Vague language and corresponding models of inference and information processing is an important and challenging topic as witnessed by a number of recent monographs and collections of essays devoted to the topic.This volume collects fifteen papers, the majority of which originated with talks presented at the conference "Logical Models of Reasoning with VagueInformation (LoMoReVI)", September 14-17, 2009, in Cejkovice, that initiated a EUROCORES/LogICCC project with the same title.At least two features set the current volume apart from other texts: first, the interdisciplinary nature of the topic is nicely reflected by the wide range ofinterests of the authors, who include philosophers, linguists, logicians, as well as mathematicians and computer scientists. Secondly, all the papers areaccompanied by comments written by other authors and a few outside experts. These comments and corresponding replies by the authors document the very lively ongoing debate on adequate models of vague language.