Towards Mathematical Philosophy

area and in applications to linguistics, formal epistemology, and the study of norms. The second contains papers on non-classical and many-valued logics, with an eye on applications in computer science and through it to engineering. The third concerns the logic of belief management,whichis likewise closely connected with recent work in computer science but also links directly with epistemology, the philosophy of science, the study of legal and other normative systems, and cognitive science. The grouping is of course rough, for there are contributions to the volume that lie astride a boundary; at least one of them is relevant, from a very abstract perspective, to all three areas. We say a few words about each of the individual chapters, to relate them to each other and the general outlook of the volume. Modal Logics The ?rst bundle of papers in this volume contains contribution to modal logic. Three of them examine general problems that arise for all kinds of modal logics. The ?rst paper is essentially semantical in its approach, the second proof-theoretic, the third semantical again: • Commutativity of quanti?ers in varying-domain Kripke models,by R. Goldblatt and I. Hodkinson, investigates the possibility of com- tation (i.e. reversing the order) for quanti?ers in ?rst-order modal logics interpreted over relational models with varying domains. The authors study a possible-worlds style structural model theory that does not v- idate commutation, but satis?es all the axioms originally presented by Kripke for his familiar semantics for ?rst-order modal logic.

David Makinson, Visiting Professor in Department of Philosophy, London School of Economics, author of 'Bridges from Classical to Nonmonotonic Logic' (College Publications, 2005) and 'Sets Logic and Maths for Computing' (Springer 2008)

Jacek Malinowski, Professor of Logic at Institute of Philosophy, Polish Academy of Sciences and at Department of Logic, Nicolaus Copernicus University. Editor-in-Chief of Studia Logica

Heinrich Wansing, Professor of Philosophy of Science and Logic, Dresden University of Technology; managing editor of Studia Logica; author of 'The Logic of Information Structures' (1993) and 'Displaying Modal Logic (1998)'