The hedgehog and the fox. An argumentation-based …groups.di.unipi.it › ~morge › publis › morge07mfimargo_show.pdfThe hedgehog and the fox. An argumentation-based decision support

The hedgehog and the fox.

An argumentation-based decision support system∗.

Maxime Morge† and Paolo Mancarella†

†Dipartimento di InformaticaUniversità di Pisa

MFI, May 2007

∗is supported by the Sixth Framework IST programme of the EC, under the 035200 ARGUGRID project.

Maxime Morge (ARGUGRID) MFI May 2007 1 / 16

Which kind of decision maker are you ? [Tetlock 06]

Hedgehog say:

◮ “it is annoying to listen to someone whocannot seem to make up his or her mind”

◮ “the most common error indecision-making is to abandon good ideastoo quickly”

Hedgehogs know one big thing, have intuitions, and never surrender.

Fox say:

◮ “when considering most conflicts, I canusually see how both sides could be right”

◮ “I prefer interacting with people whoseopinions are very different from my own”

Foxes knows many little things, interact, and change their mind.


Interaction-based explanation of the decision

Decision support system

decide

inform


Interaction-based explanation of the decision

Argumentation engine

challenge

argue

inform


Outline

Abstract decision structure

Concrete data structures

Argumentation framework

Interaction amongst arguments

Semantics and procedure

Summary & Future works



Influence diagram [Clemen. 06]

Suitable location (g0)

Regulation (g1) Accesible (g2)

Taxes (g3) Permit (g4) Assistance (g5) Sewage (g6) Transport (g7)

Decision

Sea? Road?

Decision

Abstract value

Concrete value



Influence diagram [Clemen. 06]

Suitable location (g0)

g2 ≺ g1

Regulation (g1)

g5 ≺ g4 ≺ g3 ≺ g4 + g5

Accesible (g2)

g7 ≺ g6

Taxes (g3)

a1 ≺ a2

Permit (g4)

a2 ≺ a1

Assistance (g5)

a2 ≺ a1

Sewage (g6)

a2?a1

Transport (g7)

a1 ≺ a2

Decision

London(a1) or Pisa(a2)

Sea? Road?

Sea(a2) ¬Road(a2) ≺ Road(a2)

Decision

Abstract value

Concrete value



Data strutures and priorities: hierarchies of conflicting rules

The theory compiles:

◮ goal rules such as R012 : g0 ← g1, g2

◮ epistemic rules such as R123 : b1 ← b2,¬b3

◮ decision rules such as R11 : g1 ← D(a1), b1

Different priorities for different rules:

◮ the priority over goal rules comes from preferences, eg R01 : g0 ← g1

has priority over R02 : g0 ← g2

◮ the priority over epistemic rules comes from probabilities,eg F1 : Road(pisa)← has priority over F2 : ¬Road(pisa)←

◮ the priority over decision rules come from expected utililies,eg R11 : g1 ← D(a1), b1 has priority over R12 : g1 ← D(a1), b2



A walk through the example

g0

g2 ≺ g1

g1

g5 ≺ g4 ≺ g3 ≺ g4 + g5

g2

g7 ≺ g6

g3 g4 g5 g6 g7

D(x)

Sea ? Road ?

The goal theory

R012 : g0 ← g1, g2

R1345 : g1 ← g3, g4, g5

R267 : g2 ← g6, g7

R145 : g1 ← g4, g5

R01 : g0 ← g1

R13 : g1 ← g3

R26 : g2 ← g6

R02 : g0 ← g2

R14 : g1 ← g4

R27 : g2 ← g7

R15 : g1 ← g5




g0

g1 g2

g3 g4 g5 g6 g7

D(x)

Sea ? Road ?

Sea(a2) ¬Road(a2) ≺ Road(a2)

The epistemic theory

F1 : Road(a2)←F2 : Sea(a2)←F3 : ¬Road(a2)←




g0

g1 g2

g3

a1 ≺ a2

g4

a2 ≺ a1

g5

a2 ≺ a1

g6

a2?a1

g7

a1 ≺ a2

D(x)

London (a1) or Pisa(a2)

Sea ? Road ?

The decision theory

R32 : g3 ← D(a2)R41 : g4 ← D(a1)R51 : g5 ← D(a1)R61 : g6 ← D(a1)R62 : g6 ← D(a2)R71(x) : g7 ← D(x), Road(x)R31 : g3 ← D(a1)R42 : g4 ← D(a2)R52 : g5 ← D(a2)R72(x) : g7 ← D(x), Sea(x)


Argumentation framework

Struture of arguments: abductive tree

Definition

An argument A = 〈conc, premise, hyp〉 is:

1. hypothetical, i.e. built upon an hypothesissent(A) = hyp(A)A = 〈D(pisa), ∅, [D(pisa)]〉 or A = 〈Sea(pisa), ∅, [Sea(pisa)]〉

2. trivial, i.e. built upon an unconditional ground statementsent(A) = premise(A)A = 〈Road(pisa), [Road(pisa)], ∅〉 orA = 〈¬Road(pisa), [¬Road(pisa)], ∅〉

3. tree, i.e. built upon a top rule where all literals in the body are theconclusions of subargument s.asent(A) = ∪Ai=subarg(A)sent(Ai ) ∪ body(R)A = 〈g7, (D(pisa), Sea(pisa)), (D(pisa))〉



Interaction: choice between different explanations

Definition (Attack relation)

attacks (A, B) iff conc(A) I sent(B)

⇒ build explanations:

◮ B1 = 〈g7, (D(pisa), Sea(pisa)), (D(pisa))〉;

◮ B2 = 〈g7, (D(pisa), Road(pisa)), (D(pisa))〉;

◮ A1 = 〈g7, (D(london), Sea(london)),(D(london), Sea(london))〉;

◮ A2 = 〈g7, (D(london), Road(london)),(D(london), Road(london))〉.



Interaction: choice between different explanations (cont.)

Definition (Hypothesis size)

1. if A is a hypothetical argument, then hypsize(A) = 1;

2. if A is a trivial argument, then hypsize(A) = 0

3. if A is a tree argument then hypsize(A) = ΣA′∈subarg(A)hypsize(A′).

Definition (Strength relation)

A1 a hypothetical argument, and A2, A3 two built arguments:

1. A2 ≻A A1;

2. If (top(A2) ≺ top(A3)) ∧ ¬(top(A3) ≺ top(A2)), then A3 ≻A A2;

3. If (top(A2) ∼ top(A3)) ∧ (hypsize(A2) ≤ hypsize(A3)) , thenA2 ≻

A A3;



Interaction: choice between different explanations (cont.)

Definition (Defeat relation)

A defeats B

1. attacks (A, B)

2. ¬(B ≻A A).

◮ B1 = 〈g7, (D(pisa), Sea(pisa)), (D(pisa))〉;

◮ B2 = 〈g7, (D(pisa), Road(pisa)), (D(pisa))〉;

◮ A1 = 〈g7, (D(london), Sea(london)), (D(london), Sea(london))〉;

◮ A2 = 〈g7, (D(london), Road(london)), (D(london), Road(london))〉.

Since

◮ A1/A2) attack B1/B2,

◮ (top(A2) ∼ top(B2)) ≺ (top(A1) ∼ top(B1)),

◮ hypsize(B1) = hypsize(B2) = 1 and hypsize(A1) = hypsize(A1) = 2,

B1 (resp. A1) defeats A2 (resp. B2) and B1 is stronger than A1.



Semantics: status of arguments/alternatives

Definition (Acceptability [Dung, Mancarella & Toni 07])

A set X of arguments is :

◮ admissible iff X does not attack itself and X attacks every argumentY such that Y attacks X;

◮ preferred iff X is maximally admissible;

◮ ideal iff X is admissible and it is contained in every preferred sets.

◮ The semantics is:◮ either credulous, eg admissible;◮ or sceptical, eg ideal, or sceptically preferred semantics.

Definition (Suggestion)

The decision D(a1) is suggested iff D(a1) is a hypothesis of one argumentin an admissible set.



Procedure and its implementation: meta-CaSAPI to relax

goals requirement and to make hypotheses



Take away MARGO (Multicriteria ARGumentation

framework for Opinion justification)

A argumentation framework for practical reasoning→֒ Formalization of a decision making

◮ Influence diagram→֒ Abstract representation

◮ Goal/Decision/Epistemic rules→֒ Specific data structures

◮ Priority over epistemic/goal/decision rules→֒ Intuitions about probability/preferences/expected utilities

◮ Abductive tree argument→֒ Interaction-based explanation of the decision



Outlook: Agents’ mind

◮ Design◮ Representation of

◮ state-of-mind (goals,plans, actions, beliefs,qualitive/quantitativepreferences)

◮ communications acts◮ contracts in state-of-mind

◮ Argumentation-based decision

◮ Implementationa Prolog prototypehttp://margo.sourceforge.ent

◮ Applicationreal-world scenarios in ebusiness

Body

Mind

◮ Goals

◮ Actions

◮ BeliefsPrior

itie

s

Argumentation engine

question/challenge

assert/argue



References

Philip E. TetlockExpert Political Judgment: How Good is It? How Can We Know?Princeton university press, 2006.

R. T. Clemen.Making Hard Decisions.Duxbury. Press, 1996.

Phan Minh Dung, Paolo Mancarella, Francesca ToniA dialectic procedure for sceptical, assumption-based argumentation,1st International Conference on Computational Models of Argument,September 2006.


Documents

The hedgehog and the fox. An argumentation-based …groups.di.unipi.it › ~morge › publis › morge07mfimargo_show.pdfThe hedgehog and the fox. An argumentation-based decision support