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Huimin Dong Norbert Gratzl Open Reading for Free Choice Permission A Perspective from Substructural Logics Colloquium Logicum 2016, Universitt Hamburg September 12th 2016, Hamburg Outlines Motivations Open Reading Substructural Logics An

SLIDE 1

Huimin Dong Norbert Gratzl

Open Reading for Free Choice Permission

A Perspective from Substructural Logics

Colloquium Logicum 2016, Universität Hamburg September 12th 2016, Hamburg

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Outlines

Motivations Open Reading Substructural Logics An Example Conclusions

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 2 / 18

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History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

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History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

SLIDE 5

History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

SLIDE 6

History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

SLIDE 7

History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

SLIDE 8

History

Standard Deontic Logic: Permission =df the dual of Obligation

O(A ∧ B) ⊂⊃ OA ∧ OB P(A ∨ B) ⊂⊃ PA ∨ PB

Many faces of permissions: strong/weak permission, explicit/implied/tacit permission, free choice permission (FCP), open reading, etc. Dynamic approach of free choice permission: P(A) = [A]¬Violation Canonical Form of FCP: P(A ∨ B) ⊃ PA ∧ PB

G.H. von Wright. An essay in deontic logic and the general theory of action. 1968.

F. Dignum, J.-J. Ch. Meyer, and R.J. Wieringa. Free choice and contextually permitted actions.

Studia Logica, 1996.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 3 / 18

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Problems of FCP

1 PA ⊃ P(A ∧ B)

Monotonic case: Vegetarian free lunch P(Order) ⊃ P(Order ∧ not Pay) Resource insensitive case: P(Eat a cookie) ⊃ P(Eat a cookie ∧ Eat a cookie)

2 P(A∨ ∼ A) ⊃ PB

Irrelevant case: P(Open Window ∨ not Open Window) ⊂⊃P(Sell House ∨ not Sell House) ⊃P(Sell House)

Sven Ove Hansson. The varieties of permissions. Handbook of Deontic Logic and Normative Systems, volume 1. 2013.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 4 / 18

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Problems of FCP

1 PA ⊃ P(A ∧ B)

Monotonic case: Vegetarian free lunch P(Order) ⊃ P(Order ∧ not Pay) Resource insensitive case: P(Eat a cookie) ⊃ P(Eat a cookie ∧ Eat a cookie)

2 P(A∨ ∼ A) ⊃ PB

Irrelevant case: P(Open Window ∨ not Open Window) ⊂⊃P(Sell House ∨ not Sell House) ⊃P(Sell House)

Sven Ove Hansson. The varieties of permissions. Handbook of Deontic Logic and Normative Systems, volume 1. 2013.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 4 / 18

SLIDE 11

Problems of FCP

1 PA ⊃ P(A ∧ B)

Monotonic case: Vegetarian free lunch P(Order) ⊃ P(Order ∧ not Pay) Resource insensitive case: P(Eat a cookie) ⊃ P(Eat a cookie ∧ Eat a cookie)

2 P(A∨ ∼ A) ⊃ PB

Irrelevant case: P(Open Window ∨ not Open Window) ⊂⊃P(Sell House ∨ not Sell House) ⊃P(Sell House)

Sven Ove Hansson. The varieties of permissions. Handbook of Deontic Logic and Normative Systems, volume 1. 2013.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 4 / 18

SLIDE 12

Problems of FCP

1 PA ⊃ P(A ∧ B)

Monotonic case: Vegetarian free lunch P(Order) ⊃ P(Order ∧ not Pay) Resource insensitive case: P(Eat a cookie) ⊃ P(Eat a cookie ∧ Eat a cookie)

2 P(A∨ ∼ A) ⊃ PB

Irrelevant case: P(Open Window ∨ not Open Window) ⊂⊃P(Sell House ∨ not Sell House) ⊃P(Sell House)

Sven Ove Hansson. The varieties of permissions. Handbook of Deontic Logic and Normative Systems, volume 1. 2013.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 4 / 18

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Possible Solutions

Resource Sensitivity

Chris Barker. Freechoicepermissionasresource-sensitivereasoning. Semantics and Pragmat- ics, 2010.

Negation

Sun Xin and H. Dong. The deontic dilemma of action negation, and its solution. LOFT 2014.

Three Difgiculties in FCP

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

and so on...

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 5 / 18

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Our Strategy

1 Open Reading (OR):

An action type A is permitted ifg each token of A is normatively OK.

2 FCP inference

A ⊸ B ⊢ PB ⊃ PA

3 Our two-fold strategy: 1 To avoid the problems: (A ∧ B) ⊸ A, (A ∧ ⋯ ∧ A) ⊸ A, and

(A∨ ∼ A) ⧟ (B∨ ∼ B)

2 To save the plausible case:

(Order ∧ Pay) ⊸ Order ⊢ P(Order) ⊃ P(Order ∧ Pay)

4 A ⊸ B: “If A, normally, then B.”

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 6 / 18

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Our Strategy

1 Open Reading (OR):

An action type A is permitted ifg each token of A is normatively OK.

2 FCP inference

A ⊸ B ⊢ PB ⊃ PA

3 Our two-fold strategy: 1 To avoid the problems: (A ∧ B) ⊸ A, (A ∧ ⋯ ∧ A) ⊸ A, and

(A∨ ∼ A) ⧟ (B∨ ∼ B)

2 To save the plausible case:

(Order ∧ Pay) ⊸ Order ⊢ P(Order) ⊃ P(Order ∧ Pay)

4 A ⊸ B: “If A, normally, then B.”

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 6 / 18

SLIDE 16

Our Strategy

1 Open Reading (OR):

An action type A is permitted ifg each token of A is normatively OK.

2 FCP inference

A ⊸ B ⊢ PB ⊃ PA

3 Our two-fold strategy: 1 To avoid the problems: (A ∧ B) ⊸ A, (A ∧ ⋯ ∧ A) ⊸ A, and

(A∨ ∼ A) ⧟ (B∨ ∼ B)

2 To save the plausible case:

(Order ∧ Pay) ⊸ Order ⊢ P(Order) ⊃ P(Order ∧ Pay)

4 A ⊸ B: “If A, normally, then B.”

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 6 / 18

SLIDE 17

Our Strategy

1 Open Reading (OR):

An action type A is permitted ifg each token of A is normatively OK.

2 FCP inference

A ⊸ B ⊢ PB ⊃ PA

3 Our two-fold strategy: 1 To avoid the problems: (A ∧ B) ⊸ A, (A ∧ ⋯ ∧ A) ⊸ A, and

(A∨ ∼ A) ⧟ (B∨ ∼ B)

2 To save the plausible case:

(Order ∧ Pay) ⊸ Order ⊢ P(Order) ⊃ P(Order ∧ Pay)

4 A ⊸ B: “If A, normally, then B.”

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 6 / 18

SLIDE 18

Our Strategy

1 Open Reading (OR):

An action type A is permitted ifg each token of A is normatively OK.

2 FCP inference

A ⊸ B ⊢ PB ⊃ PA

3 Our two-fold strategy: 1 To avoid the problems: (A ∧ B) ⊸ A, (A ∧ ⋯ ∧ A) ⊸ A, and

(A∨ ∼ A) ⧟ (B∨ ∼ B)

2 To save the plausible case:

(Order ∧ Pay) ⊸ Order ⊢ P(Order) ⊃ P(Order ∧ Pay)

4 A ⊸ B: “If A, normally, then B.”

AlbertJ.J.Anglberger, H.Dong, andOlivierRoy. Openreadingwithoutfreechoice. DEON2014.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 6 / 18

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Why Substructural Logic?

To achieve a systematic view of semantic variety in the landscape of logics for FCP.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 7 / 18

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Language

Definition (Formulas)

The set L of well-formed formulas of normality is defined as follows: A := p ∣ ⊥ ∣ ¬A ∣ (A ⊎ A) ∣ (A ◦ A) ∣ (A ⊸ A) ∣ P(A) where p ∈ Act0 where Act0 is the set of all atomic propositions with regards to actions. A ⊃ B =def ¬A ⊎ B.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 8 / 18

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Examples

How to understand A ◦ B:

“doing A together with doing B” concurrent action: Listen ◦ Write Note

How to understand A ⊸ B:

“doing A counting as doing B” count-as relations: Cycle ⊸ Travel By Vehicle, Order Lunch ⊸ Pay

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 9 / 18

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Examples

How to understand A ◦ B:

“doing A together with doing B” concurrent action: Listen ◦ Write Note

How to understand A ⊸ B:

“doing A counting as doing B” count-as relations: Cycle ⊸ Travel By Vehicle, Order Lunch ⊸ Pay

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 9 / 18

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Language

Definition (Structures)

The set S of structures of normality is defined as follows: X := A ∣ 1 ∣ (X; X) ∣ (X, X). where A ∈ L is a well-formed formula.

X[Y] means a structure X with a substructure Y, while X[Z/Y] means a structure X with replacing the occurrences of the substructure Y by Z.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 10 / 18

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Frames

A frame for normality is a tuple F = ⟨W, M, OK⟩ where W is a non-empty set of events M ⊆ W × W × W is a ternary relation on W OK ⊆ W × W is a binary relation on W Possible readings:

1 Mwyz:

An event w combining/composing with an event y leads to an event z.

2 OK(y, w):

Seeing from event w, y is normatively OK.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 11 / 18

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Frames

A frame for normality is a tuple F = ⟨W, M, OK⟩ where W is a non-empty set of events M ⊆ W × W × W is a ternary relation on W OK ⊆ W × W is a binary relation on W Possible readings:

1 Mwyz:

An event w combining/composing with an event y leads to an event z.

2 OK(y, w):

Seeing from event w, y is normatively OK.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 11 / 18

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Frames

A frame for normality is a tuple F = ⟨W, M, OK⟩ where W is a non-empty set of events M ⊆ W × W × W is a ternary relation on W OK ⊆ W × W is a binary relation on W Possible readings:

1 Mwyz:

An event w combining/composing with an event y leads to an event z.

2 OK(y, w):

Seeing from event w, y is normatively OK.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 11 / 18

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Models

Let a tuple M = ⟨F, V⟩ be a model based on a frame F for normality, a function V : Act0 → ℘(W) assigning a set of events such that V(p) ⊆ W for all p ∈ Act0, where p ∈ Act0. A well-formed formula A ∈ is true at event w in model M, written M, w ⊧ A, and a structure X is true at w in M, written M, w ⊧ X, are defined as follows: M, w ⊧ p ifg w ∈ V(p) M, w / ⊧ ⊥ for all w ∈ W M, w ⊧ ¬A ifg M, w / ⊧ A M, w ⊧ A ⊎ B ifg M, w ⊧ A or M, w ⊧ B M, w ⊧ A ⊸ B ifg ∀y, z ∈ W.(M, y ⊧ A & Mwyz ⇒ M, z ⊧ B) M, w ⊧ A ◦ B ifg ∃y, z ∈ W. (M, y ⊧ A, M, z ⊧ B & Myzw) M, w ⊧ PA ifg ∀y, z ∈ W. (M, y ⊧ A ⇒ OK(y, w)) M, w ⊧ 1 for each w ∈ W M, w ⊧ X; Y ifg ∃y, z ∈ W. (M, y ⊧ X, M, z ⊧ Y & Myzw) M, w ⊧ X, Y ifg M, w ⊧ X and M, w ⊧ Y

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 12 / 18

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A Basic Logic

A basic sequent calculus N0 of normality: (◦R) X ⊢ A Y ⊢ B X; Y ⊢ A ◦ B (◦L) X[A; B] ⊢ C X[A ◦ B] ⊢ C (⊸ R) X; A ⊢ B X ⊢ A ⊸ B (⊸ L) X ⊢ A Y[B] ⊢ C Y[A ⊸ B; X] ⊢ C (Id) p ⊢ p where p ∈ Act0 (Cut) X ⊢ A Y[A] ⊢ B Y[X/A] ⊢ B (Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C (OR) X; A ⊢ B X, P(B) ⊢ P(A)

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 13 / 18

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One Extension NRaM

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ◦ B) ⊸ ⊥) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 14 / 18

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Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

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Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

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Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

SLIDE 33

Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

SLIDE 34

Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

SLIDE 35

Frame Conditions

Normality: ∀w∀x∀y′[∀y(Mwy′y ⊃ OK(y, x)) ⊃ OK(y′, x)].

(OR) X; A ⊢ B X, P(B) ⊢ P(A)

Transitivity of Normality: ∀x∀y∀z∃u[Mxyz ⊃ Mxyu ∧ Mxuz].

(Tra) X; A ⊢ B Y; B ⊢ C (X, Y); A ⊢ C

Rational Monotonicity: ∀x∀y∀z∀s∀u∀y′∀z′∀s′∀u′[(Mxyz ∧ Msuy) ∧ (Mxy′z′ ∧ Mz′s′u′) ⊃ (Mxsz ∨ Mxy′z)].

(RaM) X ⊢ A ⊸ C X ⊢ ¬((A ⊸ (B ⊸ ⊥)) ⊃ (A ◦ B) ⊸ C

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 15 / 18

SLIDE 36

An Example

An acceptable rational monotonic case:

(1) Order ⊸ Order ⊢ Order ⊸ Order (Id) (2) Order ⊸ Order ⊢ ¬(Order ◦ Pay ⊸ ⊥) ⊃ (Order ◦ Pay) ⊸ Order (1), (RaM) (3) Order ⊸ Order, ¬(Order ◦ Pay ⊸ ⊥) ⊢ P(Order) ⊃ P(Order ◦ Pay) (2), (OR) where Order, Pay ∈ Act0.

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 16 / 18

SLIDE 37

Conclusions and Future Works

1 The logics N0 and NRaM can avoid the undesired FCP results. In

addition, NRaM can implies the desired FCP by applying (RaM).

2 Define obligation in this substructural framework, and check the

interaction of obligation and permission.

3 Compare this ternary framework with the binary framework proposed

by van Benthem (1979).

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 17 / 18

SLIDE 38

Thank you!

Huimin Dong, Norbert Gratzl September 12th 2016, Hamburg 18 / 18