A Translation-based Approach for Revision of Argumentation Frameworks

(1)

A Translation-based Approach for Revision of Argumentation Frameworks

Sylvie Coste-Marquis S´ebastien Konieczny Jean-Guy Mailly Pierre Marquis

Centre de Recherche en Informatique de Lens Universit´e d’Artois – CNRS UMR 8188

14th European Conference on Logics in Artificial Intelligence September 24th - 26th – Madeira

1/25 AMANDE

(2)

Schematic Explanation of the Approach

I F: an argumentation framework

I σ: a semantics to define acceptable arguments

I ϕ: a propositional formula indicating how to reviseF

F, σ, ϕ

F ? ϕ

F encoded Revision ofF encoded σ-encoding

◦

?

σ-decoding

AGM Revision AF Revision

2/25 AMANDE

(3)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

2/25 AMANDE

(4)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

F encoded

Revision ofF encoded

σ-encoding

◦

?

σ-decoding

2/25 AMANDE

(5)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

2/25 AMANDE

(6)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

AGM Revision

AF Revision

2/25 AMANDE

(7)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

AGM Revision

AF Revision

2/25 AMANDE

(8)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

AGM Revision

AF Revision

2/25 AMANDE

(9)

Schematic Explanation of the Approach

F, σ, ϕ F ? ϕ

◦

?

σ-decoding

2/25 AMANDE

(10)

Plan

Introduction

Abstract Argumentation Belief Revision

Translation-based Revision Encoding

Distance-based Operators and Minimal Change Characterization of Operators in theacc Case Extensions of the Method

Conclusion and Future Work

3/25 AMANDE

(11)

Abstract Argumentation [Dung 1995]

I An abstract argumentation framework is a pair hA,Ri with R ⊆ A × A:

a b c

I An extension is a set of arguments that can be accepted together

I Different semantics to define the extensions: complete, stable, preferred, grounded, etc.

I The aim is to know whether an argument is accepted or not w.r.t. the chosen semantics σ

I An argumenta∈ Ais (skeptically) accepted iff it belongs to every extension of the AF w.r.t. the considered semanticsσ:

F|∼_σa⇔a∈\

Extσ(F)

4/25 AMANDE

(12)

AGM framework for Belief Revision

I Principles of Belief Revision:

I Primacy of update

I Consistency

I Minimal change

I Set of postulates: characterizes the “good” operators

[Alchourr´on, G¨ardenfors and Makinson 1985],[Katsuno et Mendelzon 1991] I Representation theorem: “An operator satisfies the postulates

iff it belongs to a particular class”

5/25 AMANDE

(13)

AGM framework for Belief Revision

I Primacy of update

I Consistency

I Minimal change

5/25 AMANDE

(14)

AGM framework for Belief Revision

I Primacy of update

I Consistency

I Minimal change

5/25 AMANDE

(15)

AGM framework for Belief Revision

I Primacy of update

I Consistency

I Minimal change

5/25 AMANDE

(16)

AGM framework for Belief Revision

I Primacy of update

I Consistency

I Minimal change

[Alchourr´on, G¨ardenfors and Makinson 1985],[Katsuno et Mendelzon 1991]

I Representation theorem: “An operator satisfies the postulates iff it belongs to a particular class”

5/25 AMANDE

(17)

AGM framework for Belief Revision

I Primacy of update

I Consistency

I Minimal change

[Alchourr´on, G¨ardenfors and Makinson 1985],[Katsuno et Mendelzon 1991]

I Representation theorem: “An operator satisfies the postulates iff it belongs to a particular class”

5/25 AMANDE

(18)

AFs Revision

I Aim: Incorporation of a new piece of information about the attack relation and/or the acceptance statuses of arguments

I Two kind of minimal change:

Attack 6= Acceptance

6/25 AMANDE

(19)

Propositional Language

I ∀x ∈A,acc(x) = x is skeptically accepted by F

I ∀x,y ∈A,att(x,y) =x attacksy in F

I PropA ={acc(x)|x ∈A} ∪ {att(x,y)|x,y ∈A}

I L_A is the propositional language built on the set of variables Prop_A and the connectives¬,∨,∧

7/25 AMANDE

(20)

Encoding an AF

σ-formula of F

Given an AFF =hA,Ri and a semanticsσ, theσ-formula ofF is f_σ(F) = ^

(x,y)∈R

att(x,y)∧ ^

(x,y)6∈R

¬att(x,y)

∧th_σ(A)

where theσ-theory ofA thσ(A) is a formula which encodes the semanticsσ.

8/25 AMANDE

(21)

Encoding an AF

σ-formula of F

Given an AFF =hA,Ri and a semanticsσ, theσ-formula ofF is f_σ(F) = ^

(x,y)∈R

att(x,y)∧ ^

(x,y)6∈R

¬att(x,y) ∧th_σ(A)

where theσ-theory ofA thσ(A) is a formula which encodes the semanticsσ.

8/25 AMANDE

(22)

Encoding the Stable Semantics (1)

Stable extensions of an AF F =hA,Ri [Besnard and Doutre 2004]

^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)

Example

F1= a b c d One stable extension: {a,c}

9/25 AMANDE

(23)

Encoding the Stable Semantics (1)

Stable extensions of an AF F =hA,Ri [Besnard and Doutre 2004]

^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)

Example

F1= a b c d One stable extension: {a,c}

9/25 AMANDE

(24)

Encoding the Stable Semantics (2)

Skeptical acceptance of an argument a_i

|= (^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

equivalent to

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

10/25 AMANDE

(25)

Encoding the Stable Semantics (2)

Skeptical acceptance of an argument a_i

|= (^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai) equivalent to

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

10/25 AMANDE

(26)

Encoding the Stable Semantics (3)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

I Knowledge of the AF is required a priori

I We useatt(x,y) to relax this requirement

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b∈A

(att(b,a)⇒ ¬b))⇒a_i)

Stable theory of the set A th_st(A) = V

ai∈A(acc(a_i)⇔ ∀a₁, . . . ,a_n, (V

a∈A(a⇔V

b∈A(att(b,a)⇒ ¬b))⇒ai))

11/25 AMANDE

(27)

Encoding the Stable Semantics (3)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b∈A

ai∈A(acc(a_i)⇔ ∀a₁, . . . ,a_n, (V

a∈A(a⇔V

11/25 AMANDE

(28)

Encoding the Stable Semantics (3)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

∀a₁, . . . ,a_n,(^

a∈A

(a⇔ ^

b∈A

ai∈A(acc(a_i)⇔ ∀a₁, . . . ,a_n, (V

a∈A(a⇔V

11/25 AMANDE

(29)

Encoding the Stable Semantics (3)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

∀a₁, . . . ,a_n,(^

a∈A

(a⇔ ^

b∈A

ai∈A(acc(a_i)⇔ ∀a₁, . . . ,a_n, (V

a∈A(a⇔V

11/25 AMANDE

(30)

Encoding the Stable Semantics (3)

∀a₁, . . . ,an,(^

a∈A

(a⇔ ^

b:(b,a)∈R

¬b)⇒ai)

∀a₁, . . . ,a_n,(^

a∈A

(a⇔ ^

b∈A

ai∈A(acc(a_i)⇔∀a₁, . . . ,a_n, (V

a∈A(a⇔V

11/25 AMANDE

(31)

Example

F₁ = a b c d

th_st(A) =

acc(a)⇔ ∀a,b,c,d,[[(a⇔((att(a,a)⇒ ¬a)∧(att(b,a)⇒ ¬b)

∧(att(c,a)⇒ ¬c)∧(att(d,a)⇒ ¬d)))

∧(b⇔((att(a,b)⇒ ¬a)∧(att(b,b)⇒ ¬b)

∧(att(c,b)⇒ ¬c)∧(att(d,b)⇒ ¬d)))

∧(c ⇔((att(a,c)⇒ ¬a)∧(att(b,c)⇒ ¬b)

∧(att(c,c)⇒ ¬c)∧(att(d,c)⇒ ¬d)))

∧(d ⇔((att(a,d)⇒ ¬a)∧(att(b,d)⇒ ¬b)

∧(att(c,d)⇒ ¬c)∧(att(d,d)⇒ ¬d)))]⇒a]

∧ acc(b)⇔ ∀a,b,c,d,[· · · ⇒b]

∧ acc(c)⇔ ∀a,b,c,d,[· · · ⇒c]

∧ acc(d)⇔ ∀a,b,c,d,[· · · ⇒d]

12/25 AMANDE

(32)

Example

F₁ = a b c d

th_st(A) =

∧(att(c,a)⇒ ¬c)∧(att(d,a)⇒ ¬d)))

∧(b⇔((att(a,b)⇒ ¬a)∧(att(b,b)⇒ ¬b)

∧(att(c,b)⇒ ¬c)∧(att(d,b)⇒ ¬d)))

∧(c ⇔((att(a,c)⇒ ¬a)∧(att(b,c)⇒ ¬b)

∧(att(c,c)⇒ ¬c)∧(att(d,c)⇒ ¬d)))

∧(d ⇔((att(a,d)⇒ ¬a)∧(att(b,d)⇒ ¬b)

∧(att(c,d)⇒ ¬c)∧(att(d,d)⇒ ¬d)))]⇒a]

∧ acc(b)⇔ ∀a,b,c,d,[· · · ⇒b]

∧ acc(c)⇔ ∀a,b,c,d,[· · · ⇒c]

∧ acc(d)⇔ ∀a,b,c,d,[· · · ⇒d]

12/25 AMANDE

(33)

Example

F₁ = a b c d

th_st(A) =

∧(att(c,a)⇒ ¬c)∧(att(d,a)⇒ ¬d)))

∧(b⇔((att(a,b)⇒ ¬a)∧(att(b,b)⇒ ¬b)

∧(att(c,b)⇒ ¬c)∧(att(d,b)⇒ ¬d)))

∧(c ⇔((att(a,c)⇒ ¬a)∧(att(b,c)⇒ ¬b)

∧(att(c,c)⇒ ¬c)∧(att(d,c)⇒ ¬d)))

∧(d ⇔((att(a,d)⇒ ¬a)∧(att(b,d)⇒ ¬b)

∧(att(c,d)⇒ ¬c)∧(att(d,d)⇒ ¬d)))]⇒a]

∧ acc(b)⇔ ∀a,b,c,d,[· · · ⇒b]

∧ acc(c)⇔ ∀a,b,c,d,[· · · ⇒c]

∧ acc(d)⇔ ∀a,b,c,d,[· · · ⇒d]

12/25 AMANDE

(34)

Example

F₁ = a b c d

th_st(A) =

∧(att(c,a)⇒ ¬c)∧(att(d,a)⇒ ¬d)))

∧(b⇔((att(a,b)⇒ ¬a)∧(att(b,b)⇒ ¬b)

∧(att(c,b)⇒ ¬c)∧(att(d,b)⇒ ¬d)))

∧(c ⇔((att(a,c)⇒ ¬a)∧(att(b,c)⇒ ¬b)

∧(att(c,c)⇒ ¬c)∧(att(d,c)⇒ ¬d)))

∧(d ⇔((att(a,d)⇒ ¬a)∧(att(b,d)⇒ ¬b)

∧(att(c,d)⇒ ¬c)∧(att(d,d)⇒ ¬d)))]⇒a]

∧ acc(b)⇔ ∀a,b,c,d,[· · · ⇒b]

∧ acc(c)⇔ ∀a,b,c,d,[· · · ⇒c]

∧ acc(d)⇔ ∀a,b,c,d,[· · · ⇒d]

12/25 AMANDE

(35)

Example

F₁ = a b c d

th_st(A) =

∧(att(c,a)⇒ ¬c)∧(att(d,a)⇒ ¬d)))

∧(b⇔((att(a,b)⇒ ¬a)∧(att(b,b)⇒ ¬b)

∧(att(c,b)⇒ ¬c)∧(att(d,b)⇒ ¬d)))

∧(c ⇔((att(a,c)⇒ ¬a)∧(att(b,c)⇒ ¬b)

∧(att(c,c)⇒ ¬c)∧(att(d,c)⇒ ¬d)))

∧(d ⇔((att(a,d)⇒ ¬a)∧(att(b,d)⇒ ¬b)

∧(att(c,d)⇒ ¬c)∧(att(d,d)⇒ ¬d)))]⇒a]

∧ acc(b)⇔ ∀a,b,c,d,[· · · ⇒b]

∧ acc(c)⇔ ∀a,b,c,d,[· · · ⇒c]

∧ acc(d)⇔ ∀a,b,c,d,[· · · ⇒d]

12/25 AMANDE

(36)

Example

F₁ = a b c d

I f_st(F₁) =th_st(A)∧V

(a,b)∈Ratt(a,b)∧V

(a,b)6∈R¬att(a,b)

I Propagating the values of theatt(x,y) variables, we get the values of the acc(x):

acc(a) =acc(c) =true and acc(b) =acc(d) =false So the arguments accepted byF₁ are:{a,c}

13/25 AMANDE

(37)

Reminder

F, σ, ϕ F ? ϕ

f_σ(F) f_σ(F)◦(ϕ∧th_σ(A)) Encoding

◦

?

Decoding

:Proj_att(Φ) arg(Mods_att)

14/25 AMANDE

(38)

Reminder

F, σ, ϕ F ? ϕ

◦

?

Decoding

14/25 AMANDE

(39)

Reminder

F, σ, ϕ F ? ϕ

◦

?

Decoding

14/25 AMANDE

(40)

Reminder

F, σ, ϕ F ? ϕ

◦

?

Decoding:Proj_att(Φ) arg(Mods_att)

14/25 AMANDE

(41)

Decoding Tools

I Proj_att(Φ): projection of the models of Φ on the variables att(x,y)

I arg(Modsatt): generation of AFs from models projected onatt(x,y)

Example of decoding

WithA={a,b}, the revised models could be:

Mod(Φ) ={{acc(a),¬acc(b),¬att(a,a),att(a,b),¬att(b,a),¬att(b,b)}}. So,Proj_att(Φ) ={{¬att(a,a),att(a,b),¬att(b,a),¬att(b,b)}}and

arg(Projatt(Φ)) ={F} with F the AF below:

a b

15/25 AMANDE

(42)

Decoding Tools

I arg(Modsatt): generation of AFs from models projected onatt(x,y) Example of decoding

Mod(Φ) ={{acc(a),¬acc(b),¬att(a,a),att(a,b),¬att(b,a),¬att(b,b)}}.

So,Proj_att(Φ) ={{¬att(a,a),att(a,b),¬att(b,a),¬att(b,b)}}and arg(Projatt(Φ)) ={F} with F the AF below:

a b

15/25 AMANDE

(43)

Decoding Tools

a b

15/25 AMANDE

(44)

Decoding Tools

a b

15/25 AMANDE

(45)

Translation-based Revision Operator

Translation-based Revision

Let◦ be a KM revision operator. For every semanticsσ, every AF F =hA,Ri and every formula ϕ∈ L_A, the associated

translation-based revision operator? is defined by:

F ? ϕ=arg(Proj_att(f_σ(F)◦(ϕ∧th_σ(A))))

16/25 AMANDE

(46)

Translation-based Revision Operator

Translation-based Revision

Let◦ be a KM revision operator. For every semanticsσ, every AF F =hA,Ri and every formula ϕ∈ L_A, the associated

translation-based revision operator? is defined by:

F ? ϕ=arg(Proj_att(f_σ(F)◦(ϕ∧th_σ(A))))

16/25 AMANDE

(47)

Distance-based Revision

Letd be a distance between interpretations on L_A. Given a formulaψ∈ L_A, the pre-order ≤_ψ is defined by:

ω≤_ψ ω⁰ iff d(ω,Mod(ψ))≤d(ω⁰,Mod(ψ))

The KM revision operator ◦_d based ond is defined by: Mod(ψ◦_dα) = min(Mod(α),≤_ψ)

The AF revision operator ?_d based on distance d is defined by: F ?_dϕ=arg(Projatt(fσ(F)◦_d(ϕ∧thσ(A))))

17/25 AMANDE

(48)

Distance-based Revision

ω≤_ψ ω⁰ iff d(ω,Mod(ψ))≤d(ω⁰,Mod(ψ)) The KM revision operator ◦_d based ond is defined by:

Mod(ψ◦_dα) = min(Mod(α),≤_ψ)

The AF revision operator ?_d based on distance d is defined by: F ?_dϕ=arg(Projatt(fσ(F)◦_d(ϕ∧thσ(A))))

17/25 AMANDE

(49)

Distance-based Revision

ω≤_ψ ω⁰ iff d(ω,Mod(ψ))≤d(ω⁰,Mod(ψ)) The KM revision operator ◦_d based ond is defined by:

Mod(ψ◦_dα) = min(Mod(α),≤_ψ)

The AF revision operator ?_d based on distance d is defined by:

F ?_dϕ=arg(Projatt(fσ(F)◦_d(ϕ∧thσ(A))))

17/25 AMANDE

(50)

Distances and Minimal Change

Priority to Minimal Change on Acceptance Statuses LetAbe a set of arguments, and N=|A|²+ 1.

d_H^acc(ω, ω⁰) =

N×

P

a∈A(ω(acc(a))⊕ω⁰(acc(a))) +P

a,b∈A(ω(att(a,b))⊕ω⁰(att(a,b)))

Priority to Minimal Change on the Attack Relation LetAbe a set of arguments, and N=|A|+ 1.

d_H^att(ω, ω⁰) = P

a∈A(ω(acc(a))⊕ω⁰(acc(a)))

+N×P

18/25 AMANDE

(51)

Distances and Minimal Change

d_H^acc(ω, ω⁰) = N×P

Priority to Minimal Change on the Attack Relation LetAbe a set of arguments, and N=|A|+ 1.

+N×P

18/25 AMANDE

(52)

Distances and Minimal Change

d_H^acc(ω, ω⁰) = N×P

a,b∈A(ω(att(a,b))⊕ω⁰(att(a,b))) Priority to Minimal Change on the Attack Relation LetAbe a set of arguments, and N=|A|+ 1.

+N×P

18/25 AMANDE

(53)

Example

F1= a b c d Accepted arguments: {a,c} Revision byϕ=acc(a)∧ ¬att(a,b) with priority to minimal change on...

...the attack relation: 1 acceptance status change

I {a}

1 attack change

I removal of (a,b)

F₂= a b c d

...acceptance statuses: 0 status change

I {a,c} 2 attack changes

I removal of (a,b)

I addition of (d,b)

F₃= a b c d

19/25 AMANDE

(54)

Example

...the attack relation:

1 acceptance status change

I {a}

1 attack change

I removal of (a,b)

F₂= a b c d

...acceptance statuses: 0 status change

I {a,c} 2 attack changes

I removal of (a,b)

I addition of (d,b)

F₃ = a b c d

19/25 AMANDE

(55)

Example

...the attack relation:

1 acceptance status change

I {a}

1 attack change

I removal of (a,b)

F₂= a b c d

...acceptance statuses:

0 status change

I {a,c}

2 attack changes

I removal of (a,b)

I addition of (d,b)

F3 = a b c d

19/25 AMANDE

(56)

Restriction to Acceptance Formulae

Postulates adapted from the standard belief revision

[Katsuno et Mendelzon 1991]

(AS1) Sc_σ(F ? ϕ)⊆ S(ϕ)

(AS2) IfSc_σ(F)∩ S(ϕ)6=∅, then Sc_σ(F ? ϕ) =Sc_σ(F)∩ S(ϕ)

(AS3) Ifϕis acc-consistent, then Sc_σ(F ? ϕ)6=∅ (AS4) Ifϕ≡_acc ψ, thenSc_σ(F ? ϕ) =Sc_σ(F ? ψ) (AS5) Scσ(F ? ϕ)∩ S(ψ)⊆Scσ(F ?(ϕ∧ψ)) (AS6) IfScσ(F ? ϕ)∩ S(ψ)6=∅, then

Scσ(F ?(ϕ∧ψ))⊆Scσ(F ? ϕ)∩ S(ψ)

20/25 AMANDE

(57)

AF Revision based on a Distance

Proposition

Given a pseudo-distanced between sets of arguments, and an AF F,≤^d_F is the total pre-order between sets of arguments defined by:

ε1≤^d_F ε2 iffd(ε1,Scσ(F))≤d(ε2,Scσ(F)).

Givenϕandacc-formula,the revision operator based on the pseudo-distance d ?d which satisfies

Sc_σ(F ?_d ϕ) = min(S(ϕ),≤^d_F) satisfies(AS1)- (AS6).

21/25 AMANDE

(58)

Coming Back to Minimal Change on Arguments Statuses

Proposition

The revision operator with priority to minimal change on the arguments statuses, restricted to acceptance formulae, satisfies postulates(AS1)-(AS6).

Intuition: can be proved by reducing this operator to another one based on a distance between sets of arguments.

22/25 AMANDE

(59)

Possible Extensions of the Approach

Open World Revision

GivenF =hA,Ri an AF,B a non-empty set of arguments such thatA∩B=∅,ϕ∈ L_A∪B a formula and◦ a KM revision operator, the associatedopen world revision operator?_B is defined by:

F ?B ϕ=arg(Projatt(fσ(F)◦(ϕ∧thσ(A∪B))))

Constrained Revision

GivenF =hA,Ri an AF,ϕ, µ∈ L_A two formulae and◦a KM revision operator, the associatedµ-constrained revision operator is defined by:

F ?_µϕ=arg(Proj_att(f_σ(F)◦(ϕ∧th_σ(A)∧µ)))

23/25 AMANDE

(60)

Possible Extensions of the Approach

Open World Revision

GivenF =hA,Ri an AF,B a non-empty set of arguments such thatA∩B=∅,ϕ∈ L_A∪B a formula and◦ a KM revision operator, the associatedopen world revision operator?_B is defined by:

F ?B ϕ=arg(Projatt(fσ(F)◦(ϕ∧thσ(A∪B)))) Constrained Revision

GivenF =hA,Ri an AF,ϕ, µ∈ L_A two formulae and ◦a KM revision operator, the associatedµ-constrained revision operator is defined by:

F ?_µϕ=arg(Proj_att(f_σ(F)◦(ϕ∧th_σ(A)∧µ)))

23/25 AMANDE

(61)

Summary of this Work

I Revision method for AFs by translation into propositional logic

I Generic method: works for any semantics

I Extended to open world revision and constrained revision

I Use of a rich language:acc(x) and att(x,y)

I Encoding skeptical acceptance for stable and complete semantics

I Definition of a family of revision operators: distance-based revision operators

I Operators adapted to both kind of minimal change: acceptance statuses and attacks

I Characterization of revision operators restricted to theacc case

24/25 AMANDE

(62)

Future Work

I Characterization of other semantics and credulous acceptance

I Rationality postulates for other kinds of operators:

I Minimal change on the attack relation

I Formulae on attacks/Unrestricted formulae

I Open world revision, constrained revision

I Implementations of revision operators: SAT solvers

Thank you for your attention!

25/25 AMANDE

(63)

Future Work

I Characterization of other semantics and credulous acceptance

I Rationality postulates for other kinds of operators:

I Minimal change on the attack relation

I Formulae on attacks/Unrestricted formulae

I Open world revision, constrained revision

I Implementations of revision operators: SAT solvers Thank you for your attention!

25/25 AMANDE