition or
the negation of a proposition)
Restricted set of symbols , ?, ?
9
State beliefs
( ?, P)
? is a literal (e.g. ? a or ? b) and
represents the actual state belief.
P ?1,2,3, is the preference level of the
belief and indicates how confident the agent is
of the belief, with 1 being the most confident.
10
Examples of state beliefs
Proposition a represents the fact that Mrs
Browns has a breast lump. Proposition c
represents the fact that Mrs Brown should be
referred urgently. State beliefs (a, 1) (c,
2)
The agent is as confident as can be that Mrs
Brown has a breast lump.
11
Examples of state beliefs
Proposition a represents the fact that Mrs
Browns has a breast lump. Proposition c
represents the fact that Mrs Brown should be
referred urgently. State beliefs (a, 1) (c,
2)
The agent is fairly confident that Mrs Brown
should be referred urgently.
12
Domain beliefs
( ?1 ? ? ?n ? ?, P)
?1, , ?n, ? are all literals. ?1 ? ? ?n ? ?
represents the actual domain belief.
P ?1,2,3, is the preference level of the
belief and indicates how confident the agent is
of the belief, with 1 being the most confident.
13
Example of a domain belief
Proposition a represents the fact that Mrs
Browns has a breast lump. Proposition b
represents the fact that Mrs Brown is over
40. Proposition c represents the fact that Mrs
Brown should be referred urgently. (a ? b ? c,
2)
If Mrs B has a breast lump and she is over 40
then she should be referred urgently. The agent
is reasonably confident of this rule as it has
come from a respected guideline.
14
Defn Arguments
CONCLUSION
SUPPORT

• Arguments are formed from state and domain
  beliefs.
• An argument is a tuple lt?, ?gt where
• ? (?1, P1), , (?n, Pn) contains state and
  domain beliefs
• ? is a literal
• ?1, , ?n - ?
• ?1, , ?n is consistent and minimal

15
Proposition a represents the fact that Mrs
Browns has a breast lump. Proposition b
represents the fact that Mrs Brown is over 40.
Proposition c represents the fact that Mrs Brown
should be referred urgently.
Agent P
(a, 1) (b, 1) (a ? b ? c, 2)
16
Proposition a represents the fact that Mrs
Browns has a breast lump. Proposition b
represents the fact that Mrs Brown is over 40.
Proposition c represents the fact that Mrs Brown
should be referred urgently.
Agent P
Internal reasoning
(a, 1) (b, 1) (c, 2) (a ? b ? c, 2)
Form argument lt (a,1),(b,1),(a?b?c,2), cgt
Preference level of the new belief is the same as
that of the least preferred element of the
support of the argument
17
Argument attacks
lt (a,1),(b,1),(a?b?c,2), c gt
Undercut
Rebuttal
18
Defn Defeat

• Let A1 and A2 be two arguments. We say that A1
  defeats A2 iff
• A1 attacks A2 (either A1 undercuts A2 or A1
  rebuts A2), and
• The preference level of A1 (equal to that of the
  least preferred element of the support of A1) is
  either the same or more preferred than the
  preference level of A2.

lt (e,1),(e?b,1), b gt defeats
lt(a,1),(b,1),(a?b?c,2), c gt
19
Defn Defeat

• Let A1 and A2 be two arguments. We say that A1
  defeats A2 iff
• A1 attacks A2 (either A1 undercuts A2 or A1
  rebuts A2), and
• The preference level of A1 (equal to that of the
  least preferred element of the support of A1) is
  either the same or more preferred than the
  preference level of A2.

lt (f,2),(f?c,3), c gt does not
defeat lt(a,1),(b,1),(a?b?c,2), c gt
20
Defn Defeat

• Let A1 and A2 be two arguments. We say that A1
  defeats A2 iff
• A1 attacks A2 (either A1 undercuts A2 or A1
  rebuts A2), and
• The preference level of A1 (equal to that of the
  least preferred element of the support of A1) is
  either the same or more preferred than the
  preference level of A2.

lt(a,1),(b,1),(a?b?c,2), c gt defeats
lt
(f,2),(f?c,3), c gt
21
Argument status

• Have a whole load of arguments
• Arguments are defeated by arguments that may
  also be defeated by other arguments, and those
  might also be defeated by other arguments and so
  on.
• An agent needs a mechanism for deciding whether
  a particular argument is defeated or undefeated
  given all of the other interacting arguments.

22
Dialectical trees
A5
A1
A7
A3
A2
A4
A6
A3 defeats A1. A4 defeats A3. A6 defeats A1. A7
defeats A6. A5 defeats A6. A2 defeats A7.
23
Dialectical trees
A1
24
Dialectical trees
Mark all leaf nodes as undefeated (green) For all
other nodes N, if every child of N is defeated
then N is marked undefeated, else if one or more
of Ns children is undefeated then N is marked
defeated (red)
25
Dialectical trees
A1
26
Dialectical trees
A1
A3
A6
A4
A7
A5
A2
27
Dialectical trees
A1
A3
A6
A4
A7
A5
A2
28
Dialectical trees
A1
A3
A6
A4
A7
A5
A2
29
Dialectical trees
A1
A3
A6
A4
A7
A5
A2
30
Dialectical trees
A1 is undefeated and so its conclusion is
warranted
A1
A3
A6
A4
A7
A5
A2
31
Dialectical argumentation in dialogues
Aim to take this internal argumentation and
reproduce it as intra-agent argumentation between
two agents.

• Scenario
• Two agents
• Clinicians agent containing only specific
  state beliefs such as Mrs Brown is 45, Mrs
  Brown has a breast lump.
• Guideline agent containing only domain beliefs
  representing the knowledge from the breast cancer
  guideline, such as If patient has breast lump
  and patient is over 40 then she should be
  referred urgently.

32
Medical scenario
Guideline agent
Patients with nipple discharge managed in
practice Very worried patients should be
referred .. ..
GP agent
Patient 40 years old Pre menopausal Nipple
discharge
Situational beliefs
Domain knowledge
33
Dialectical argumentation in dialogues
Centralised guideline agent means that we can
easily monitor and update the guideline
information. When a clinician agent needs to
make a decision about whether a patient should be
referred or not, it enters into a dialogue with
the guideline agent and they pool their knowledge
to come up with the answer.
34
Two types of dialogue

• Discussion dialogues a clinician agent will
  enter into a discussion dialogue with a guideline
  agent in order to discuss whether a state belief
  (such as Mrs B should be referred) is warranted
  given the combined knowledge of the agents.

35
Two types of dialogue

• Argument search dialogues these are embedded
  within discussion dialogues and allow the agents
  to pool their knowledge to try and come up with
  an argument for a certain conclusion.

36
Dialogues

• Sequence of moves
• Legal function returns the set of moves that it
  is legal to make at any point in the dialogue.
• Strategy function returns one of the set of
  legal moves at any point in the dialogue.

37
Commitment stores

• Two commitment stores one for each agent
• Any time an agent asserts an argument the
  support and the conclusion of the argument gets
  added to the agents commitment store.
• An agent can only add things to its own
  commitment store but it can use elements of the
  other agents commitment store when forming new
  arguments.

38
Discussion dialogue moves
ltX, open, dialogue(discussion, ?)gt - starts the
discussion dialogue with topic ?, where ? is a
state belief . ltX, assert, lt?,?gt gt - where lt?,?gt
is an argument that X is asserting. ltX, missGo,
? gt - where ? is the topic of the dialogue. ltX,
close, dialogue(discussion, ?) gt - where ? is the
topic of the dialogue. ltX, open, dialogue(as, ?1
? ? ?n ? ?) gt - starts an embedded argument
search dialogue with topic ?1 ? ? ?n ? ?, where
?1 ? ? ?n ? ? is a domain belief.
39
Argument search dialogue moves
ltX, assert, lt?,?gt gt - where lt?,?gt is an argument
that X is asserting. ltX, question, ? gt - where ?
is a state belief. ltX, missGo, ? gt - where ? is
the topic of the dialogue. ltX, close,
dialogue(as, ?1 ? ? ?n ? ?) gt - where ?1 ?
? ?n ? ? is the topic of the dialogue.
40
Red arrows write, blue arrows read
Agent I
Agent R
Beliefs, Internal reasoning
Beliefs, Internal reasoning
CS
CS
Legal function. E.g. It is only legal to assert
an argument if you can form that argument from
your beliefs and the other agents commitment
store, and that argument is warranted given your
beliefs and the other agents commitment store.
Strategy function. E.g. If it is legal to make an
assert move then do so. If it is legal to make
more than one assert move then assert the
most preferred argument.
mT Next move
41
Dialogue outcomes

• Need a way of evaluating the outcome of
  terminated dialogues.
• Dialectical tree created from the union of the
  two commitment stores, with the topic of the
  dialogue at the root called the dialogue tree.
• The dialogue tree evolves over the course of the
  dialogue.

42
X
Y
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
43
X
Y
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
lt X, open, dialogue(discussion, b)gt
44
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
lt X, open, dialogue(discussion, b)gt
45
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt
46
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt
47
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
48
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt
49
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt
U
50
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo, bgt
51
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt
52
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt
53
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt
54
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt
55
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
56
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt
57
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt

58
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt
59
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt
60
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt
61
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1) (d,1) (d?c,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt ltY, assert, lt(d,1),(d?c,1),bgtgt
62
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1) (d,1) (d?c,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt ltY, assert, lt(d,1),(d?c,1),bgtgt
ltX, missGo, bgt
63
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1) (d,1) (d?c,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt ltY, assert, lt(d,1),(d?c,1),bgtgt
ltX, missGo, bgt ltY, close, dialogue(discussion
, b)gt
64
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1) (d,1) (d?c,1)
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt ltY, assert, lt(d,1),(d?c,1),bgtgt
ltX, missGo, bgt ltY, close, dialogue(discussion
, b)gt ltX, close, dialogue(discussion, b)gt
65
X
Y
CS
CS
(a?b,2) (c?b,1) (d?c,1)
(a,2) (c,1) (d,1)
(a,2) (c,1) (d,1)
(a,2) (a?b,2) (c,1) (c?b,1) (d,1) (d?c,1)
Warranted (undefeated) argument for b
lt X, open, dialogue(discussion, b)gt ltY,
open, dialogue(as, a?b) gt ltX, assert,
lt(a,2),agtgt ltY, close, dialogue(as, a?b)gt
ltX, close, dialogue(as, a?b)gt ltY, assert,
lt(a,2),(a?b,2),bgtgt ltX, missGo,
bgt ltY,open, dialogue(as, c?b)gt ltX,
assert, lt(c,1), cgtgt ltY, close,
dialogue(as, c?b)gt ltX, close, dialogue(as,
c?b)gt ltY, assert, lt(c,1),(c?b,1),bgtgt
ltX, missGo, bgt ltY,open, dialogue(as, d?c)gt
ltX, assert, lt(d,1), dgtgt ltY, close,
dialogue(as, d?c)gt ltX, close, dialogue(as,
d?c)gt ltY, assert, lt(d,1),(d?c,1),bgtgt
ltX, missGo, bgt ltY, close, dialogue(discussion
, b)gt ltX, close, dialogue(discussion, b)gt
66
What Im looking at

• Strategy functions very little work on them
• Investigating different strategies that give us
  different desirable dialogue properties

67
Sound and complete dialogues

• When is the outcome to a dialogue right?
• Compare the dialogue tree to the dialectical
  tree that we get from using the union of the two
  agents beliefs called the actual tree.
• Dialogue is sound if when the root node of the
  final dialogue tree is undefeated then the root
  node of the actual tree is also undefeated.
• Dialogue is complete if when the root node of
  the final dialogue tree is defeated then the root
  node of the actual tree is also defeated.

68
How can dialogue tree be better?

• Reduce the redundancies in the tree
• Reduce the number of interactions needed in the
  dialogue
• Improve the visualisation of the tree

69
A
C
B
D
E
F
I
G
F
G
G
H
H
H
70
A
C
B
D
E
F
I
G
F
G
G
H
H
H
71
A
C
B
D
E
F
I
G
F
G
G
H
H
H
Repeated node redundancy
72
A
C
B
E
F
G

• Efficient Strategy
• Removes repeated node redundancies
• Removes status redundancy type 2
• Reduces status redundancy type 1
• Reduces number of dialogue interactions

H
73
Conclusions

• Modular system for dialogue agents, allowing us
  to investigate different types of dialogues by
  changing the legal and strategy functions.
• Looking at different variations of legal and
  strategy function in and proving whether various
  desirable (and undesirable) properties hold of
  those functions in different scenarios.