Link to publication General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Dynamic Logics of Evidence-Based BeliefsDedicated to Professor Ryszard Wójcicki on the occasion of his 80th birthday * Abstract. This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of "evidence management", ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

This book series contains textbooks on various topics in logic. Though each book can be read independently, the series as a whole gives readers a comprehensive view of logic at the present time. Each book in the series is written clearly and concisely, providing plenty of well-planned examples and exercises, and supplying explanations of the scope and motivation of the topics. The topics discussed in the series range from mathematical and philosophical logic to logical methods applied to computer science, artificial intelligence and cognitive science. The series will contain both introductory and advanced texts. The intended readership includes advanced undergraduate and graduate students in philosophy, mathematics, computer science and related fields. The series is also suitable for self-taught learning.

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Abstract. Neighbourhood structures are the standard semantic tool used to reason about non-normal modal logics. The logic of all neighbourhood models is called classical modal logic. In coalgebraic terms, a neighbourhood frame is a coalgebra for the contravariant powerset functor composed with itself, denoted by 2 2 . We use this coalgebraic modelling to derive notions of equivalence between neighbourhood structures. 2 2 -bisimilarity and behavioural equivalence are well known coalgebraic concepts, and they are distinct, since 2 2 does not preserve weak pullbacks. We introduce a third, intermediate notion whose witnessing relations we call precocongruences (based on pushouts). We give back-and-forth style characterisations for 2 2 -bisimulations and precocongruences, we show that on a single coalgebra, precocongruences capture behavioural equivalence, and that between neighbourhood structures, precocongruences are a better approximation of behavioural equivalence than 2 2 -bisimulations. We also introduce a notion of modal saturation for neighbourhood models, and investigate its relationship with definability and image-finiteness. We prove a Hennessy-Milner theorem for modally saturated and for image-finite neighbourhood models. Our main results are an analogue of Van Benthem's characterisation theorem and a model-theoretic proof of Craig interpolation for classical modal logic.

Stit semantics grows out of a modal tradition in the logic of action that concentrates on an operator representing the agency of an individual in seeing to it that some state of affairs holds, rather than on the actions the individual performs in doing so. The purpose of this paper is to enrich stit semantics, and especially epistemic stit semantics, by supplementing the overall framework with an explicit treatment of action types. We show how the introduction of these new action types allows us to define a modal operator capturing an epistemic sense of agency, and how this operator can be used to express an epistemic sense of ability.