Temporal Logic: Mathematical Foundations and Computational Aspects

We are happy to present the reader with volume 1 of our book on temporal logic. Work on this volume was begun in 1979 by Dov Gabbay, who prepared a draft manuscript [Gabbay, 1981c] which covered earlier versions of chapters 1-3, 6-11, and 13. The 1981 manuscript was intended as a research monograph covering Gabbay's results on expressive completeness, H-dimension, the Irreflexivity Rule and separation theory. In 1983 Gabbay moved to the computing department at Imperial College and his research activities were enriched by the multitude of theoretical and practical problems confronting the computing community. Temporal logic research took a more practical turn (see volume 2). In 1985 Mark Reynolds, and later Ian Hodkinson, joined the temporal logic group. A serious theoretical research programme (with PhD and MSc students) into the mathematical foundations of temporal logic and its applications to practical problems was launched. Following the new research, further chapters were written by Gabbay, Hodkinson, Reynolds and Marcelo Finger. The old chapters, namely, chapters 1-3, 6-11, and 13, were edited, corrected, and expanded by Hodkinson and Reynolds. The following is a guide to the work done in 1983-92.