Knowledge, Strategies, and Know-How
|
|
- Susanna Boyd
- 5 years ago
- Views:
Transcription
1 KR 2018, Tempe, AZ, USA Knowledge, Strategies, and Know-How Jia Tao Lafayette College Pavel Naumov Claremont McKenna College
2 "!! Knowledge, Strategies, Know-How!!?!! #!!
3 Epistemic Logic! # Alice K A (Alice has a pumpkin mask) Bob K B (Alice has a pumpkin mask) K C K B (Alice has a pumpkin mask) Cathy K C (Alice has a pumpkin mask) K A (K B (Alice has a pumpkin mask) K C (Alice has a pumpkin mask))
4 Epistemic Logic!! # #! Alice Bob # Cathy K B (Alice has a pumpkin mask)
5 Epistemic Logic!! # #! Alice Bob # Cathy K A (K B (Alice has a pumpkin mask) K C (Alice has a pumpkin mask))
6 Epistemic States! # Alice Bob Cathy Cathy Alice! Alice Bob Cathy Bob Alice! # # Bob Cathy
7 Epistemic Model (W, { a } a A, π) W a π is a set of states is an indistinguishability equivalence relation is a valuation function w p iff w π(p) w φ iff w φ w φ ψ iff w φ or w ψ w K a φ iff u φ for all u W such that w a u
8 Model Example p a p b u v w u p u K a p v K a p v K b p w p w K a p w K b p w K b (K a p K a p)
9 Indistinguishability Relation Reflexive u a u Symmetric u a v v a u Transitive u a v v a w u a w
10 Multiagent S5 all propositional tautologies K a φ φ K a φ K a K a φ K a φ K a K a φ K a (φ ψ) (K a φ K a ψ) φ, φ ψ ψ φ K a φ
11 Proof of Positive Introspection Lemma 1 K a φ K a K a φ Proof K a K a φ K a φ K a φ K a K a φ K a K a φ K a K a K a φ K a φ K a K a K a φ K a φ K a K a φ K a K a φ K a φ K a ( K a K a φ K a φ) K a K a K a φ K a K a φ K a φ K a K a φ
12 Soundness and Completeness Theorems If φ, then w φ for each state w of each epistemic model. If w φ for each state w of each epistemic model, then φ.
13 Alice s Knowledge! #! #! Alice Bob # Cathy K A ("Either Bob or Cathy has a ghost mask.") K A ("Cathy has a ghost mask.")
14 Bob s Knowledge! #! #! Alice Bob K B ("Either Alice or Cathy has a ghost mask.") K B ("Cathy has a ghost mask.") # Cathy
15 Distributed Knowledge! #! #! #! #! Alice Bob # Cathy K A,B ("Cathy has a ghost mask.")
16 Epistemic States! # Alice Bob Cathy Cathy Alice! Alice Bob Cathy Bob! # # Alice Bob Cathy
17 Epistemic Model (W, { a } a A, π) W a π is a set of states is an indistinguishability equivalence relation is a valuation function Notation: w C u if a C(w a u). w p iff w π(p) w φ iff w φ w φ ψ iff w φ or w ψ w K C φ iff u φ for all u W such that w C u
18 Distributed Knowledge Axioms all propositional tautologies K C φ φ K C φ K C K C φ K C (φ ψ) (K C φ K C ψ) K C φ K D φ, where C D φ, φ ψ ψ φ K C φ
19 Soundness and Completeness Theorems If φ, then w φ for each state w of each epistemic model. If w φ for each state w of each epistemic model, then φ.
20 Group Knowledge
21 Forms of Group Knowledge Individual Knowledge Alice and Bob both know the value of x Distributed Knowledge Alice knows x, Bob knows y, they distributedly know the value of x+y Common Knowledge two generals problem
22 Logic of Coalition Power
23 "!! Strategies!!?!! #!!
24 Coalition Strategies! Alice Bob # Cathy 0/1 0/1 0/1 sum=3 p p u S a p u v sum=1,2 u S a p p 0,1 u S abc p s v S abc p 0,1,2 2,3 v S Ø p sum=0,1 p w S abc p w w S ab p s S a p u S abc S Ø p s S a
25 Game Definition (W, Δ, M, π) W is a set of states. Δ is a nonempty domain of actions. M W Δ A W is a mechanism. π is a function from propositional variables into subsets of W.
26 Formal Semantics w p iff w π(p), w φ iff w φ, w φ ψ iff w φ or w ψ, w S C φ iff there is an action profile s Δ C of coalition C such that for each complete action profile δ Δ A and each state u W if s = C δ and (w, δ, u) M, then u φ.
27 Examples of Statements S a p = Alice has an action that guarantees p in the next state. S Ø p = p is unavoidable in the next state. S Ø = there is no next state. S a S b p = Alice has an action after which Bob will not have an action that guarantees p (S a p S b p) S ab p = Although neither Alice nor Bob has an action that guarantees p they have a joint action that does.
28 Marc Pauly s Logic of Coalitional Power all propositional tautologies S C (φ ψ) (S D φ S C D ψ), where C D = Ø φ, φ ψ ψ φ S C φ M. Pauly, A modal logic for coalitional power in games, Journal of Logic and Computation (2002)
29 Example of Derivation Lemma 1. S C φ S D φ, where C D. Proof. φ φ S D C (φ φ) Since C D, by the Cooperation axiom, S D C (φ φ) (S C φ S D φ) S C φ S D φ
30 Soundness and Completeness Theorems If φ, then w φ for each state w of each game. If w φ for each state w of each game, then φ.
31 Coalition Strategies! 0/1 p a,b,c p Alice u sum is odd sum is even v 0/1 s p Bob sum is even p sum is odd # 0/1 w Cathy u S abc p?
32 Knowledge and Strategies
33 Game with Imperfect Information a,b,c u S a p! Alice 0/1 0/1 u sum=0,1 s p sum=3 v u S a,b p v S a,b p u K a,b S a,b p Bob u S a,b,c p # 0/1 sum=2,3 w p sum=0,1,2 v S a,b,c p Cathy u K a,b,c S a,b,c p
34 Game with Imperfect Information (W, { a } a A, Δ, M, π) W is a set of states. a is an indistinguishability equivalence relation. Δ is a nonempty domain of actions. M W Δ A W is a mechanism. π is a function from propositional variables into subsets of W. Thomas Ågotnes and Natasha Alechina (2012). "Epistemic Coalition Logic: Completeness and Complexity." International Conference on Autonomous Agents and Multiagent Systems
35 Formal Semantics w p iff w π(p), w φ iff w φ, w φ ψ iff w φ or w ψ, w S C φ iff there is an action profile s Δ C of coalition C such that for each complete action profile δ Δ A and each state u W if s = C δ and (w, δ, u) M, then u φ, w K C φ iff u φ for all u W such that w C u.
36 Distributed Knowledge and Strategies all propositional tautologies K C φ φ φ, φ ψ φ φ ψ K C φ S C φ K C φ K C K C φ K C (φ ψ) (K C φ K C ψ) K C φ K D φ, where C D S C (φ ψ) (S D φ S C D ψ), where C D = Ø Completeness: Thomas Ågotnes and Natasha Alechina (2012). "Epistemic Coalition Logic: Completeness and Complexity." International Conference on Autonomous Agents and Multiagent Systems
37 "!! Know-How!!?!! #!!
38 Know-How a,b! Alice 0/1 0/1 u sum=0,1 s p sum=3,2 v u S a,b p v S a,b p u K a,b S a,b p Bob u H a,b p # 0/1 sum=2,3 w p sum=0,1 u H a,b,c p Cathy
39 Another Example a,b,c! Alice 0/1 0/1 u sum=0,1 s p sum=0 v u S a,b p v S a,b p u H a,b p Bob u H a,b,c p sum=2,3 p sum=1,2,3 # Cathy 0/1 w
40 Formal Semantics w S C φ iff there is an action profile s Δ C of coalition C such that for each complete action profile δ Δ A and each state u W, if s = C δ and (w, δ, u) M, then u φ w H C φ iff there is an action profile s Δ C of coalition C such that for each state v and each complete action profile δ Δ A and each state u W, if w C v, s = C δ, and (v, δ, u) M, then u φ
41 Term Know-How Strategies uniform strategies - van Benthem (2001) difference between an agent knowing that he has a suitable strategy and knowing the strategy itself - Jamroga and van der Hoek (2004) knowledge to identify and execute a strategy - Jamroga and Ågotnes (2007) knowingly doing Broersen (2008) knowing how - Wang (2015) knows how or knowledge de re - Ågotnes and Alechina (2016) executable or know-how strategy - Naumov and Tao (2017)
42 Knowledge and Know-How all propositional tautologies K C φ φ φ, φ ψ φ φ ψ K C φ H C φ K C φ K C K C φ K C (φ ψ) (K C φ K C ψ) K C φ K D φ, where C D H C (φ ψ) (H D φ H C D ψ), where C D = Ø H C φ K C H C φ K Ø φ H Ø φ
43 Strategic Negative Introspection Lemma 1. (Alechina, private communication) Proof. H C φ K C H C φ H C φ K C H C φ K C H C φ H C φ K C H C φ H C φ H C φ K C H C φ K C ( K C H C φ H C φ) K C K C H C φ K C H C φ K C H C φ K C K C H C φ H C φ K C H C φ K C H C φ K C H C φ
44 Strategic Monotonicity Lemma 2. H C φ H D φ, where C D. Proof. φ φ H D C (φ φ) H D C (φ φ) (H C φ H (D C) C φ) H C φ H (D C) C φ H C φ H D φ
45 Knowledge and Know-How all propositional tautologies K C φ φ φ, φ ψ φ φ ψ K C φ H C φ K C φ K C K C φ K C (φ ψ) (K C φ K C ψ) K C φ K D φ, where C D H C (φ ψ) (H D φ H C D ψ), where C D = Ø H C φ K C H C φ K Ø φ H Ø φ
46 Soundness and Completeness Theorems If φ, then w φ for each state w of each game with imperfect information. If w φ for each state w of each game with imperfect information, then φ.
47 Break
48 Multi-Step Strategies a q p! 0/1 w u Alice a w S a p u S a q w H a p u H a q
49 Single-Player Multi-Step Strategies to Achieve a Goal all propositional tautologies Kφ φ Kφ K Kφ K(φ ψ) (Kφ Kψ) Hφ KHφ HHφ Hφ Hφ HKφ Kφ Hφ H (due to verifiability) φ, φ ψ φ φ ψ φ(p) ψ Kφ Hφ Hψ φ[ψ/p] Completeness: Raul Fervari, Andreas Herzig, Yanjun Li, Yanjing Wang (2017), Strategically Knowing How, International Joint Conference on Artificial Intelligence (IJCAI)
50 Coalitional Multi-Step Strategies to Maintain a Goal all propositional tautologies H C (φ ψ) (H D φ H C D ψ), where C D = Ø K C φ φ H C φ K C φ K C φ K C K C φ H C φ H C H C φ K C (φ ψ) (K C φ K C ψ) K Ø φ H Ø φ K C φ K D φ, where C D φ, φ ψ ψ φ H C φ Completeness: Pavel Naumov and Jia Tao (2017), Coalition Power in Epistemic Transition Systems, International Conference on Autonomous Agents and Multiagent Systems (AAMAS)
51 Blind Date Failure! # K a ("date is at 6pm") K b ("date is at 6pm") K a K b ("date is at 6pm") K b K a ("date is at 6pm") K a K b K a ("date is at 6pm") K b K a K b ("date is at 6pm") K a K b K a K b ("date is at 6pm") K b K a K b K a ("date is at 6pm")
52 Common Knowledge! # C a,b,c ("date is at 6pm") 6pm, enjoy Cathy
53 Common Knowledge and Strategies all propositional tautologies S A (φ ψ) (S B φ S A B ψ), where A B = Ø K a φ φ K a φ K a K a φ φ, φ ψ ψ φ C A φ φ S A φ K a (φ ψ) (K a φ K a ψ) C A φ a A K a (φ C A φ) ψ a A K a (φ ψ) ψ C A φ Completeness: Thomas Ågotnes and Natasha Alechina (2012). "Epistemic Coalition Logic: Completeness and Complexity." International Conference on Autonomous Agents and Multiagent Systems
54 Common-Know-How? CH A (φ ψ) (CH B φ CH A B ψ), where A B = Ø
55 Distributed Knowledge, Strategies, and Know-How all propositional tautologies H C (φ ψ) (H D φ H C D ψ), where C D = Ø K C φ φ H C φ K C H C φ K Ø φ H Ø φ K C φ K C K C φ φ, φ ψ φ φ φ K C (φ ψ) (K C φ K C ψ) ψ K C φ S C φ H C φ K C φ K D φ, where C D H C φ S C φ S C S C (φ ψ) (S D φ S C D ψ), where C D = Ø H C (φ ψ) (K C S Ø φ H C ψ) Completeness: Pavel Naumov and Jia Tao (2018), Together We Know How to Achieve: An Epistemic Logic of Know-How, Journal of Artificial Intelligence
56 No Perfect Recall! Alice 0/1 w 0 u p a v 1 w S a p u K a p w S a K a p w H a p w H a K a p
57 Perfect Recall Semantics (w 0, δ 1, w 1,, δ n, w n ) p iff w π(p), (w 0, δ 1, w 1,, δ n, w n ) φ iff (w 0, δ 1, w 1,, δ n, w n ) φ, (w 0, δ 1, w 1,, δ n, w n ) φ ψ iff (w 0, δ 1, w 1,, δ n, w n ) φ or (w 0, δ 1, w 1,, δ n, w n ) ψ, (w 0, δ 1, w 1,, δ n, w n ) K C φ iff (w 0, δ 1, w 1,, δ n, w n ) φ for all (w 0, δ 1, w 1,, δ n, w n ) such that (w 0, δ 1, w 1,, δ n, w n ) C (w 0, δ 1, w 1,, δ n, w n ) (w 0, δ 1, w 1,, δ n, w n ) H C φ iff there is an action profile s Δ C of coalition C such that for each history (w 0, δ 1, w 1,, δ n, w n ), each complete action profile δ Δ A, and each state u W if (w 0, δ 1, w 1,, δ n, w n ) C (w 0, δ 1, w 1,, δ n, w n ), s = C δ, and (w n, δ, u) M, then (w 0, δ 1, w 1,, δ n, w n, δ, u) φ
58 Knowledge and Know-How with Perfect Recall all propositional tautologies H C (φ ψ) (H D φ H C D ψ), where C D = Ø K C φ φ H C φ K C H C φ K Ø φ H Ø φ K C φ K C K C φ φ, φ ψ φ φ K C (φ ψ) (K C φ K C ψ) ψ K C φ H C φ K C φ K D φ, where C D H D φ H D K C φ, where D C Ø H C Completeness: Pavel Naumov and Jia Tao (2018), Strategic Coalitions with Perfect Recall, AAAI Conference on Artificial Intelligence (AAAI 18)
59 Linear Plans 010 q p! 0/1 w u Alice H(q, p) H(p, q)
60 Linear Plans 000 p p q q! Alice 0/ H(p, q)
61 Axioms for Single-Agent Linear Plans all propositional tautologies H(φ, ψ) NH(φ, ψ) Nφ φ H(φ, ψ) N H(φ, ψ) N(φ ψ) (Nφ Nψ) H(φ, ψ) (H(ψ, χ) H(φ, χ)) φ, φ ψ ψ φ Nφ N(φ ψ) H(φ, ψ) Completeness: Yanjing Wang (2016), A logic of goal-directed knowing how, Synthese
62 Linear Plans with Intermediate Constraints 10 p r! 0/1 w u Alice q H(p, q, r)
63 Axioms for Plans with Intermediate Constraints all propositional tautologies Nφ φ H(φ, τ, ψ) NH(φ, τ, ψ) H(φ, τ, ψ) N H(φ, τ, ψ) N(φ ψ) (Nφ Nψ) φ, φ ψ ψ φ Nφ H(φ, τ, ψ) (H(ψ, τ, χ) (N(ψ τ) H(φ, τ, χ))) N(φ ψ) H(φ,, ψ) H(φ, τ, ψ) ( H(φ,, ψ) H(φ,, τ)) N(φ φ) (H(φ, τ, ψ) H(φ, τ, ψ)) N(ψ ψ ) (H(φ, τ, ψ) H(φ, τ, ψ )) N(τ τ ) (H(φ, τ, ψ) H(φ, τ, ψ)) Completeness: Yanjun Li and Yanjing Wang (2017), Achieving while maintaining: A logic of knowing how with intermediate constraints, Indian Conference on Logic and Its Applications
64 Second-Order Know-How a,b! Alice 0/1 0/1 u sum=0,1 s p sum=3,2 v u S a,b p v S a,b p u K a,b S a,b p Bob u H a,b p # 0/1 sum=2,3 w p sum=0,1 u H a,b,c p Cathy u H a,b c p
65 Second-Order Know-How w H C φ iff there is an action profile s Δ C of coalition C such that for each state v and each complete action profile δ Δ A and each state u W if w C v, s = C δ, and (v, δ, u) M, then u φ w H D C φ iff there is an action profile s ΔD of coalition D such that for each state v and each complete action profile δ Δ A and each state u W if w C v, s = D δ, and (v, δ, u) M, then u φ
66 Axioms for Second-Order Know-How all propositional tautologies H D 1 C 1 (φ ψ) (H D 2 C 2 φ H D 1 D 2 C 1 C 2 ψ), where D 1 D 2 = Ø K C φ φ K C φ K C K C φ K C (φ ψ) (K C φ K C ψ) H D C φ K C HD C φ K C H Ø D φ HØ C φ K Ø φ H Ø Ø φ K C φ K D φ, where C D φ, φ ψ ψ φ K C φ φ H D C φ Completeness: Pavel Naumov and Jia Tao (2018), International Conference on Autonomous Agents and Multiagent Systems (AAMAS 18)
67 Strategies and Responsibility R a φ agent a used strategy that made φ unavoidable. Nφ statement φ is always true N a φ N a φ Nφ φ Nφ N Nφ N(φ ψ) (Nφ Nψ) R a φ φ R a φ R a R a φ R a (φ ψ) (R a φ R a ψ) Nφ R a φ NR a1 φ 1 NR a2 φ 2 NR an φ n N(R a1 φ 1 R a2 φ 2 R an φ n ) Belnap N., Perloff M., Xu M., Facing the Future: Agents and Choices in our Indeterminist World, Oxford, 2001
68 Group Responsibility R C φ coalition C used strategy that made φ unavoidable. R Ø φ Nφ N a φ N a φ R C φ φ R C R C φ R Ø φ R C φ R C R C φ R C (φ ψ) (R C φ R C ψ) R C φ R D φ, where C D Jan Broersen, Andreas Herzig, and Nicolas Troquard. What groups do, can do, and know they can do: an analysis in normal modal logics. Journal of Applied Non-Classical Logics, 19(3): , 2009
69 Responsibility and Knowledge
70 Blameworthiness
71 Thank you!
Strategic Coalitions with Perfect Recall
Strategic Coalitions with Perfect Recall Pavel Naumov Department of Computer Science Vassar College Poughkeepsie, New York 2604 pnaumov@vassar.edu Jia Tao Department of Computer Science Lafayette College
More informationSecond-Order Know-How Strategies
Vassar ollege Digital Window @ Vassar Faculty Research and Reports Summer 7-0-08 Pavel Naumov pnaumov@vassar.edu Jia Tao Lafayette ollege, taoj@lafayette.edu Follow this and additional works at: https://digitalwindow.vassar.edu/faculty_research_reports
More informationStrategically Knowing How
Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence (IJCAI-17) Strategically Knowing How Raul Fervari University of Córdoba CONICET Andreas Herzig University of Toulouse
More informationThe Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract)
The Ceteris Paribus Structure of Logics of Game Forms (Extended Abstract) Davide Grossi University of Liverpool D.Grossi@liverpool.ac.uk Emiliano Lorini IRIT-CNRS, Toulouse University François Schwarzentruber
More informationA Strategic Epistemic Logic for Bounded Memory Agents
CNRS, Université de Lorraine, Nancy, France Workshop on Resource Bounded Agents Barcelona 12 August, 2015 Contents 1 Introduction 2 3 4 5 Combining Strategic and Epistemic Reasoning The goal is to develop
More informationValentin Goranko Stockholm University. ESSLLI 2018 August 6-10, of 29
ESSLLI 2018 course Logics for Epistemic and Strategic Reasoning in Multi-Agent Systems Lecture 5: Logics for temporal strategic reasoning with incomplete and imperfect information Valentin Goranko Stockholm
More informationLogic and Artificial Intelligence Lecture 21
Logic and Artificial Intelligence Lecture 21 Eric Pacuit Currently Visiting the Center for Formal Epistemology, CMU Center for Logic and Philosophy of Science Tilburg University ai.stanford.edu/ epacuit
More informationKnowledge and action in labeled stit logics
Knowledge and action in labeled stit logics John Horty Eric Pacuit April 10, 2014 Abstract Stit semantics supplements branching time models with an operator representing the agency of an individual in
More informationLogics of Rational Agency Lecture 3
Logics of Rational Agency Lecture 3 Eric Pacuit Tilburg Institute for Logic and Philosophy of Science Tilburg Univeristy ai.stanford.edu/~epacuit July 29, 2009 Eric Pacuit: LORI, Lecture 3 1 Plan for the
More informationResource-bounded alternating-time temporal logic
Resource-bounded alternating-time temporal logic Natasha Alechina University of Nottingham Nottingham, UK nza@cs.nott.ac.uk Brian Logan University of Nottingham Nottingham, UK bsl@cs.nott.ac.uk Abdur Rakib
More informationLogic and Social Choice Theory. A Survey. ILLC, University of Amsterdam. November 16, staff.science.uva.
Logic and Social Choice Theory A Survey Eric Pacuit ILLC, University of Amsterdam staff.science.uva.nl/ epacuit epacuit@science.uva.nl November 16, 2007 Setting the Stage: Logic and Games Game Logics Logics
More informationModal Logic XX. Yanjing Wang
Modal Logic XX Yanjing Wang Department of Philosophy, Peking University May 6th, 2016 Advanced Modal Logic (2016 Spring) 1 Completeness A traditional view of Logic A logic Λ is a collection of formulas
More informationA Logic for Cooperation, Actions and Preferences
A Logic for Cooperation, Actions and Preferences Lena Kurzen Universiteit van Amsterdam L.M.Kurzen@uva.nl Abstract In this paper, a logic for reasoning about cooperation, actions and preferences of agents
More informationLogic and Artificial Intelligence Lecture 22
Logic and Artificial Intelligence Lecture 22 Eric Pacuit Currently Visiting the Center for Formal Epistemology, CMU Center for Logic and Philosophy of Science Tilburg University ai.stanford.edu/ epacuit
More informationA Modal Logic for Beliefs and Pro Attitudes
A Modal Logic for Beliefs and Pro Attitudes Kaile Su 1,2 and Abdul Sattar 1 and Han Lin 3 and Mark Reynolds 4 1 Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, Australia
More informationConcurrent Game Structures for Temporal STIT Logic
Concurrent Game Structures for Temporal STIT Logic ABSTRACT Joseph Boudou IRIT Toulouse University Toulouse, France The paper introduces a new semantics for temporal STIT logic the logic of seeing to it
More informationNeighborhood Semantics for Modal Logic Lecture 3
Neighborhood Semantics for Modal Logic Lecture 3 Eric Pacuit ILLC, Universiteit van Amsterdam staff.science.uva.nl/ epacuit August 15, 2007 Eric Pacuit: Neighborhood Semantics, Lecture 3 1 Plan for the
More informationMarketing Impact on Diffusion in Social Networks
Marketing Impact on Diffusion in Social Networks Pavel Naumov Vassar College, Poughkeepsie, New York, USA Jia Tao The College of New Jersey, Ewing, New Jersey, USA Abstract The article proposes a way to
More informationA plausibility driven STIT-operator
A plausibility driven STIT-operator Rob Franken Supervisor: dr. Jan Broersen August 27, 2013 Contents 1 Introduction 3 2 Preliminary notations and definitions 5 3 Introducing plausibility models 7 4 XSTIT
More informationRelaxing Exclusive Control in Boolean Games
Relaxing Exclusive Control in Boolean Games Francesco Belardinelli IBISC, Université d Evry and IRIT, CNRS, Toulouse belardinelli@ibisc.fr Dominique Longin IRIT, CNRS, Toulouse dominique.longin@irit.fr
More informationLogics for MAS: a critical overview
Logics for MAS: a critical overview Andreas Herzig CNRS, University of Toulouse, IRIT, France IJCAI 2013, August 9, 2013 1 / 37 Introduction 2 / 37 Introduction Multi-Agent Systems (MAS): agents with imperfect
More informationAn Extended Interpreted System Model for Epistemic Logics
Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence (2008) An Extended Interpreted System Model for Epistemic Logics Kaile Su 1,2 and Abdul Sattar 2 1 Key laboratory of High Confidence
More informationLOGICS OF AGENCY CHAPTER 5: APPLICATIONS OF AGENCY TO POWER. Nicolas Troquard. ESSLLI 2016 Bolzano 1 / 66
1 / 66 LOGICS OF AGENCY CHAPTER 5: APPLICATIONS OF AGENCY TO POWER Nicolas Troquard ESSLLI 26 Bolzano 2 / 66 OVERVIEW OF THIS CHAPTER Remarks about power and deemed ability Power in Coalition Logic and
More informationGroup Announcement Logic
Group Announcement Logic Thomas Ågotnes joint work with: Philippe Baliani Hans van Ditmarsch Palo Sean Elevator pitch Group Announcement Logic extends pulic announcement logic with: G φ : Group G can make
More informationA Modal Logic of Epistemic Games
Submitted to Games. Pages 1-49. OPEN ACCESS games ISSN 2073-4336 www.mdpi.com/journal/games Article A Modal Logic of Epistemic Games Emiliano Lorini 1, François Schwarzentruber 1 1 Institut de Recherche
More informationA Logic for Reasoning about Counterfactual Emotions
A Logic for Reasoning about Counterfactual Emotions Emiliano Lorini IRIT, Toulouse, France lorini@irit.fr François Schwarzentruber IRIT, Toulouse, France schwarze@irit.fr Abstract The aim of this work
More informationAlternating-time Temporal Logics with Irrevocable Strategies
Alternating-time Temporal Logics with Irrevocable Strategies Thomas Ågotnes Dept. of Computer Engineering Bergen University College, Bergen, Norway tag@hib.no Valentin Goranko School of Mathematics Univ.
More informationCombinations of Stit and Actions
Noname manuscript No. (will be inserted by the editor) Combinations of Stit and Actions Ming Xu Received: date / Accepted: date Abstract We present a simple theory of actions against the background of
More informationBetter Eager Than Lazy? How Agent Types Impact the Successfulness of Implicit Coordination
Better Eager Than Lazy? How Agent Types Impact the Successfulness of Implicit Coordination Thomas Bolander DTU Compute Technical University of Denmark tobo@dtu.dk Thorsten Engesser and Robert Mattmüller
More informationPossibilistic Boolean Games: Strategic Reasoning under Incomplete Information
Possibilistic Boolean Games: Strategic Reasoning under Incomplete Information Sofie De Clercq 1, Steven Schockaert 2, Martine De Cock 1,3, and Ann Nowé 4 1 Dept. of Applied Math., CS & Stats, Ghent University,
More informationTowards Symbolic Factual Change in Dynamic Epistemic Logic
Towards Symbolic Factual Change in Dynamic Epistemic Logic Malvin Gattinger ILLC, Amsterdam July 18th 2017 ESSLLI Student Session Toulouse Are there more red or more blue points? Are there more red or
More informationSTIT is dangerously undecidable
STIT is dangerously undecidable François Schwarzentruber and Caroline Semmling June 2, 2014 Abstract STIT is a potential logical framework to capture responsibility, counterfactual emotions and norms,
More informationSome Remarks on Alternating Temporal Epistemic Logic
Some Remarks on Alternating Temporal Epistemic Logic Corrected version: July 2003 Wojciech Jamroga Parlevink Group, University of Twente, Netherlands Institute of Mathematics, University of Gdansk, Poland
More informationA Preference Logic With Four Kinds of Preferences
A Preference Logic With Four Kinds of Preferences Zhang Zhizheng and Xing Hancheng School of Computer Science and Engineering, Southeast University No.2 Sipailou, Nanjing, China {seu_zzz; xhc}@seu.edu.cn
More informationNeighborhood Semantics for Modal Logic Lecture 5
Neighborhood Semantics for Modal Logic Lecture 5 Eric Pacuit ILLC, Universiteit van Amsterdam staff.science.uva.nl/ epacuit August 17, 2007 Eric Pacuit: Neighborhood Semantics, Lecture 5 1 Plan for the
More informationModal Logic XXI. Yanjing Wang
Modal Logic XXI Yanjing Wang Department of Philosophy, Peking University May 17th, 2017 Advanced Modal Logic (2017 Spring) 1 Completeness via Canonicity Soundness and completeness Definition (Soundness)
More informationModal Probability Logic
Modal Probability Logic ESSLLI 2014 - Logic and Probability Wes Holliday and Thomas Icard Berkeley and Stanford August 14, 2014 Wes Holliday and Thomas Icard: Modal Probability 1 References M. Fattorosi-Barnaba
More informationChanging Types. Dominik Klein Eric Pacuit. April 24, 2011
Changing Types Dominik Klein Eric Pacuit April 24, 2011 The central thesis of the epistemic program in game theory (Brandenburger, 2007) is that the basic mathematical models of a game situation should
More informationMarketing Impact on Diffusion in Social Networks
Marketing Impact on Diffusion in Social Networks Pavel Naumov Department of Computer Science Illinois Wesleyan University Bloomington, Illinois, the United States pnaumov@iwu.edu Jia Tao Department of
More informationPDL as a Multi-Agent Strategy Logic
PDL as a Multi-Agent Strategy Logic Extended Abstract Jan van Eijck CWI and ILLC Science Park 123 1098 XG Amsterdam, The Netherlands jve@cwi.nl ABSTRACT Propositional Dynamic Logic or PDL was invented
More informationarxiv: v3 [cs.ai] 9 Jul 2015
A Logic of Knowing How Yanjing Wang y.wang@pku.edu.cn Department of Philosophy, Peking University arxiv:1505.06651v3 [cs.ai] 9 Jul 2015 Abstract. In this paper, we propose a single-agent modal logic framework
More informationBudget-Constrained Knowledge in Multiagent Systems
Budget-Constrained Knowledge in Multiagent Systems Pavel Naumov Mathematics and Computer Science McDaniel College Westminster, MD 20853 pavel@pavelnaumov.com Jia Tao Department of Computer Science Bryn
More informationRelaxing Exclusive Control in Boolean Games
Relaxing Exclusive Control in Boolean Games Francesco Belardinelli IBISC, Université d Evry and IRIT, CNRS, Toulouse belardinelli@ibisc.fr Dominique Longin IRIT, CNRS, Toulouse dominique.longin@irit.fr
More informationProduct Update and Looking Backward
Product Update and Looking Backward Audrey Yap May 21, 2006 Abstract The motivation behind this paper is to look at temporal information in models of BMS product update. That is, it may be useful to look
More informationA Logical Theory of Coordination and Joint Ability
A Logical Theory of Coordination and Joint Ability Hojjat Ghaderi and Hector Levesque Department of Computer Science University of Toronto Toronto, ON M5S 3G4, Canada {hojjat,hector}@cstorontoedu Yves
More informationHow to share knowledge by gossiping
How to share knowledge by gossiping Andreas Herzig and Faustine Maffre University of Toulouse, IRIT http://www.irit.fr/lilac Abstract. Given n agents each of which has a secret (a fact not known to anybody
More informationOn Logics of Strategic Ability based on Propositional Control
Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI-16) On Logics of Strategic Ability based on Propositional Control Francesco Belardinelli 1 and Andreas Herzig
More informationarxiv: v1 [math.lo] 3 Feb 2013
Functional Dependence in Strategic Games arxiv:1302.0447v1 [math.lo] 3 Feb 2013 Kristine Harjes and Pavel Naumov Department of Mathematics and Computer Science McDaniel College, Westminster, Maryland,
More informationIFI TECHNICAL REPORTS. Institute of Computer Science, Clausthal University of Technology. IfI-05-10
IFI TECHNICAL REPORTS Institute of Computer Science, Clausthal University of Technology IfI-05-10 Clausthal-Zellerfeld 2005 Constructive Knowledge: What Agents Can Achieve under Incomplete Information
More informationWhat will they say? Public Announcement Games
What will they say? Public Announcement Games Thomas Ågotnes Hans van Ditmarsch Abstract Dynamic epistemic logics describe the epistemic consequences of actions. Public announcement logic, in particular,
More informationMULTI-AGENT ONLY-KNOWING
MULTI-AGENT ONLY-KNOWING Gerhard Lakemeyer Computer Science, RWTH Aachen University Germany AI, Logic, and Epistemic Planning, Copenhagen October 3, 2013 Joint work with Vaishak Belle Contents of this
More informationThe Muddy Children:A logic for public announcement
The Muddy Children: Jesse Technical University of Eindhoven February 10, 2007 The Muddy Children: Outline 1 2 3 4 The Muddy Children: Quincy Prescott Baba: At least one of you is muddy. Quincy: I don t
More informationAn internal version of epistemic logic
Guillaume Aucher An internal version of epistemic logic Abstract. Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying
More informationEpistemic Oughts in Stit Semantics
Epistemic Oughts in Stit Semantics John Horty *** Draft *** Version of: April 5, 2018 Contents 1 Introduction 1 2 Stit semantics 3 2.1 Branching time.................................. 3 2.2 The stit operator.................................
More informationMaximal Introspection of Agents
Electronic Notes in Theoretical Computer Science 70 No. 5 (2002) URL: http://www.elsevier.nl/locate/entcs/volume70.html 16 pages Maximal Introspection of Agents Thomas 1 Informatics and Mathematical Modelling
More informationValentin Goranko Stockholm University. ESSLLI 2018 August 6-10, of 33
ESSLLI 2018 course Logics for Epistemic and Strategic Reasoning in Multi-Agent Systems Lecture 4: Logics for temporal strategic reasoning with complete information Valentin Goranko Stockholm University
More informationTowards A Multi-Agent Subset Space Logic
Towards A Multi-Agent Subset Space Logic A Constructive Approach with Applications Department of Computer Science The Graduate Center of the City University of New York cbaskent@gc.cuny.edu www.canbaskent.net
More informationAction, Failure and Free Will Choice in Epistemic stit Logic
Action, Failure and Free Will Choice in Epistemic stit Logic Jan Broersen Department of Information and Computing Sciences Utrecht University, The Netherlands Symposium "What is really possible?" Utrecht,
More informationA Note on Logics of Ability
A Note on Logics of Ability Eric Pacuit and Yoav Shoham May 8, 2008 This short note will discuss logical frameworks for reasoning about an agent s ability. We will sketch details of logics of can, do,
More informationAction Types in Stit Semantics
Action Types in Stit Semantics John Horty Eric Pacuit *** DRAFT *** Version of: May 11, 2016 Contents 1 Introduction 1 2 A review of stit semantics 2 2.1 Branching time..................................
More informationProperties of Knowledge Forgetting
Properties of Knowledge Forgetting Yan Zhang and Yi Zhou Intelligent Systems Laboratory University of Western Sydney, Australia E-mail: {yan,yzhou}@scm.uws.edu.au Abstract In this paper we propose a formal
More informationA logical formalism for the subjective approach in a multi-agent setting
logical formalism for the subjective approach in a multi-agent setting Guillaume ucher Université Paul Sabatier, Toulouse (F) University of Otago, Dunedin (NZ) aucher@irit.fr bstract. Representing an epistemic
More informationKnowing Values and Public Inspection
Knowing Values and Public Inspection Malvin Gattinger with Jan van Eijck & Yanjing Wang arxiv.org/abs/1609.03338 slides at w4eg.de/malvin 2016-10-14, LIRa ILLC, Amsterdam Introduction Knowing that announcing
More informationSocial Choice Theory for Logicians Lecture 5
Social Choice Theory for Logicians Lecture 5 Eric Pacuit Department of Philosophy University of Maryland, College Park ai.stanford.edu/ epacuit epacuit@umd.edu June 22, 2012 Eric Pacuit: The Logic Behind
More informationIntroduction to Epistemic Reasoning in Interaction
Introduction to Epistemic Reasoning in Interaction Eric Pacuit Center for Logic and Philosophy of Science Tilburg University ai.stanford.edu/~epacuit December 9, 2009 Eric Pacuit 1 We are interested in
More informationLogic and Artificial Intelligence Lecture 12
Logic and Artificial Intelligence Lecture 12 Eric Pacuit Currently Visiting the Center for Formal Epistemology, CMU Center for Logic and Philosophy of Science Tilburg University ai.stanford.edu/ epacuit
More informationWhat is DEL good for? Alexandru Baltag. Oxford University
Copenhagen 2010 ESSLLI 1 What is DEL good for? Alexandru Baltag Oxford University Copenhagen 2010 ESSLLI 2 DEL is a Method, Not a Logic! I take Dynamic Epistemic Logic () to refer to a general type of
More informationThe Axiomatic Method in Social Choice Theory:
The Axiomatic Method in Social Choice Theory: Preference Aggregation, Judgment Aggregation, Graph Aggregation Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Ulle Endriss
More informationEpistemic Informativeness
Epistemic Informativeness Yanjing Wang and Jie Fan Abstract In this paper, we introduce and formalize the concept of epistemic informativeness (EI) of statements: the set of new propositions that an agent
More informationKnowing Whether in Proper Epistemic Knowledge Bases
Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (AAAI-16) Knowing Whether in Proper Epistemic Knowledge Bases Tim Miller, Paolo Felli, Christian Muise, Adrian R. Pearce, Liz Sonenberg
More informationEpistemic Logic: VI Dynamic Epistemic Logic (cont.)
Epistemic Logic: VI Dynamic Epistemic Logic (cont.) Yanjing Wang Department of Philosophy, Peking University Oct. 26th, 2015 Two basic questions Axiomatizations via reduction A new axiomatization Recap:
More informationDEL-sequents for Regression and Epistemic Planning
DEL-sequents for Regression and Epistemic Planning Guillaume Aucher To cite this version: Guillaume Aucher. DEL-sequents for Regression and Epistemic Planning. Journal of Applied Non-Classical Logics,
More informationUndecidability in Epistemic Planning
Undecidability in Epistemic Planning Thomas Bolander, DTU Compute, Tech Univ of Denmark Joint work with: Guillaume Aucher, Univ Rennes 1 Bolander: Undecidability in Epistemic Planning p. 1/17 Introduction
More informationProperties of the Integers
Properties of the Integers The set of all integers is the set and the subset of Z given by Z = {, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, }, N = {0, 1, 2, 3, 4, }, is the set of nonnegative integers (also called
More informationa + b = b + a and a b = b a. (a + b) + c = a + (b + c) and (a b) c = a (b c). a (b + c) = a b + a c and (a + b) c = a c + b c.
Properties of the Integers The set of all integers is the set and the subset of Z given by Z = {, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, }, N = {0, 1, 2, 3, 4, }, is the set of nonnegative integers (also called
More informationSemantics for Dynamic Syntactic Epistemic Logics
Semantics for Dynamic Syntactic Epistemic Logics Thomas Ågotnes University of Bergen Norway agotnes@ii.uib.no Natasha Alechina University of Nottingham UK nza@cs.nott.ac.uk Abstract Traditional epistemic
More informationA Logic for Reasoning About Game Strategies
A Logic for Reasoning About Game Strategies Dongmo Zhang The University of Western Sydney Australia d.zhang@uws.edu.au Michael Thielscher The University of New South Wales Australia mit@cse.unsw.edu.au
More informationGraph Theory and Modal Logic
Osaka University of Economics and Law (OUEL) Aug. 5, 2013 BLAST 2013 at Chapman University Contents of this Talk Contents of this Talk 1. Graphs = Kripke frames. Contents of this Talk 1. Graphs = Kripke
More informationLecture 4: Coordinating Self-Interested Agents
Social Laws for Multi-Agent Systems: Logic and Games Lecture 4: Coordinating Self-Interested Agents Thomas Ågotnes Department of Information Science and Media Studies University of Bergen, Norway NII Tokyo
More informationA Logic of Games and Propositional Control
A Logic of Games Propositional Control Nicolas Troquard Wiebe van der Hoek Michael Wooldridge Department of Computer Science University of Liverpool Liverpool L69 3BX, UK { nico, wiebe.van-der-hoek, mjw
More informationKnowable as known after an announcement
RESEARCH REPORT IRIT/RR 2008-2 FR Knowable as known after an announcement Philippe Balbiani 1 Alexandru Baltag 2 Hans van Ditmarsch 1,3 Andreas Herzig 1 Tomohiro Hoshi 4 Tiago de Lima 5 1 Équipe LILAC
More informationLogic and Artificial Intelligence Lecture 20
Logic and Artificial Intelligence Lecture 20 Eric Pacuit Currently Visiting the Center for Formal Epistemology, CMU Center for Logic and Philosophy of Science Tilburg University ai.stanford.edu/ epacuit
More informationLogics for multi-agent systems: an overview
Logics for multi-agent systems: an overview Andreas Herzig University of Toulouse and CNRS, IRIT, France EASSS 2014, Chania, 17th July 2014 1 / 40 Introduction course based on an overview paper to appear
More informationReasoning about Memoryless Strategies under Partial Observability and Unconditional Fairness Constraints
Reasoning about Memoryless Strategies under Partial Observability and Unconditional Fairness Constraints Simon Busard a,1, Charles Pecheur a, Hongyang Qu b,2, Franco Raimondi c a ICTEAM Institute, Université
More informationCTL.STIT: enhancing ATL to express important multi-agent system verification properties
CTL.STIT: enhancing ATL to express important multi-agent system verification properties Jan Broersen Department of Information and Computing Sciences Utrecht University The Netherlands broersen@cs.uu.nl
More informationAn Extension of BDI CTL with Functional Dependencies and Components
An Extension of BDI CTL with Functional Dependencies and Components Mehdi Dastani 1 and Leendert van der Torre 2 1 Institute of Information and Computer Sciences, Utrecht University mehdi@cs.uu.nl 2 Department
More informationModel Checking Strategic Ability Why, What, and Especially: How?
Model Checking Strategic Ability Why, What, and Especially: How? Wojciech Jamroga 1 Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland w.jamroga@ipipan.waw.pl Abstract Automated
More informationNested Epistemic Logic Programs
Nested Epistemic Logic Programs Kewen Wang 1 and Yan Zhang 2 1 Griffith University, Australia k.wang@griffith.edu.au 2 University of Western Sydney yan@cit.uws.edu.au Abstract. Nested logic programs and
More informationPrinciples of Knowledge Representation and Reasoning
Principles of Knowledge Representation and Reasoning Modal Logics Bernhard Nebel, Malte Helmert and Stefan Wölfl Albert-Ludwigs-Universität Freiburg May 2 & 6, 2008 Nebel, Helmert, Wölfl (Uni Freiburg)
More informationThe Modal Logic S4F, the Default Logic, and the Logic Here-and-There
The Modal Logic S4F, the Default Logic, and the Logic Here-and-There Mirosław Truszczyński Department of Computer Science, University of Kentucky, Lexington, KY 40506-0046, USA Abstract The modal logic
More informationSocially Friendly and Group Protecting Coalition Logics
Socially Friendly and Group Protecting Coalition Logics Valentin Goranko 1,2 and Sebastian Enqvist 1 1 Stockholm University, Sweden 2 University of Johannesburg, South Africa (visiting professorship) valentin.goranko@philosophy.su.se,
More informationCharacterizing the NP-PSPACE Gap in the Satisfiability Problem for Modal Logic
Characterizing the NP-PSPACE Gap in the Satisfiability Problem for Modal Logic Joseph Y. Halpern Computer Science Department Cornell University, U.S.A. e-mail: halpern@cs.cornell.edu Leandro Chaves Rêgo
More informationPreferences in Game Logics
Preferences in Game Logics Sieuwert van Otterloo Department of Computer Science University of Liverpool Liverpool L69 7ZF, United Kingdom sieuwert@csc.liv.ac.uk Wiebe van der Hoek wiebe@csc.liv.ac.uk Michael
More informationA Survey of Topologic
Illuminating New Directions Department of Computer Science Graduate Center, the City University of New York cbaskent@gc.cuny.edu // www.canbaskent.net/logic December 1st, 2011 - The Graduate Center Contents
More informationNeighborhood Semantics for Modal Logic An Introduction May 12-17, ESSLLI 2007
An Introduction May 12-17, ESSLLI 2007 Eric Pacuit staff.science.uva.nl/ epacuit epacuit@staff.science.uva.nl July 3, 2007 Welcome to! The course will consist of five 90 minute lectures roughly organized
More informationPossibilistic Safe Beliefs
Possibilistic Safe Beliefs Oscar Estrada 1, José Arrazola 1, and Mauricio Osorio 2 1 Benemérita Universidad Autónoma de Puebla oestrada2005@gmail.com, arrazola@fcfm.buap.mx. 2 Universidad de las Américas
More informationThis is an author-deposited version published in : Eprints ID : 19194
Open Archive TOULOUSE Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited
More informationA simplified proof of arithmetical completeness theorem for provability logic GLP
A simplified proof of arithmetical completeness theorem for provability logic GLP L. Beklemishev Steklov Mathematical Institute Gubkina str. 8, 119991 Moscow, Russia e-mail: bekl@mi.ras.ru March 11, 2011
More informationDynamic Logics of Knowledge and Access
Dynamic Logics of Knowledge and Access Tomohiro Hoshi (thoshi@stanford.edu) Department of Philosophy Stanford University Eric Pacuit (e.j.pacuit@uvt.nl) Tilburg Center for Logic and Philosophy of Science
More informationArtificial Intelligence
Artificial Intelligence 173 (2009) 45 79 Contents lists available at ScienceDirect Artificial Intelligence www.elsevier.com/locate/artint Reasoning about coalitional games Thomas Ågotnes a,, Wiebe van
More information