MoL-2001-07: Updating Epistemic Uncertainty: an essay in the logic of information change

MoL-2001-07: Rodenhäuser, Ben (2001) Updating Epistemic Uncertainty: an essay in the logic of information change. [Report]

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The results of this thesis may be summarized as follows. In chapter 2, we have introduced and motivated a general framework for analyzing informational update, given by the concept of an update frame; the main topic of this thesis was the comparison of this setting with what seems to be the most general proposal for solving the update problem: the operation of product update, introduced in the work of Baltag, Solecki, and Moss. We stressed the differences between the two settings: update frames are not tied to a specific rule of updating, while the product update provides just that. But even when restricting the class of update frames to those that obey such a rule, the basic perspective is different: update frames provide a bird's eye view on streams of epistemic interaction, while the product operation locally performs updates in a specific situation. Section 2.4 compared the two settings, product update, and update frames, focussing on the interplay between the local and the global level. The main result was a characterization of the relationship between product update and update frames that applies to several interesting classes of update frames. On the way, several features of the product update operation became clear: first and foremost, it encodes a notion of - what we called - epistemic height, that we recovered in the setting of update frames. Also, it became clear how the product update operation generates a stream of information flow in an algorithmic manner. The next chapter introduced the language L_{BMS} of [BMS99], and the extension L^*_{BMS} . The main feature of this semantics we stressed is that it builds the product update operation right into the interpretation of the language. Chapter 4 introduced a new language, L_{EDA}, drawing upon the insights of Baltag et al. , but also using tools known from the literature on dynamic arrow logic and hybrid logic. Its main novelty is the use of epistemic operators both on the level of states and on the level of actions. Additional operators enable the study of preconditions and postconditions. Chapter 5 was devoted to comparing the two approaches. We showed how to characterize the operation of product update using the system L_{EDA}. A comparison of the structural notions of bisimulations for the two languages shed light on the circumstances in which dynamic and epistemic bisimulation ``collapse'', in that they mutually imply each other. We then showed how to simulate L^*_{BMS} , the extension of L BMS with common knowledge operators, using L^*_{EDA} , which itself is obtained by extending L_{EDA} with common knowledge/learning operators both on states and actions. Chapter 6 dealt with the closure and preservation problems raised by the product update operation. We analyzed them using the basic multi-modal language L_{ML}, which is a sublanguage of both systems discussed in the preceding chapters of this thesis. We established some results concerning the purely semantic side of the enterprize, closure under update. Linguistically, we presented a preservation result for first-order logic, and a fine structure analysis of preservation questions for modal logic on models.

Item Type: Report
Report Nr: MoL-2001-07
Series Name: Master of Logic Thesis (MoL) Series
Year: 2001
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38

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