The Secret of My Success

Abstract

ABSTRACT. In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is 'fact p is true and you don't know that', after which you know that p, which entails the negation of the announcement formula. The announcement of such a formula in a given information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and 'philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas. Heraclitus As they step into the same rivers, other and still other waters flow upon them.

Logic and Its Applications

“…For instance, the equivalence problem of non-deterministic FST is undecidable, and the undecidability proof is non surprisingly based on PCP [28]. For instance, two FST may not produce there output letters at the same time when reading the same input position, but still, they can be equivalent.…”

Dynamic epistemic logic with branching temporal structures

“…This phenomenon is also related to the idea of a successful update as discussed in van Ditmarsch and Kooi (2006). We can call a public announcement successful when the formula announced is true after the update, and unsuccessful when the formula announced becomes false.…”

“…Fagin et al (1995); Parikh and Ramanujam (2003) for ETL and to e.g. Baltag et al (1998); Gerbrandy (1999); van Benthem et al (2006); van Ditmarsch et al (2007) for DEL. Below, we fix a finite set A of agents and a countable set At of propositional letters.…”

“…from the models of Dynamic Epistemic Logic (DEL: e.g Baltag et al 1998;Gerbrandy 1999;van Benthem et al 2006;van Ditmarsch et al 2007…”

On Being in an Undiscoverable Position

“…That repeated announcement of a sentence containing indexical expressions referring to epistemic states may start with a true announcement and wind up in a false announcement is a phenomenon that has been thoroughly investigated in the field of dynamic epistemic logic (see Holliday, Hoshi, and Icard ; Holliday and Icard ; van Benthem ; van Ditmarsch and Kooi ). Gerbrandy () argues that this phenomenon is behind the surprise exam paradox.…”