The Second World Conference on Mathematics at the Service of Man was held at the Universidad Politecnica de Las Palmas, Canary Islands, Spain, June 28 to July 3, 1982. The first volume of the Proceedings of the Conference, entitled "Functional Equations-Theory and Applications" has appeared in the Reidel series "Mathematics and Its Applications". The papers in this volume consist of the invited lectures delivered at the Conference, Section 7: Non-Classical Logics and Modelling, as well as some selected papers which offer an introduction to the philosophy, methodology and to the lite­ rature of the broad and fascinating field of vagueness, imprecision and uncertainty. The contributed papers appeared in the volume of photo-offset preprints distributed at the Conference. It is our hope that the papers present a good sample with respect to the background, the formalism and practice of this area of research as far as we understand it today. As the subject "Vagueness" touches many aspects of human thinking, the contributions have been made from a broad spectrum ranging from philo~ophy through pure mathematics to probability theory and mathematical economics, therefore the careful reader should find some new insights here. In conclusion, the editors want to thank all authors who have contributed to this volume; the publishers of "Commenta­ tiones Mathematicae Universitatis Carolinae" for permission to reprint the paper "Fuzziness and Fuzzy Equality", Commentationes Mathematicae Universitatis Carolinae 23 (1982), 249-267, and D. Reidel for friendly cooperation.

Notes on Vagueness and Mathematics.- Fuzzy Set Theory: Some Aspects of the Early Development.- Plausibility Measures - A General Framework for Possibility and Fuzzy Probability Measures.- Controlled-Error Theories of Proximity and Dominance.- Impartial Truth.- A Geometry of Logic.- Representations of Transitive Fuzzy Relations.- Fuzziness and Fuzzy Equality.- Large Societies and Individual Strategy Selection: A Case Study of Ambiguity.- The Alternative Set Theory and its Approach to Cantor's Set Theory.- Aspects of Vagueness and Some Epistemological Problems Related to their Formalization.- An Inquiry into Indistinguishability Operators.- A Theory of Commonsense Knowledge.- Index of Names.- Index of Subjects.