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1、Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Logic of Communication Jan van Eijck CWI and ILLC, Amsterdam Happy New Year Event, ILLC January 13, 2012 Quick Intro to Dynamic Epistemic Logic
2、 (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Outline Quick Intro to Dynamic Epistemic Logic (DEL) Question Answering for Logicians Kripke Models, Action Models, Communication Axiomatisation A Riddle and a Protocol Quick Intro
3、to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Outline Quick Intro to Dynamic Epistemic Logic (DEL) Question Answering for Logicians Kripke Models, Action Models, Communication Axiomatisation A Riddle a
4、nd a Protocol Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Outline Quick Intro to Dynamic Epistemic Logic (DEL) Question Answering for Logicians Kripke Models, Action Models, Communication
5、 Axiomatisation A Riddle and a Protocol Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Outline Quick Intro to Dynamic Epistemic Logic (DEL) Question Answering for Logicians Kripke Models, Ac
6、tion Models, Communication Axiomatisation A Riddle and a Protocol Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Outline Quick Intro to Dynamic Epistemic Logic (DEL) Question Answering for L
7、ogicians Kripke Models, Action Models, Communication Axiomatisation A Riddle and a Protocol Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Very Brief History of (Dynamic) Epistemic Logic Dav
8、id LewisJaakko HintikkaRobert Aumann Joe HalpernJan Plaza A. Baltag Johan van Benthem Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Very Brief History of (Dynamic) Epistemic Logic David Lew
9、isJaakko HintikkaRobert Aumann Joe HalpernJan Plaza A. Baltag Johan van Benthem Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Very Brief History of (Dynamic) Epistemic Logic David LewisJaak
10、ko HintikkaRobert Aumann Joe HalpernJan Plaza A. Baltag Johan van Benthem Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Very Brief History of (Dynamic) Epistemic Logic David LewisJaakko Hin
11、tikkaRobert Aumann Joe HalpernJan Plaza A. Baltag Johan van Benthem Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Very Brief History of (Dynamic) Epistemic Logic David LewisJaakko HintikkaR
12、obert Aumann Joe HalpernJan Plaza A. Baltag Johan van Benthem Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Individual Ignorance You have to fi nish a paper, and you are faced with a choice
13、: do it today, or put it off until tomorrow. Result of coin fl ip under a cup: w : h w0: h Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Individual Ignorance You have to fi nish a paper, an
14、d you are faced with a choice: do it today, or put it off until tomorrow. Result of coin fl ip under a cup: w : h w0: h Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance S
15、uppose Alice and Bob have a get-together, and Alice tosses a coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?
16、b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance Suppose Alice and Bob have a get-together, and Alice tosses a
17、 coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh.
18、Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance Suppose Alice and Bob have a get-together, and Alice tosses a coin under a cup. The result of a hidden coin toss with the
19、 coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answeri
20、ng for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance Suppose Alice and Bob have a get-together, and Alice tosses a coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the
21、 cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationA
22、xiomatisationA Riddle and a Protocol Multi Agent Ignorance Suppose Alice and Bob have a get-together, and Alice tosses a coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the
23、 outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance S
24、uppose Alice and Bob have a get-together, and Alice tosses a coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?
25、b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Multi Agent Ignorance Suppose Alice and Bob have a get-together, and Alice tosses a
26、 coin under a cup. The result of a hidden coin toss with the coin heads up: w : h w0: h Alice is taking a look under the cup, while Bob is watching. w : h w0: h Now Alice knows the outcome. ?ah ?ah. Bob knows that Alice knows the outcome. ?b(?ah ?ah). Bob does not know the outcome himself. ?bh ?bh.
27、Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle a
28、nd a Protocol What Goes on in Logician Question Answering? Question “Does everyone want beer?” triggers the following instruction: If ?i(b1 b2 b3) then i says “Yes”. If ?i(b1 b2 b3) then i says “No”. Otherwise, i says “I dont know”. These answers themselves serve as updates: i says “Yes”: update wit
29、h public announcement of ?i(b1 b2 b3) i says “No”: update with public announcement of ?i(b1 b2 b3). i says “I dont know”: update with public announcement of ?i(b1 b2 b3) ?i(b1 b2 b3). Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, Communicat
30、ionAxiomatisationA Riddle and a Protocol What Goes on in Logician Question Answering? Question “Does everyone want beer?” triggers the following instruction: If ?i(b1 b2 b3) then i says “Yes”. If ?i(b1 b2 b3) then i says “No”. Otherwise, i says “I dont know”. These answers themselves serve as update
31、s: i says “Yes”: update with public announcement of ?i(b1 b2 b3) i says “No”: update with public announcement of ?i(b1 b2 b3). i says “I dont know”: update with public announcement of ?i(b1 b2 b3) ?i(b1 b2 b3). Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models
32、, Action Models, CommunicationAxiomatisationA Riddle and a Protocol What Goes on in Logician Question Answering? Question “Does everyone want beer?” triggers the following instruction: If ?i(b1 b2 b3) then i says “Yes”. If ?i(b1 b2 b3) then i says “No”. Otherwise, i says “I dont know”. These answers
33、 themselves serve as updates: i says “Yes”: update with public announcement of ?i(b1 b2 b3) i says “No”: update with public announcement of ?i(b1 b2 b3). i says “I dont know”: update with public announcement of ?i(b1 b2 b3) ?i(b1 b2 b3). Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering
34、 for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol What Goes on in Logician Question Answering? Question “Does everyone want beer?” triggers the following instruction: If ?i(b1 b2 b3) then i says “Yes”. If ?i(b1 b2 b3) then i says “No”. Otherwise, i says “
35、I dont know”. These answers themselves serve as updates: i says “Yes”: update with public announcement of ?i(b1 b2 b3) i says “No”: update with public announcement of ?i(b1 b2 b3). i says “I dont know”: update with public announcement of ?i(b1 b2 b3) ?i(b1 b2 b3). Quick Intro to Dynamic Epistemic Lo
36、gic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol : “want beer”. : 1. : 2. : 3. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a
37、Protocol : “want beer”. : 1. : 2. : 3. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol : “want beer”. : 1. : 2. : 3. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for Logicia
38、nsKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol : “want beer”. : 1. : 2. : 3. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Action Models,
39、Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M A given by: WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic Epistemic L
40、ogic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Action Models, Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M A given by:
41、WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Action Mo
42、dels, Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M A given by: WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic Epist
43、emic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Action Models, Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M A give
44、n by: WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Act
45、ion Models, Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M A given by: WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic
46、 Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Kripke Models, Action Models, Communication Kripke models M = (WM,VM,RM,UM). Bisimulation M N. Action models A = (WA,preA,RA.UA). Action model update See 3, 1, 2. M
47、A given by: WMA= (w,x) | w WM,x WA,M |=wpre(x). (w,x) a (w0,x0) iff w a w0and x a x0. VMA(w,x) = VM(w). UMA= (w,x) WMA| w UM,x UA. Quick Intro to Dynamic Epistemic Logic (DEL)Question Answering for LogiciansKripke Models, Action Models, CommunicationAxiomatisationA Riddle and a Protocol Public Announcement Everyone wants beer: b1 b2 b3. i knows that everyone wants beer: ?i(b1 b2 b3). i knows whether everyone wants beer: ?i(b1 b2 b3) ?i(b1 b2 b3). i does not