AISC 2004, the 7th International Conference on Arti?cial Intelligence and S- bolicComputation,wasthelatestintheseriesofspecializedbiennialconferences foundedin1992byJacquesCalmetoftheUniversitat .. KarlsruheandJohnCa- bell of University College London with the initial title Arti?cial Intelligence and Symbolic Mathematical Computing (AISMC).TheM disappeared from the title between the 1996 and 1998 conferences. As the editors of the AISC 1998 p- ceedings said, the organizers of the current meeting decided to drop the adjective 'mathematical' and toemphasize that the conference is concerned with all aspects of symbolic computation in AI: mathematical foundations, implementations, and applications, including applications in industry and academia. This remains the intended pro?le of the series, and will ?gure in the call for papersfor AISC 2006,whichis intended to takeplaceinChina. Thedistribution of papers in the present volume over all the areas of AISC happens to be rather noticeably mathematical, an e?ect that emerged because we were concerned to select the best relevant papers that were o?ered to us in 2004, irrespective of their particular topics; hence the title on the cover.Nevertheless, we encourage researchersovertheentirespectrumofAISC,asexpressedbythe1998quotation above,to be intouchwith us abouttheir interestsandthe possibility ofeventual submission of papers on their work for the next conference in the series. The papers in the present volume are evidence of the health of the ?eld of AISC. Additionally, there are two reasons for optimism about the continuation of this situation.