argumentation logics lecture 7: argumentation with structured arguments (3) rationality postulates,...
TRANSCRIPT
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Argumentation LogicsLecture 7:
Argumentation with structured arguments (3)
Rationality postulates, Self-defeat
Henry PrakkenChongqing
June 4, 2010
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Overview Argumentation with structured
arguments: Rationality postulates Self-defeat Odd and even defeat cycles
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Rationality postulates(Caminada & Amgoud 2007)
Let E be any stable, preferred or grounded extension:
1. If B Sub(A) and A E then B E
2. The set {| = Conc(A) for some A E } is
closed under RS; directly and indirectly consistent.
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Rationality postulatesfor ASPIC system
Closure under subarguments always satisfied
Direct and indirect consistency: without ‘real’ preferences satisfied if
Rs closed under transposition, or AS closed under contraposition (and some further conditions)
with ‘real’ preferences satisfied if in addition a is weakest or last-link ordering
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Subtleties concerning rebuttals (1)
d1: Ring Married d2: Party animal Bachelor s1: Bachelor ¬Married K: Ring, Party animal
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Subtleties concerning rebuttals (2)
d1: Ring Married d2: Party animal Bachelor s1: Bachelor ¬Married s2: Married ¬Bachelor K: Ring, Party animal
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Subtleties concerning rebuttals (3)
Rd = {, }Rs = all deductively valid inference rulesK: d1: Ring Married d2: Party animal Bachelor n1: Bachelor ¬Married Ring, Party animal
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Parallel ‘self-defeat’
p p
q q
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Serial self-defeat
p
A’
q,r p
A’ A
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r1: W says that p p
r2: W is unreliable ¬r1
k1: Alice says that Alice is unreliable
¬r1
A is unreliable
A: “A is unreliable”
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¬r1
A is unreliable
A: “A is unreliable”
J is the killer
A: “J is the killer”
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¬r1
A is unreliable
A: “A is unreliable”
J is the killer
A: “J is the killer”
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¬r1
A is unreliable
A: “A is unreliable”
J is the killer
A: “J is the killer”
J is the not killer
B: “J is not the killer”
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A B
C
DE
A: Alice says that Bob is unreliable, so Bob is unreliable
B: Bob says that Carole is unreliable, so Carole is unreliable
C: Carole says that Alice is unreliable, so Alice is unreliable
D: Bob says that John was the killer,so John was the killer
E: Eric says that John was not the killer,so John was not the killer
R: W says that p p
Exception: W is unreliable
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A: Alice says that Bob is unreliable, so Bob is unreliable
B: Bob says that Carole is unreliable, so Carole is unreliable
C: Carole says that Fred is unreliable, so Fred is unreliable
F: Fred says that Alice is unreliable,so Alice is unreliable
D: Bob says that John was the killer,so John was the killer
R: W says that p p
A B
DE
CFE: Eric says that John was not the killer,so John was not the killer
Exception: W is unreliable
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A: Alice says that Bob is unreliable, so Bob is unreliable
B: Bob says that Carole is unreliable, so Carole is unreliable
C: Carole says that Fred is unreliable, so Fred is unreliable
F: Fred says that Alice is unreliable,so Alice is unreliable
D: Bob says that John was the killer,so John was the killer
R: W says that p p
A B
DE
CFE: Eric says that John was not the killer,so John was not the killer
Exception: W is unreliable
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A B
C
DE
A B
DE
CF
1. An argument is In if all arguments defeating it are Out.2. An argument is Out if it is defeated by an argument that is In.
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A B
C
DE
A B
DE
CF
1. An argument is In if all arguments defeating it are Out.2. An argument is Out if it is defeated by an argument that is In.
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A B
C
DE
A B
DE
CF
1. An argument is In if all arguments defeating it are Out.2. An argument is Out if it is defeated by an argument that is In.
E is not justifiedE is justified
3. An argument is justified if it is In in all labellings
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A B
DE
CF
S defends A if all defeaters of A are defeated by a member of S
S is admissible if it is conflict-free and defends all its members
{A,C,E} is admissible …
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A B
DE
CF
S defends A if all defeaters of A are defeated by a member of S
S is admissible if it is conflict-free and defends all its members
{A,C,E} is admissible …
{B,D,F} is admissible …
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A B
C
DE
S defends A if all defeaters of A are defeated by a member of S
S is admissible if it is conflict-free and defends all its members
{E} is admissible …
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A B
C
DE
S defends A if all defeaters of A are defeated by a member of S
S is admissible if it is conflict-free and defends all its members
{E} is admissible …
but {B,D} is not …
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A B
C
DE
S defends A if all defeaters of A are defeated by a member of S
S is admissible if it is conflict-free and defends all its members
{E} is admissible …
but {B,D} is not …
and {A,B,D} is not
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A problem(?) with grounded semantics
We have: We want(?):
A B
C
D
A B
C
D
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A problem(?) with grounded semantics
A B
C
D
A = Frederic Michaud is French since he has a French nameB = Frederic Michaud is Dutch since he is a marathon skaterC = F.M. likes the EU since he is European (assuming he is not Dutch or French)D = F.M. does not like the EU since he looks like a person who does not like the EU
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A problem(?) with grounded semantics
A B
C
D
A = Frederic Michaud is French since Alice says soB = Frederic Michaud is Dutch since Bob says soC = F.M. likes the EU since he is European (assuming he is not Dutch or French)D = F.M. does not like the EU since he looks like a person who does not like the EU
E
E = Alice and Bob are unreliable since they contradict each other