David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 158 (2):165 - 179 (2007)
Multi-modal versions of propositional logics S5 or S4—commonly accepted as logics of knowledge—are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves certain kind of problems involving public communications—among them well known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics.
|Keywords||Logics of knowledge Communications Kripke models (applicable in) expert systems|
|Categories||categorize this paper)|
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References found in this work BETA
Jaakko Hintikka (1962). Knowledge and Belief. Ithaca, N.Y.,Cornell University Press.
Robert C. Stalnaker & Richmond H. Thomason (1968). Abstraction in First-Order Modal Logic. Theoria 34 (3):203-207.
Citations of this work BETA
Hannes Leitgeb & Krister Segerberg (2007). Dynamic Doxastic Logic: Why, How, and Where To? Synthese 155 (2):167 - 190.
Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper (2009). Keep 'Hoping' for Rationality: A Solution to the Backward Induction Paradox. Synthese 169 (2):301 - 333.
Fenrong Liu & Yanjing Wang (2013). Reasoning About Agent Types and the Hardest Logic Puzzle Ever. Minds and Machines 23 (1):123-161.
Vincent F. Hendricks & John Symons (2006). Where's the Bridge? Epistemology and Epistemic Logic. Philosophical Studies 128 (1):137 - 167.
Patrick Allo (2013). The Many Faces of Closure and Introspection. Journal of Philosophical Logic 42 (1):91-124.
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