The annual conference of the European Association for Computer Science Logic (EACSL), CSL 2009, was held in Coimbra (Portugal), September 7–11, 2009. The conference series started as a programme of International Workshops on Computer Science Logic, and then at its sixth meeting became the Annual C- ference of the EACSL. This conference was the 23rd meeting and 18th EACSL conference; it was organized at the Department of Mathematics, Faculty of S- ence and Technology, University of Coimbra. In response to the call for papers, a total of 122 abstracts were submitted to CSL 2009of which 89 werefollowedby a full paper. The ProgrammeCommittee selected 34 papers for presentation at the conference and publication in these proceedings. The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. The awardrecipient for 2009 was Jakob Nordstr ̈ om. Citation of the award, abstract of the thesis, and a biographical sketch of the recipient may be found at the end of the proceedings. The award was sponsored for the years 2007–2009 by Logitech S.A.

Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.

This volume contains the papers selected for presentation at the conference and two abstracts from invited speakers. The programme committee selected these 25 papers from 12 countries out of 65 submissions from 17 countries. The rst JELIA meeting was in Rosco , France, ten years ago. Afterwards, it took place in the Netherlands, Germany, United Kingdom, Portugal, and now again in Germany. The proceedings of the last four meetings appeared in the Springer-Verlag LNCS series, and a selected series of papers of the English and the Portuguese meeting appeared as special issues in the Journal of Applied Non-Classical Logics and in the Journal of Automated Reasoning, respectively. The aim of JELIA was and still is to provide a forum for the exchange of ideas and results in the domain of foundations of AI, focusing on rigorous descriptions of some aspects of intelligence. These descriptions are promoted by applications, and produced by logical tools and methods. The papers contained in this volume cover the following topics: 1. Logic programming 2. Epistemic logics 3. Theorem proving 4. Non-monotonic reasoning 5. Non-standard logics 6. Knowledge representation 7. Higher order logics We would like to warmly thank the authors, the invited speakers, the m- bers of the program committee, and the additional reviewers listed below. They all have made these proceedings possible and ensured their quality.