In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This volume reflects the multi-dimensional nature of the interplay between logic and science. It presents contributions from the world's leading scholars under the following headings:

- Proof, Knowledge and Computation

- Truth Values beyond Bivalence

- Category-Theoretic Structures

- Independence, Evaluation Games, and Imperfect Information

- Dialogue and Pragmatics

The contents exemplify the liveliness of modern perspectives on the philosophy of logic and mathematics and demonstrate the growth of the discipline. It describes new trends, possible developments for research and new issues not normally raised in the standard agenda of the philosophy of logic and mathematics. It transforms rigid classical partitions into a more open field for improvisation.

Acknowledgments.- 1. Introduction: Alternative Logics and Classical Concerns; J. van Benthem.- Part I Proof, Knowledge and Computation. 2. Epistemic Models, Logical Monotony and Substructural Logics; M. Cozic. 3. Semantics as Based on Inference; J. Peregrin. 4. Effectiveness; S. Shapiro. 5. Does Gödel’s Incompleteness Theorem Prove thatTruth Transcends Proof?; J. Vidal-Rosset. 6. Transpositions; H. Visser.- Part II Truth Values Beyond Bivalence.- 7. Many-Valued and Kripke Semantics; J.-Y. Béziau. 8. The Logic of Complementarity; N. C. A. da Costa, D. Krause. 9. Semantics for Naive Set Theory in Many-Valued Logics; T. Libert.- Part III Category-Theoretic Structures. 10. Continuity and Logical Completeness. An Application of Sheaf Theory and Topoi; S. Awodey. 11. What is Categorical Structuralism?; G. Hellman. 12. Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism; E. Landry. 13. Categories, Sets and the Nature of Mathematical Entities; J.-P. Marquis.-
Part IV Independence, Evaluation Games and Imperfect Information. 14. Truth, Negation and Other Basic Notions of Logic; J. Hintikka. 15. Signalling in IF Games: A Tricky Business; T. M.V. Janssen, F. Dechesne. 16. Independence-Friendly Logic and Games of Incomplete Information; A.-V. Pietarinen. 17. IF and Epistemic Action Logic; M. Rebuschi.- Part V Dialogue and Pragmatics. 18. Naturalizing Dialogic Pragmatics; G. Heinzmann. 19. Logic as a Tool of Science Versus Logic as a Scientific Subject; K. Lorenz. 20. Non-Normal Dialogics for a WonderfulWorld and More; S. Rahman.- Part VI Appendices. A: Louis Joly as a Platonist Painter?; Roger Pouivet.-
Index.