Listen to me! Public announcements to agents that pay attention or - - PowerPoint PPT Presentation

Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Listen to me! Public announcements to agents that pay attention — or not

Hans van Ditmarsch1, Andreas Herzig2, Emiliano Lorini3, Francois Schwarzentruber4

LORI4

10 october 2013

1CNRS, LORIA, Nancy 2CNRS, IRIT, Toulouse 3CNRS, IRIT, Toulouse 4ENS Cachan, Brittany extension, France... soon ENS Rennes! 1 / 53

Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Please, listen to me!

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Policies in Facebook

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Our environment: now and in the future

Use logic to reason about epistemic programs socialnetwork AMAISON.fr

• Internet and objects

Video games Robots: cooperation during a rescue in nuclear plant e-commerce, e-voting

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Dynamic epistemic logic

Real events (private announcements...) modeled by Kripke event models E, e pre : p pre : ⊤ {green guy} all agents friends

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Problem with the swiss army knife logic DEL

Once upon a time... in Rennes... He said: I do not understand what E, e is I will never use DEL.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Problem with the swiss army knife logic DEL

Problem How do you model real situations by event models E, e? E1, e1 (DEL) E2, e2 (DEL) ? ?

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Our solution

Our new language ABAL

(high-level language)

DEL (assembly language)

s p e c i fi e d i n s p e c i fi e d i n embedded in

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Advertisement

Features of ABAL: No semantic objects in the language ✘✘✘

✘

[E, e]ϕ; Strictly more expressive that public announcement logic; Easy to write specifications; Good complexities

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Outline

1

Our logic ABAL Syntax Semantics Axiomatization

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Outline

1

Our logic ABAL Syntax Semantics Axiomatization

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Syntax of attention-based announcement logic

ϕ, ψ . . . ::= p | ha | ¬ϕ | (ϕ ∧ ψ) | Baϕ | [ϕ]ψ ha: agent a pays attention; Baϕ: agent a believes ϕ; [ϕ]ψ: after the announcement of ϕ, ψ holds. Example ha ∧ hb ∧ ¬Bbhb ∧ [p]Ba¬Bbp

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Outline

1

Our logic ABAL Syntax Semantics Axiomatization

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Models

M = (W , R1, . . . , Rn, V ) with W : possible worlds Ri ⊆ W × W : accessibility relation for agent i V : ATM → 2W : valuation Example p, ¬ha, hb ¬p, ¬ha, hb p, ha, hb ¬p, ha, hb b a b a a, b a, b a, b a, b

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Truth conditions

Standard: M, w | = p iff p ∈ V (w); M, w | = ha iff ha ∈ V (w); M, w | = Baϕ iff for all u ∈ Ra(w), M, u | = ϕ; Announcement operator: M, w | = [ϕ]ψ iff Mϕ, (w, 0) | = ψ.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Model updated by ϕ

initial model model updated by ϕ ¬ϕ ¬ha × a a

×

a

a copy of initial model

we remove edges pointing to a ¬ϕ-world we redirect edges when a does not hear

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Example of a model updated by p

p, ¬ha, hb ¬p, ¬ha, hb p, ha, hb ¬p, ha, hb p, ¬ha, hb ¬p, ¬ha, hb p, ha, hb ¬p, ha, hb b a b a, b b a, b b a b a a, b a, b a, b a, b a a a a

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Outline

1

Our logic ABAL Syntax Semantics Axiomatization

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Syntax Semantics Axiomatization

Axiomatization

all propositional tautologies Ba(ϕ → ψ) → (Baϕ → Baψ) [ϕ](ψ ∧ χ) ↔ ([ϕ]ψ ∧ [ϕ]χ) [ϕ]¬ψ ↔ ¬[ϕ]ψ [ϕ]q ↔ q modus ponens From ϕ infer Baϕ From ϕ infer [ψ]ϕ Key axiom [ϕ]Baψ ↔ ((ha → Ba(ϕ → [ϕ]ψ)) ∧ (¬ha → Baψ))

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic Representing events in DEL Product update Representing attention-based announcements

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic Representing events in DEL Product update Representing attention-based announcements

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Event Kripke models

E = (E, →1, . . . , →n, Pre) with E : possible events →a⊆ E × E : accessibility relation for agent a Pre : E → L : preconditions

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Example 1

Announcement of p... public for agents 1 and 2. pre : b 1, 2

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Example 2

Announcement of p where: 1 pays attention; 2 does not pay attention. pre : p pre : ⊤ 2 1, 2 1

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic Representing events in DEL Product update Representing attention-based announcements

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Updated models

Given M E We define the updated model M ⊗ E = (W ⊗, R⊗, V ⊗) by: (v, e) ∈ W ⊗ if v ∈ W , e ∈ E and M, v | = Pre(e) (v, e)R⊗

a (u, f )

if vRau and e →a f , (v, e) ∈ V ⊗(p) if M, v | = p.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Pointed updated models

Given M, w E, e the pointed updated model M ⊗ E, (w, e) is defined iff M, w | = Pre(e)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic Representing events in DEL Product update Representing attention-based announcements

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

THE action model that corresponds to announcement of ϕ

pre : ¬ϕ, ¬ha, ¬hb pre : ¬ϕ, ¬ha, hb pre : ¬ϕ, ha, ¬hb pre : ¬ϕ, ha, hb pre : ϕ, ¬ha, ¬hb pre : ϕ, ¬ha, hb pre : ϕ, ha, ¬hb pre : ϕ, ha, hb pre : ⊤ a, b a b a, b a b a, b a b a, b a b a, b

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Representing events in DEL Product update Representing attention-based announcements

Embedding of ABAL into DEL

tr([ϕ]ψ) = [Eϕ, Eϕ]tr(ψ) PAL ABAL DEL

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Satisfiability problem

SAT ϕ

• yes, if there exists M, w

such that M, w | = ϕ

• no otherwise

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Result

PAL ABAL DEL NEXPTIME-complete PSPACE-complete PSPACE-complete

Adaptation to ABAL of the tableau method of PAL [Balbiani et al.]

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Tableau method

Non-deterministic rewriting system of set of terms (σ Σ ϕ): in the world σ, after the announcements Σ, ϕ holds; (σ Σ ): the world σ survives the announcements Σ; (σ Σ ⊗): the world σ does not survive the announcements Σ; (σ Ra σ1)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Tableau rules

(σ Σ ϕ ∧ ψ) (σ Σ ϕ) (σ Σ ψ) (∧) (σ Σ ¬¬ϕ) (σ Σ ϕ) (¬¬) (σ Σ ¬(ϕ ∧ ψ)) (σ Σ ¬ϕ) | (σ Σ ¬ψ) (¬∧) (σ Σ p)(σ Σ ¬p) ⊥ (⊥) (σ Σ [ϕ]ψ) (σ Σ :: ϕ ψ) ([ϕ]) (σ Σ ¬[ϕ]ψ) (σ Σ : ϕ ¬ψ) (¬[ϕ]) (σ Σ p) (σ [] p) (←p) (σ Σ ¬p) (σ [] ¬p) (←¬p)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Tableau rules

(σ Σ :: ϕ ) (σ Σ ϕ) (σ Σ ) () (σ Σ :: ϕ ⊗) (σ Σ ) (σ Σ ¬ϕ) (σ Σ ⊗) (⊗) (σ Σ ⊗)(σ Σ ) ⊥ (clash,⊗) (σ [] ⊗) ⊥ ([]⊗)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Tableau rules

(σ Σ Baϕ)(σ [] ha) (σ Ra σ1) (σ1 Σ ) (σ1 Σ ϕ) (σ1 Σ ⊗) (Ba) (σ Σ Baϕ)(σ [] ¬ha) (σ Ra σ1) (σ1 [] ϕ) (Ba) (σ [] ha)(σ Σ ¬Baϕ) (σ Ra σnew) (σnew Σ ) (σnew Σ ¬ϕ) (¬Ba) (σ [] ¬ha)(σ Σ ¬Baϕ) (σ Ra σnew) (σnew [] ¬ϕ) (¬Ba) (σ [] ha) (σ [] ¬ha) (hear)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change Joint attention Attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change Joint attention Attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Joint attention

hA :=

a∈A ha

CBAϕ: there is common belief among agents in A that ϕ. | = (hA ∧ CBAhA)

• join attention

→ [p]CBAp | = [p]CBAp ↔ CBA

• a∈A(ha ∨ Bap)

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change Joint attention Attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Example: initial state

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Example: announcement

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Example: final state

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Update model M+G for attention change hG := ⊤

initial model updated model ¬hb b × b

a copy of initial model

we set hG := ⊤ we redirect edges when b ∈ G does not hear

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Dynamic operator for attention change

M, s | = [+G]ψ iff M+G, (s, 0) | = ψ | = [+a][+b]ϕ ↔ [+b][+a]ϕ; | = [+a, b]ϕ ↔ [+b][+a]ϕ.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Reduction axioms

[+G]Baϕ ↔

• Ba[+G]ϕ

if a ∈ G (ha → Ba[+G]ϕ) ∧ (¬ha → Baϕ) if a ∈ G [−G]Baϕ ↔

• Ba[−G]ϕ

if a ∈ G (ha → Ba[−G]ϕ) ∧ (¬ha → Baϕ) if a ∈ G

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Joint attention Attention change

Embedding of public and private announcements

Public announcement of ϕ: [+AGT][ϕ]ψ; Private announcement of ϕ to group G: [+G][−(AGT \ G)][ϕ]ψ. [Gerbrandy 1999]

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Outline

1

Our logic ABAL

2

Embedding in Dynamic Epistemic Logic

3

Automated reasoning

4

Joint attention and attention change

5

Conclusion

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Comparison with DEL

In DEL: ‘private/public’ is encoded in the event; In ABAL: ‘private/public’ is encoded in the state.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Advertisement

Features of ABAL: No semantic objects in the language ✘✘✘

✘

[E, e]ϕ; Natural language; Can embed a lot of private announcements; Dynamics; PSPACE-complete.

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Future work

Comparing with other existing framework Modal language to specify event models [M4M2011, JELIA2012] Technical issues Common knowledge... complexity? axiomatization? Extending the expressivity of the language lying (ℓa), trust (ta), hearing (ha,b), etc. study more deeply dynamic changes of hearing

Convince my colleague in Rennes...

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Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion

Thank you for your... attention!

I hope that ha for all a in the audience!

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