T14 Argumentation for agent societies

Argumentation for Agent Societies
Part I

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1

Introduction to the tutorial

Argumentation for Agent Societies

(Some) answers to the following two questions:
1.  What’s argumentation?
! mainly today
2.  What is argumentation good for (in the MAS context)?
! mainly tomorrow

Let’s start with the first question…

2

An informal example (1)

We should run Large Hadron Collider The conclusion

LHC allows us to Understanding
understand the Laws the Laws of the The reason
of the Universe Universe is good

We are justified in believing that we should run LHC !

3


We should run Large Hadron Collider The conclusion

LHC allows us to Understanding
understand the Laws the Laws of the The reason
of the Universe Universe is good

We are justified in believing that we should run LHC !
BUT

In Argumentation (and in real life as well):
- reasons are not necessary “conclusive”
(they don’t logically entail conclusions)
- arguments and conclusions can be “retracted”
in front of new information, i.e. counterarguments
4


We should run Large Hadron Collider We should not run LHC

LHC allows us to Understanding LHC will generate Destroying
understand the Laws the Laws of the black holes Earth
of the Universe Universe is good destroying Earth is bad

Now we are justified in believing that we should not run LHC "

5




Black holes will
not destroy Earth

Black holes will
evaporate because
of Hawking radiation

Now we are again justified in believing that we should run LHC !
6




Hawking radiation Black holes will
does not exist not destroy Earth

Black holes will
Dr Azzeccagarbugli
evaporate because
says so

Now we are again justified in believing that we should not run LHC "
7




Hawking radiation Black holes will
does not exist not destroy Earth

Black holes will
Dr Azzeccagarbugli
evaporate because
says so

Dr Azzeccagarbugli Now we are again justified
is not expert in physics
in believing that we should

He is a lawyer run LHC !
8

What s argumentation? (1)

[Prakken 2011] Argumentation is the process of supporting claims with
grounds and defending them against attack.

[van Eemeren et al, 1996] Argumentation is a verbal and social activity
of reason aimed at increasing (or decreasing)
the acceptability of a controversial standpoint
for the listener or reader, by putting forward
a constellation of propositions intended
to justify (or refute) the standpoint
before a rational judge.

•  A framework for practical and uncertain reasoning able to cope
with partial and inconsistent knowledge
- philosophical roots: Aristotle, Toulmin (1958)
- in AI: R.P. Loui (1987), J. Pollock (1987), G. Simari & Loui (1992)
9


The elements of an argumentation system

•  The definition of argument
(possibly including an underlying logical language +
a notion of logical consequence)

•  The notion of attack and defeat (successful attack) between arguments

•  An argumentation semantics selecting acceptable (justified) arguments

10

Definition of argument: several possibilities (1)

•  ASSUMPTION-BASED ARGUMENTATION

Given a knowledge base (K, Ass)

Consistent theory Set of assumptions

ARGUMENT for p:

(A, p) such that

- A " Ass
- A # K is consistent and entails p
- There is no A’$A such that A’ # K entails p

ATTACKS to an argument: on its assumptions

[see Besnard&Hunter, Dung-Kowalski-Toni]
11


•  ARGUMENT SCHEMES

- correspond to recurring patterns of reasoning
- have associated “critical questions”

Example: Expert Testimony [WALTON 1996]

E is expert on D
E says P
P is in D
Therefore, P is the case

Critical questions:
Is E biased?
Is P consistent with what other experts say?
Is P consistent with known evidence?

12


•  ARGUMENT SCHEMES IN A MEDICAL APPLICATION

Viability Scheme
Organ O of donor D is available
No contraindications are known for donating O to recipient R
Therefore, organ O is viable

CRITICAL QUESTIONS:
Does donor D have a contraindication for donating organ O?

Nonviability Scheme

Donor D of organ O has condition C
C is a contraindication are for donating O
Therefore, organ O is nonviable

[Tolchinsky et al, 2006]
13


•  STABLE MARRIAGE PROBLEM
- Arguments of the kind <Alice, John>
- <Barbara, John> attacks <Alice, John> if John prefers Barbara to Alice

•  PLANNING
- Plans as arguments (that a goal will be achieved)
- Defeat between plans as attacks

………

In general

Arguments take different forms
(domain-independent vs. domain dependent)

Today examples will refer to rule-based approaches…

14

Rule-based approaches

•  ARGUMENT

a tree made up of rules of inference constructed from
a set of premises to reach a conclusion

•  Two kinds of rules: A (0.7)
% ¬C (0.7)
  A % B: deductive - indefeasible B (0.9)
  A ! B: non-deductive - defeasible
D (0.9) ! C (0.8)
•  A strength value may be associated to premises
and rules, giving rise to argument strength

See [J.Pollock, 1992], [G. Vreeswijk, 1997], …

15

Rule-based approaches (2)

Notion of conflict

–  Rebutting:
an argument attacks another one by denying its
[possibly intermediate] conclusion

–  Undercutting:
an argument attacks the applicability of a
defeasible rule of inference

Notion of defeat
A
An argument ' defeats ( iff: % ¬C
B
- ' undercuts (, or
- ' rebuts ( and D!C
' is not weaker than (
E!(D&C)
[Pollock 92]
16

Rule-based approaches (3)

EXAMPLE

REBUTTING DEFEAT

UNDERCUTTING
It’s It’s not DEFEAT Bob
raining raining is unreliable

Smith says Bob says Bob is drunk
it’s raining it’s not
raining
17

The ASPIC framework

•  One result of the European ASPIC Project (2004-2006)
•  Generalizes Pollock’s rule-based approach in several respects:
- any logical language (and an associated ‘contrariness function’
generalizing classical negation) can be adopted
- can be instantiated by a partial preorder on defeasible rules
- premises are distinguished into necessary, ordinary and assumption
premises (ordinary and assumption premises partially preordered)
- a partial preorder is assumed between arguments
•  Besnard & Hunter’s approach, Pollock’s system… can be obtained as
instances of ASPIC framework
•  See [H. Prakken, “An abstract framework for argumentation with
structured arguments”, Argument and Computation, 2010] for details.

18

Argumentation in the context of MAS (1)

Advantageous features

•  Several kinds of arguments can be represented
- epistemic reasoning
- practical reasoning
•  Able to handle uncertain and partial knowledge
- nonmonotonic notion of warrant:
1) wrt further information
2) wrt further reasoning steps (anytime reasoning framework)
•  A natural representation + justification of choices
(in terms of argument , rebuttal , counterargument …)
•  Argumentation has a dialogical side
(in terms of argument , attack , defence …)

19

Argumentation in the context of MAS (2)

The uses of argumentation (examples)

AUTONOMOUS MULTI-AGENT
REASONING INTERACTION
EPISTEMIC - Belief Revision
REASONING (arguing over beliefs)
- Trust management
(arguing over other - Dialectics in
agents reputation) Multiagent Interaction
PRATICAL - Decision making
REASONING (arguing about the
expected value of
possible actions)
20






21

What s abstract argumentation?

Usually “abstract” stands for a difficult thing… Here it means “simple”!





Abstract argumentation focuses on this aspect

22

Dung s argumentation framework

[Dung ’95]
AF = <A, %>
attack (or defeat) relation
[unspecified definition]

Arguments [origin and structure not specified]

•  Graphical representation as a directed graph [defeat graph], e.g.

Representation of LHC example

Representation of weather example

23

Dung s argumentation framework (2)

So, what remains to be done?

ARGUMENT EVALUATION:

GIVEN AN ARGUMENTATION FRAMEWORK,
DETERMINE THE JUSTIFICATION STATE
(ALSO CALLED DEFEAT STATUS) OF ARGUMENTS,
IN PARTICULAR: WHAT ARGUMENTS EMERGE UNDEFEATED
FROM THE CONFLICT, I.E. ARE ACCEPTABLE?

24

Argumentation semantics

•  Specification of a method for argument evaluation, or of
criteria to determine, given a set of arguments, their defeat status

Semantics
Argumentation Framework Defeat status

Undefeated

Defeat status Defeated

Provisionally Defeated

25

Labelling vs. extension-based semantics

LABELLING-BASED SEMANTICS

- Based on the notion of labelling
[assignment to each argument of a label from a predefined set]
- Specifies how to derive from an argumentation framework
a set of labellings
- Justification of arguments derived from the set of labellings

EXTENSION-BASED SEMANTICS

- Less general (at least in theory), but more common
kind of semantics
-  Based on the notion of extension
[set of arguments collectively acceptable ]

26

Extension-based semantics

Semantics S

Argumentation framework AF Set of extensions S(AF)

27

From extensions to defeat status

Set of extensions S(AF) Defeat/Justification Status

A common definition

•  Skeptically justified argument: belongs to all of the extensions
•  Credulously justified argument: belongs to at least one
•  Indefensible argument: does not belong to any extension

28

Unique-status vs. multiple-status semantics

Unique-Status Semantics

Unique extension: empty set
') ()
' and ( directly unjustified
(provisionally defeated)

') ()
Multiple-Status Semantics

') () ') ()

! ' and ( unjustified (provisionally defeated)

29

Relationship between labelling and
extension-based approaches
•  Almost all approaches adopt the set {IN, OUT, UNDEC}
- IN = belonging to the extension
- OUT = attacked by the extension
- UNDEC= not belonging to nor attacked by the extension

Unique-Status Semantics

') ()

UNDEC UNDEC
') ()
Multiple-Status Semantics

') () ') ()

IN OUT OUT IN

30

The core of Dung’s theory: complete “semantics”

Acceptability
' acceptable w.r.t. (“defended by”) S '
•  all attackers of ' are attacked by S

Admissible set S
S
•  conflict-free
•  every element acceptable w.r.t. S
(defends all of its elements) Complete semantics

Complete
IF
extension
also includes all
acceptable elements
w.r.t. itself All traditional semantics
select complete extensions
31

Complete “semantics”: examples

Chain
Admissible sets:
ø,
{'}, {', *}
') () *) Only one complete extension:

CO(AF) = {{', *}}

Nixon Diamond

') () All admissible sets
are complete

') () CO(AF) =
') ()
{ ø, {'}, {(} }

') ()
32

Complete “semantics”: examples (2)

Nixon Diamond + node

Admissible sets:
') () *) ø, {'}, {(}, {', *}

CO(AF) = {

') () *) ø

CO(AF) ') () *) {', *},

') () *) {(} }

33

The Grounded Semantics: a unique status approach

Grounded extension GE(AF):

Least complete extension

included in all extensions
of any traditional semantics

Grounded semantics is
the “most skeptical” one

Undefeated

Defeat status Defeated

Provisionally Defeated
34

Grounded semantics: examples

Chain

') () *) GE(AF) = {', *}

Nixon Diamond

') () GE(AF) = ø

Nixon Diamond + node

') () *) GE(AF) = ø

35

Floating arguments: a problem for grounded semantics

•  Actually, grounded semantics is polynomially computable
•  But sometimes a more discriminative behavior is desirable

THE CASE OF FLOATING ARGUMENTS

() ()

*) +) VS *) +)

') ')

Grounded Semantics What we (may) want

•  A problem for all possible unique status approaches

Let us consider multiple status approaches!

36

Stable Semantics

Stable extension = conflict-free set attacking all outside arguments

THE CASE OF FLOATING ARGUMENTS

() ()

*) +) *) +)

') ')

ST(AF) = { {', +}, {(, +} } ! + is justified

ODD-LENGTH CYCLES: A PROBLEM FOR STABLE SEMANTICS
')
No stable extension exists!
()

*) (and also imposing ø is not satisfactory)
37

Stable Semantics: an unsatisfactory patch

Stable extensions =
- conflict-free sets attacking all outside arguments, if there is one
- {ø}, otherwise

'1)

'3)

() *) '2)

ST(AF) = {ø } ! ( NOT justified!!!

38

Preferred semantics

Stable extensions are maximal complete extensions
•  conflict-free: by definition
•  admissible: every argument attacking an extension is outside
! attacked by the extension itself
•  maximal: no argument can be included!

Preferred semantics [P.M. Dung, 95]

Preferred extension

Maximal complete extension = max Set:
•  is conflict-free
•  defends all of its elements

39

Preferred semantics and floating arguments

()
*) +)
() ()
*) +) ')
*) +)
') ()
')
*) +)
')

PR(AF) = ST(AF) = { {', +}, {(, +} } ! + is justified

()
Grounded semantics: *) +)
')

40

Preferred semantics and odd-length cycles

')
PR(AF) = {ø}
() A big difference, isn’t it?
ST(AF) = ø
*)

GE(AF) = {ø}

No argument justified w.r.t. grounded and preferred semantics

•  As stable semantics, preferred semantics handles
the case of floating arguments
(differently wrt grounded semantics)
•  W.r.t. stable semantics it behaves “better”
in the case of odd-length cycles
(as the grounded semantics)

So, what remains to be done?
41

Semi-stable semantics (1)

•  Stable semantics
- clashes in some cases (odd-length cycles), however:
- a widely applied approach (default logic, stable models of
logic programming, answer set programming, etc.)
- a very credulous approach:
stable extensions are preferred but not viceversa
! justified arguments w.r.t. stable semantics are a
(sometimes strict) superset of arguments justified
w.r.t. preferred semantics, e.g.

,) ,)

*) ') () *) ') ()

+) +)

PR(AF)={{', !}, {"}} ST(AF) = {{', !}}
42

Semi-stable semantics (2)

•  Aims at guaranteeing existence of extensions [Verheij’96,
(differently from stable semantics) Caminada’06]
+ coinciding with stable semantics when stable extensions exist
(differently from preferred semantics)

•  Definition:
E- SST(AF) iff
E is a complete extension such that (E U {'| E% '}) is maximal

•  Main properties:
-  A semistable extension always exists (in the finite case!)
since a maximization requirement replaces “aggressive attack”
-  If a stable extension E exists, then (E U {'| E% '}) includes
all arguments, therefore semistable extensions # stable extensions
-  In any case, semistable extensions are preferred extensions, but
the opposite is not always true
43

Semi-stable semantics: examples

Example for existence
')
The unique admissible set is empty
() ! trivially maximizes (E U {'| E% '} )

*)

Example for backward compatibility
(and difference w.r.t. preferred semantics)

,)
PR(AF)={{', !}, {"}}
*) ') ()
SST(AF)={{', !}} )= ST(AF)
+)

44

CF2 semantics: motivation

Preferred/stable/semistable semantics and cycles

')
') ()
()

') () *)

')
') ()
()

*)

A different treatment for even and odd-length cycles.
Is it just a matter of symmetry and elegance?
45

Preferred/Semistable Semantics and cycles

PR(AF) =
') () +1) +2)
{{', +1}, {', +2},

VS {(, +2} }

46


PR(AF) =
') () +1) +2)
{{', +1}, {', +2},

VS {(, +2} }

()
*) +1) +2) PR(AF) = {{+2}}

')
VS

47


PR(AF) =
') () +1) +2)
{{', +1}, {', +2},

VS {(, +2} }

()
*) +1) +2) PR(AF) = {{+2}}

')
VS

()
PR(AF) =
{{', *, +2},
') *) +1) +2)
{(, +, +1}, {(, +, +2} }
+)
NOTE: grounded semantics yields the empty set in all cases 48

Pollock example revisited (1)

Jones Smith It’s It’s not
unreliable unreliable raining raining

Rob
unreliable

Rob says Smith says Jones says Smith says Bob says
Jones unrel. Rob unrel. Smith unrel. it’s raining it’s not
raining

49

Pollock example revisited (2)

Fred says
Jones unrel.

Jones
unreliable

Fred Smith It’s It’s not
unreliable unreliable raining raining

Rob
unreliable

Rob says Smith says Jones says Smith says Bob says
Fred unrel. Rob unrel. Smith unrel. it’s raining it’s not
raining
50

Preferred Semantics and Floating Arguments again…

()

[ two preferred
*) +) extensions]

')

VS

()
[empty set is the unique
*) +) .) preferred extension]

')

NB: same behavior for semistable semantics, stable semantics clashes,
grounded semantics yields the empty set in both cases
51

Strongly connected components (SCCs)

Equivalence classes under the relation of
path-equivalence (mutual reachability)

()
*) .1) .2)
')
()
*) .1) .2)
')
()
*) .1) .2)
')
52

Strongly connected components (SCCs)

SCCs form an acyclic graph

S3 S6

S1
S4

S2
S5
S7
S1 and S2 are initial SCCs
S1 is sccparent of S3, S4 and
S5
all other SCCs precede S7
53

CF2 semantics: the definition

E- CF2(AF) iff:

- E - MCF(AF) if |SCCSAF| = 1
- / S - SCCSAF
(E0S) - CF2(AF UP_AF(S,E)) otherwise

S

UP_AF(S,E)

54

CF2 semantics and odd-length cycles (1)

()

*)

')

() () ()
*) *) *)
') ') ')
Maximal conflict-free sets

55

CF2 semantics and odd-length cycles (2)

()
*) .1) .2)
')
{*,.2}, {',.1}, {',.2}, {(,.1}, {(,.2}
Yields several extensions
! all arguments not justified
in both cases
()
') *) .1) .2)
+) {',*,.2}, {(,+,.1}, {(,+,.2}

56

Floating arguments with a three-length cycle

()
*) +) .)
')
()
()
*) +) .)
*) +) .)
')
')

()
*) +) .)
')
Extensions: {*,.}, {',.}, {(,.} Defeat status
57

since we do not want problems in one in relation toknowledge base to affect other,
advantageous part of the consistency requirements, as explained in the following.
ly unrelated parts of the knowledge base. generates an argumentation framework based on a set of propositional formul
Suppose one Stable semantics is therefore not an option.
semantics have to be admissibility based? That is,rules desirable that each the propositional formulas express informatio
P and a set of defeasible is it D. The idea is that extension
an admissible (or even complete) one? Again, it ofthe defeasible rules an ultimate of thumb that can be subject
that isA problem is difficult to provide express(1)
beyond doubt and CF2 semantics rules
neral: one has to refer to specific contexts. In particular, following knowledge base:
exceptions. Now consider the in the context of instantiated
nerated from an underlying logical knowledge base, admissibility can be regarded as
P ¼ fjw; mw; sw; :ðjt ^ mt ^ stÞg
s in relation to consistency requirements, as explained in the following.
ne generates•  Considering some examples with structuredmw ) mt; sw ) it turns out that
an argumentation framework based on a set ¼ fjw ) jt; arguments, stg
D of propositional formulas
f defeasible rules D. The idea is that the propositional formulas express information and Suzy want to go cycling on
conflict-freenessexpress not entail consistency, e.g. Mary,
This example can be interpreted as follows: John,
nd doubt and the defeasible rules doesthat John wants to thaton thebe subject tois a reason to believe that John will b
tandem. The fact rules of thumb get can tandem (jw)
An introduction to argumentation semantics
Now consider the following knowledge base: The same holds for Mary and Suzy. However, since the tandem only has tw 407
on the tandem (jt).
seats, they :ðjt ^ mt ^ it with the three of them: :(jt 4 mt 4 st). From this knowledge base, w
P ¼ fjw; mw; sw;cannot be onstÞg A5
can then construct the 10 following arguments, based on an argument construction scheme
D ¼ fjw ) jt; mw ) mt; sw ) stg Amgoud (2007) and Prakken (2010):
presented in Caminada and
A1 5 :(jt 4 mt 4 st)
ple can be interpreted as follows: John, Mary, and Suzy want to go cycling on a
A2 A8 A3
A 5 tandem (jw) is a reason to believe that John will be
fact that John wants to get on2thejw
A3 5 mw
m (jt). The same holds for Mary and Suzy. However, since the tandem only has two
nnot be on it with the three A4 5 sw :(jt 4 mt 4 st). From this knowledge base, we
of them:
A1
A5 5 A2 ) jt on an argument construction scheme as
struct the 10 following arguments, based
A10 A9
Caminada and Amgoud (2007)5 A3 ) mt
A6 and Prakken (2010):
A7 5 A4 ) st
4 mt 4 st) A8 5 A6, A7, A1 - :jt
A9 5 A5, A7, A1 - :mt A4
A7 A6
A10 5 A5, A6, A1 - :st

) jt Assuming the principle of restrictednot enough to obtain consistent conclusions
Figure 20 Conflict-freeness is
rebutting23 it would then follow that A8 attacks A5, A9, an
A10, that A9 attacks A6, A8, and A10, and that A10 attacks A7, A8, and A9. This yields th 58
mt
argumentation also semi-stable and preferred extensions). It should be mentioned that the sets of conclusions
framework of Figure 20.

A problem of CF2 semantics (2)

•  By slightly complicating example, one can find a CF2 extension
which is not consistent
•  On the other hand, admissibility entails consistency
(proved by Caminada & Amgoud 2007, AIJ)

ADMISSIBILITY CAN BE A DESIRED REQUIREMENT

59

TO CONCLUDE…

GROUNDED

PRUDENT STABLE
STAGE PREFERRED

ROBUST SEMISTABLE

TOLERANT CF2

SUSTAINABLE IDEAL

EACH SEMANTICS HAS ITS OWN ROLE…
… WHICH ONE IS A GOOD RESEARCH QUESTION…!
60

What about general principles?

Here we consider only some semantics - see [Baroni & Giacomin ’06]

Grounded Preferred CF2 Semistable
CF-principle Yes Yes Yes Yes
Admissibility Yes Yes No Yes
Reinstatement Yes Yes No Yes
Weak reinstatement Yes Yes Yes Yes
CF-reinstatement Yes Yes Yes Yes
I-maximality Yes Yes Yes Yes
Directionality Yes Yes Yes No
Weak Skepticism Yes No Yes No
Adequacy [all forms]

Weak Resolution No Yes No Yes
Adequacy [all forms]

61

Applications and principles

PRINCIPLES

TO BE TO BE
STUDIED DEEPENED

APPLICATION
DOMAINS SEMANTICS

62

Semantics and attitude
SKEPTICAL REASONING CREDULOUS REASONING
E E
E1 W E2 : E1 C E2 :
/ E2 -E2, 1 E1 -E1 : E1" E2 / E1 -E1, 1 E2 -E2 : E1" E2

63

Fig. 3. S
+,
S
→ and S relations for any argumentatio

MANY THANKS
FOR YOUR KIND ATTENTION

64

Selected references (1)
Landmark argumentation papers and books

S. Toulmin, “The Uses of Argument”
Cambridge University Press, 1958.

R. P. Loui, “Defeat Among Arguments: a System of Defeasible Inference”,
Computational Intelligence, vol. 3(3), 1987.

J. Pollock, “Defeasible Reasoning”,
Cognitive Science, vol. 11(4), 1987.

G. Simari & R. P. Loui, “A mathematical treatment of defeasible reasoning and
its implementation , Artificial Intelligence, vol. 53(2-3), 1992.

Argumentation surveys

H. Prakken & G.A.W. Vreeswijk, “Logics for Defeasible Argumentation”,
in Handbook of Philosophical Logic, 2nd Edition, Kluwer Academic Publishers, 2001.

C.I. Chesnevar, A.G. Maguitman, R.P. Loui, “Logical models of argument”,
ACM Computing Surveys, vol. 32(4), 2000.
65

Argumentation semantics survey
P. Baroni, M. Caminada, M. Giacomin “An introduction to argumentation
semantics , The Knowledge Engineering Review, vol. 26(4),2011.

Books

D. Walton, “Fundamentals of critical argumentation ,
Cambridge University Press, 2006.

P. Besnard & A. Hunter, “Elements of Argumentation , MIT Press, 2008.

“Argumentation in Artificial Intelligence , edited by I. Rahwan and G. R. Simari,
Springer, 2009.

Dung s influential paper on abstract argumentation

P.M. Dung, “On the Acceptability of Arguments and Its Fundamental
Role in Nonmonotonic Reasoning, Logic Programming, and n-Person Games ,
Artificial Intelligence, vol. 77(2), 1995.
66

Semantics
P. Baroni, M. Giacomin, G. Guida, “SCC-recursiveness: a general schema
for argumentation semantics”
Artificial Intelligence, vol. 168(1-2), 2005.
B. Verheij, “Two approaches to dialectical argumentation:admissible sets
and argumentation stages”, Proc. of the 8th Dutch Conference on
Artificial Intelligence, 1996

M. Caminada, “Semi-Stable Semantics”, Proc. of 1st International Conference on
Computational Models of Arguments (COMMA 2006), 2006

P.M. Dung, P. Mancarella, F. Toni, “A dialectic procedure for sceptical,
assumption-based argumentation”, Proc. of 1st International Conference on
Computational Models of Arguments (COMMA 2006), 2006

S. Coste-Marquis, C. Devred, P. Marquis, "Prudent Semantics for Argumentation
Frameworks", Proc. of 17th IEEE International Conference on Tools with
Artificial Intelligence (ICTAI 2005), 2005

67


Semantics

H. Jakobovits & D. Vermeir, "Robust Semantics for Argumentation Frameworks",
Journal of Logic and Computation 9(2), 1999

P. Baroni, M. Giacomin, G. Guida, “SCC-recursiveness: a general schema
for argumentation semantics”

P. Baroni, M. Giacomin, “Resolution-based argumentation semantics”,
Proc. of 2nd International Conference on Computational Models of Arguments
(COMMA 2008), 2008

G.A. Bodanza, F.A. Tohmé, “Two approaches to the problems of self-attacking
arguments and general odd-length cycles of attack”
Journal of Applied Logic, to appear.

P. Baroni, P. Dunne, M. Giacomin, “Computational Properties of Resolution-based
Grounded Semantics”, IJCAI 2009, to appear.

68


General criteria for semantics evaluation and comparison

M. Caminada & L. Amgoud, “On the evaluation of argumentation formalisms”,

P. Baroni, M. Giacomin, G. Guida, “On principle-based evaluation of
extension-based argumentation semantics”, Artificial Intelligence,
vol. 171(10-15), 2007.

P. Baroni, M. Giacomin, Skepticism relations for comparing argumentation
semantics , International Journal of Approximate Reasoning, vol. 50(6), 2009.

69

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TO)%H5&,
B
I saw John killing Mary,
thus John killed Mary.

A
Wit1
If John did not kill Mary,
then John is innocent.

Judge

D
Mary was killed before 6 p.m.,
thus when Mary was killed
the show was still to begin

C
John was at the theater with Corner
me when Mary was killed,
thus John did not kill Mary.

Wit2

TO)%H5&,
B A(B) = 0.2
A(A) = 1.0 thus John killed Mary.

A
Wit1

Judge

A(D) = 0.3
D

C

Wit2 A(C) = 1.0

TO)%H5&,
B α(B) = 0.2
α(A) = 0.8 thus John killed Mary.

A
Wit1

Judge

α(D) = 0.3
D

C

Wit2 α(C) = 0.7

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