MoL-2010-14:
Demey, Lorenz
(2010)
*Agreeing to Disagree in Probabilistic Dynamic Epistemic Logic.*
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## Abstract

Aumann's agreeing to disagree theorem is a central theorem of game

theory. This result says that if two agents have a common prior, then

they cannot agree (have common knowledge of their posteriors) to

disagree (while these posteriors are not identical). This thesis looks

at the agreeing to disagree theorem from the perspective of

probabilistic dynamic epistemic logic.

The first goal of the thesis is to establish a new connection between

game theory and epistemic logic. We prove (local model-based versions

and global frame-based versions of) several semantic agreement

theorems, and show that these are natural formalizations of Aumann's

original result. We also provide axiomatizations of (dynamic)

agreement logics, in which the first of these agreement theorems can

be derived syntactically.

The second goal is the further technical development of probabilistic

dynamic epistemic logic. We mention three examples. First, to model

the experiment dynamics, we enrich the probabilistic Kripke models

with `experiment relations', thus establishing a link with the dynamic

epistemic logic of questions. Second, to model the communication

dynamics, we introduce the notion of a `dialogue about a proposition

\varphi', which is a particular sequence of public announcements; we

show that this sequence always has a fixed point, and that at this

fixed point the agents' probabilities for \varphi have become common

knowledge. Thirdly, to make sure that both types of dynamics are

well-defined, we introduce the constraint that \mu_i(w)(w)>0 for all

states w in any Kripke model, and discuss the technical and

methodological consequences of this constraint.

The third goal is to use the technical results for the purpose of

clarifying some conceptual issues surrounding the agreement

theorem. In particular, we discuss the role of common knowledge (which

we claim to be smaller than often thought), and the importance of

explicitly representing the experimentation and communication

dynamics, which is central in the intuitive motivation behind Aumann's

result.

Recently D\'{e}gremont and Roy have formalized Aumann's agreement

theorem in the context of epistemic plausibility models. Our fourth

and final goal is to provide a detailed comparison between their

approach and the one developed in this thesis, focusing on the

representation of the agents' soft information (quantitatively versus

qualitatively).

Item Type: | Report |
---|---|

Report Nr: | MoL-2010-14 |

Series Name: | Master of Logic Thesis (MoL) Series |

Year: | 2010 |

Uncontrolled Keywords: | agreement theorem, probabilistic dynamic epistemic logic, common knowledge, common prior. |

Subjects: | Logic |

Date Deposited: | 12 Oct 2016 14:38 |

Last Modified: | 12 Oct 2016 14:38 |

URI: | https://eprints.illc.uva.nl/id/eprint/839 |

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