DS-2012-07: Galliani, Pietro (2012) The Dynamics of Imperfect Information. Doctoral thesis, University of Amsterdam.
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Abstract
We examine doxastically inspired variants and extensions of Dependence
Logic which arise from the consideration of announcement operators and
non-functional dependence atoms. We solve several open questions of the
area, among them the following two:
1.The \forall^1 quantifier of (Kontinen and Väänänen, 2009) is not
uniformly definable in Dependence Logic;
2. All NP properties of teams are definable in Independence Logic.
Furthermore, we generalize Cameron and Hodges' result about the
combinatorial properties of compositional semantics for logics of imperfect
information to the infinite case, thus introducing a new notion of sensible
semantics; and we develop a "general" semantics for Independence Logic (or
logics contained in it, such as Dependence Logic) as well as a proof system
for which we prove soundness and completeness. We then examine the dynamics
of information update which lies beneath the appearance of Team Semantics,
extending van Benthem's mutual embedding result between First Order Logic
and Dynamic Game Logic (DGL) to the cases of Dependence Logic and an
imperfect-information variant of DGL. We use the insights arising from the
embedding to develop dynamic variants of Dependence Logic and a Team
Transition Semantics in which expressions are interpreted as transition
systems over teams. Finally, we show that many of the operators and
connectives considered in Team Semantics have natural interpretations in
terms of belief descriptions and belief updates, and we argue in favor of
the doxastic interpretation of this semantical framework.
Keywords:
| Item Type: | Thesis (Doctoral) |
|---|---|
| Report Nr: | DS-2012-07 |
| Series Name: | ILLC Dissertation (DS) Series |
| Year: | 2012 |
| Subjects: | Logic |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 14 Jun 2022 15:16 |
| Last Modified: | 14 Jun 2022 15:16 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2113 |
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