Towards Mathematical Philosophy

1. Front Matter

   Pages i-xiii

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2. From Logic to Mathematical Philosophy

   • David Makinson, Jacek Malinowski, Heinrich Wansing

   Pages 1-7

3. Commutativity of Quantifiers in Varying-Domain Kripke Models

   • Robert Goldblatt, Ian Hodkinson

   Pages 9-30

4. The Method of Tree-Hypersequents for Modal Propositional Logic

   • Francesca Poggiolesi

   Pages 31-51

5. All Splitting Logics in the Lattice NExt(KTB)

   • Tomasz Kowalski, Yutaka Miyazaki

   Pages 53-67

6. A Temporal Logic of Normative Systems

   • Thomas Ågotnes, Wiebe van der Hoek, Juan A. Rodríguez-Aguilar, Carles Sierra, Michael Wooldridge

   Pages 69-106

7. Reasoning with Justifications

   • Melvin Fitting

   Pages 107-123

8. Monotone Relations, Fixed Points and Recursive Definitions

   • Janusz Czelakowski

   Pages 125-164

9. Processing Information from a Set of Sources

   • Arnon Avron, Jonathan Ben-Naim, Beata Konikowska

   Pages 165-186

10. The Classical Model Existence Theorem in Subclassical Predicate Logics I

    • Jui-Lin Lee

    Pages 187-199

11. Weak Implicational Logics Related to the Lambek Calculus—Gentzen versus Hilbert Formalisms

    • Wojciech Zielonka

    Pages 201-212

12. Faithful and Invariant Conditional Probability in Łukasiewicz Logic

    • Daniele Mundici

    Pages 213-232

13. A Fuzzy Logic Approach to Non-Scalar Hedges

    • Stephan van der Waart van Gulik

    Pages 233-248

14. The Procedures for Belief Revision

    • Piotr Łukowski

    Pages 249-268

15. Shifting Priorities: Simple Representations for Twenty-Seven Iterated Theory Change Operators

    • Hans Rott

    Pages 269-296

16. The Coherence of Theories—Dependencies and Weights

    • Jason Jingshi Li, Rex Bing Hung Kwok, Norman Y. Foo

    Pages 297-318

17. On Meta-Knowledge and Truth

    • Urszula Wybraniec-Skardowska

    Pages 319-343

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.

• Formal methods
• Invariant
• Logic
• Logical investigations
• Logical systems
• Mathematical philosophy
• Methods of logic
• Philosophy
• calculus
• mathematics
• proof
• theorem

• Department of Philosophy, London School of Economics, London, United Kingdom

  David Makinson

• Institute of Philosophy and Sociology, Polish Academy of Sciences, Warszawa, Poland

  Jacek Malinowski

• Institute of Philosophy, Dresden University of Technology, Dresden, Germany

  Heinrich Wansing

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)"

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