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 Ditmarsch 1 , Andreas Herzig 2 , Emiliano Lorini 3 , Francois Schwarzentruber 4 LORI4 10 october 2013 1 CNRS, LORIA, Nancy 2 CNRS, IRIT, Toulouse 3 CNRS, IRIT, Toulouse 4 ENS 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! 2 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Policies in Facebook 3 / 53
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 AMAISON .fr socialnetwork � Internet and objects Video games Robots: cooperation during a rescue in nuclear plant e-commerce, e-voting 4 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Dynamic epistemic logic Real events Kripke (private modeled by event models E , e announcements...) friends pre : p { green guy } pre : ⊤ all agents 5 / 53
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. 6 / 53
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 ? ? E 1 , e 1 (DEL) E 2 , e 2 (DEL) ? 7 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Automated reasoning Joint attention and attention change Conclusion Our solution s p e c i fi e d i n Our new language ABAL (high-level language) n i d e fi i c e p s embedded in DEL (assembly language) 8 / 53
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 9 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Outline Our logic ABAL 1 Syntax Semantics Axiomatization Embedding in Dynamic Epistemic Logic 2 Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 10 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Outline Our logic ABAL 1 Syntax Semantics Axiomatization Embedding in Dynamic Epistemic Logic 2 Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 11 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Syntax of attention-based announcement logic ϕ, ψ . . . ::= p | h a | ¬ ϕ | ( ϕ ∧ ψ ) | B a ϕ | [ ϕ ] ψ h a : agent a pays attention; B a ϕ : agent a believes ϕ ; [ ϕ ] ψ : after the announcement of ϕ , ψ holds. Example h a ∧ h b ∧ ¬ B b h b ∧ [ p ] B a ¬ B b p 12 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Outline Our logic ABAL 1 Syntax Semantics Axiomatization Embedding in Dynamic Epistemic Logic 2 Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 13 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Models M = ( W , R 1 , . . . , R n , V ) with W : possible worlds R i ⊆ W × W : accessibility relation for agent i V : ATM → 2 W : valuation Example a , b a , b a p , ¬ h a , h b ¬ p , ¬ h a , h b b b a p , h a , h b ¬ p , h a , h b a , b a , b 14 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Truth conditions Standard: M , w | = p iff p ∈ V ( w ); M , w | = h a iff h a ∈ V ( w ); M , w | = B a ϕ iff for all u ∈ R a ( w ), M , u | = ϕ ; Announcement operator: M , w | = [ ϕ ] ψ iff M ϕ , ( w , 0) | = ψ . 15 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Model updated by ϕ initial model ¬ h a × a ¬ ϕ a copy of model initial model updated × a a by ϕ we remove edges pointing to a ¬ ϕ -world we redirect edges when a does not hear 16 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Example of a model updated by p a a a a , b a , b b a a p , ¬ h a , h b ¬ p , ¬ h a , h b p , ¬ h a , h b ¬ p , ¬ h a , h b b b b b a a p , h a , h b ¬ p , h a , h b p , h a , h b ¬ p , h a , h b a , b a , b a , b a , b 17 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Outline Our logic ABAL 1 Syntax Semantics Axiomatization Embedding in Dynamic Epistemic Logic 2 Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 18 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Syntax Automated reasoning Semantics Joint attention and attention change Axiomatization Conclusion Axiomatization all propositional tautologies B a ( ϕ → ψ ) → ( B a ϕ → B a ψ ) [ ϕ ]( ψ ∧ χ ) ↔ ([ ϕ ] ψ ∧ [ ϕ ] χ ) [ ϕ ] ¬ ψ ↔ ¬ [ ϕ ] ψ [ ϕ ] q ↔ q modus ponens From ϕ infer B a ϕ From ϕ infer [ ψ ] ϕ Key axiom [ ϕ ] B a ψ ↔ (( h a → B a ( ϕ → [ ϕ ] ψ )) ∧ ( ¬ h a → B a ψ )) 19 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Outline Our logic ABAL 1 Embedding in Dynamic Epistemic Logic 2 Representing events in DEL Product update Representing attention-based announcements Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 20 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Outline Our logic ABAL 1 Embedding in Dynamic Epistemic Logic 2 Representing events in DEL Product update Representing attention-based announcements Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 21 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Event Kripke models E = ( E , → 1 , . . . , → n , Pre) with E : possible events → a ⊆ E × E : accessibility relation for agent a Pre : E → L : preconditions 22 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Example 1 Announcement of p ... public for agents 1 and 2. 1, 2 pre : b 23 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Example 2 1 Announcement of p where: pre : p 1 pays attention; 2 does not pay attention. 2 pre : ⊤ 1, 2 24 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion Outline Our logic ABAL 1 Embedding in Dynamic Epistemic Logic 2 Representing events in DEL Product update Representing attention-based announcements Automated reasoning 3 Joint attention and attention change 4 Conclusion 5 25 / 53
Our logic ABAL Embedding in Dynamic Epistemic Logic Representing events in DEL Automated reasoning Product update Joint attention and attention change Representing attention-based announcements Conclusion 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 vR a u and e → a f , ( v , e ) ∈ V ⊗ ( p ) if M , v | = p . 26 / 53
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