- The dynamics of imperfect information
- Award date
- 21 September 2012
- Number of pages
- Amsterdam: Institute for Logic, Language and Computation
- Document type
- PhD thesis
- Interfacultary Research Institutes
- Institute for Logic, Language and Computation (ILLC)
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 ∀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.
- ILLC dissertation series DS-2012-07
Research conducted at: Universiteit van Amsterdam
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