Generalized quantifiers and computation : 9th European Summer School in Logic, Language, and Information, ESSLLI'97 workshop : Aix-en-Provence, France, August 11-22, 1997 : revised lectures

This book comprises revised full versions of lectures given during the 9th European Summer School in Logic, Languages, and Information, ESSLLI'97, held in Aix-en-Provence, France, in August 1997. The six lectures presented introduce the reader to the state of the art in the area of generalized quantifiers and computation. Besides an introductory survey by the volume editor various aspects of generalized quantifiers are studied in depth. Generalized quantifiers, an introduction -- Jouko Väänänen Counting and locality over finite structures : a survey -- Leonid Libkin, Juha Nurmonen -- A perspective on Lindström quantifiers and oracles -- Iain A. Stewart Generalized quantifiers in logic programs -- Thomas Eiter, Georg Gottlob, Helmut Veith -- A generalized quantifier concept in computational complexity theory -- Heribert Vollmer Ramsey theory is needed for solving definability problems of generalized quantifiers-- Kerkko Luosto. Generalized Quantifiers, an Introduction....Pages 1-17 Counting and Locality over Finite Structures A Survey....Pages 18-50 A Perspective on Lindström Quantifiers and Oracles....Pages 51-71 Generalized Quantifiers in Logic Programs....Pages 72-98 A Generalized Quantifier Concept in Computational Complexity Theory....Pages 99-123 Ramsey Theory Is Needed for Solving Definability Problems of Generalized Quantifiers....Pages 124-139 The ordinary quantifiers "for some" and "for all" are not sufficient for expressing some basic mathematical concepts.