This Dagstuhl Seminar brought together approximately 60 researchers covering the full spectrum of the current research on many-valued logics, ranging from mathematical foundations to computational issues and applications. Several young researchers could attend this meeting, and have fruitful interactions with more established researchers from Japan, South and North America, and from an exceptionally large number of European countries. Their contributions may be classified under the following four headings.

Enhancement of the theoretical basis: Despite its long tradition, work on foundational issues in many-valued logics still spawns new and thrilling problems and results. The rich and intriguing properties of the algebraic counterparts of many-valued logic should be firstly mentioned in this context. This algebraic perspective was strongly represented in this seminar. In the same spirit, albeit in a different setting, several talks dealt with fuzzy set theory, and their relations with rule based control.

Automated deduction - theory and tools: As a focal point in this field one must also mention the current research on complete and sound proof systems -- in particular for infinitely-valued logics. Two notable examples are given by Lukasiewicz logic and by product logic. As amply discussed during the Dagstuhl seminar, the calculi corresponding to these logics require far reaching generalisations of the classical techniques arising from Hilbert-style systems, Gentzen systems and resolution. A recurring theme in this field is the use of formulas with regular sets of signs.

Modelling of and reasoning on incomplete and uncertain knowledge: Many-valued calculi are often encountered, for instance, in possibility theory and possibilistic logic. They provide a natural framework for manipulating orderings between various interpretations. They also find use in clarifying many entrenched situations in non-monotonic reasoning. In this context we should also mention such topics as the logical manipulation of uncertainty factors, which were the main concern of a number of talks in the Dagstuhl meeting.

Applications: Applications of many-valued logics -- both in the infinitely-valued and in the finitely-valued case – are an important source of motivation for future research. During this seminar important talks focused on applications in hardware design and verification, unit commitment in power systems, and in biomedical engineering.

This Seminar was also a workshop/conference in the COST~Action~#15 on "Many-valued Logics for Computer Science Applications'', the only existing European Action on Computer Science issues. One of the objectives of this Action was the dissemination of knowledge accumulated and produced within the project to the world wide scientific community the COST action itself.

This objective has been very successfully accomplished with this Dagstuhl seminar.