This is the first book promoting Mathematical Philosophy as an interdisciplinary field. It is a collection of articles applying methods of logic and math to solve problems, some from logic itself, others from other sciences.

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.

Contains some of the highest level contributions to Logic Is the first book promoting Mathematical Philosophy as an interdisciplinary field Is a collection of articles applying methods of logic -- or more generally those of mathematics -- to solve problems from logic itself and from other sciences Includes supplementary material: sn.pub/extras

Autorentext

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)"

Klappentext

This volume contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems, some of which come from logic itself, others from other sciences. Its range of subjects is far from complete, but broadly representative.

The first group of papers in this volume consists of contributions to pure and applied modal logic. The problems discussed here range from the structure of lattices of normal and other modal propositional logics to modal proof theory and to the semantics of quantified modal logic. The second group of papers deals with Many-valued logics - an extensive domain of strictly logical investigations rooting in philosophical questions concerning the nature of logical values. Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. Towards Mathematical Philosophy deals with focal issues of belief revision. The volume concludes with contributions which may be seen to belong to the field of formal epistemology, the area applying logical, probabilistic, game-theoretic and other formal methods to problems and issues in epistemology and philosophy of science, such as those concerning anti-realism, skepticism, theory comparison and theory choice, justification, sources of knowledge and learning theories.

Inhalt
From Logic to Mathematical Philosophy.- Commutativity of Quantifiers in Varying-Domain Kripke Models.- The Method of Tree-Hypersequents for Modal Propositional Logic.- All Splitting Logics in the Lattice NExt(KTB).- A Temporal Logic of Normative Systems.- Reasoning with Justifications.- Monotone Relations, Fixed Points and Recursive Definitions.- Processing Information from a Set of Sources.- The Classical Model Existence Theorem in Subclassical Predicate Logics I.- Weak Implicational Logics Related to the Lambek CalculusGentzen versus Hilbert Formalisms.- Faithful and Invariant Conditional Probability in ?ukasiewicz Logic.- A Fuzzy Logic Approach to Non-Scalar Hedges.- The Procedures for Belief Revision.- Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators.- The Coherence of TheoriesDependencies and Weights.- On Meta-Knowledge and Truth.