A Companion to Modal Logic

Note: This book was later replaced by "A New Introduction to Modal Logic" (1996).
An earlier book of ours, entitled An Introduction to Modal Logic (IML), was published in 1968. When we wrote it, we were able to give a reasonably comprehensive survey of the state of modal logic at that time. We very much doubt, however, whether any comparable survey would be possible today, for, since 1968, the subject has developed vigorously in a wide variety of directions.
The present book is therefore not an attempt to update IML in the style of that work, but it is in some sense a sequel to it. The bulk of IML was concerned with the description of a range of particular modal systems. We have made no attempt here to survey the very large number of systems found in the recent literature. Good surveys of these will be found in Lemmon and Scott (1977), Segerberg (1971) and Chellas (1980), and we have not wished to duplicate the material found in these works. Our aim has been rather to concentrate on certain recent developments which concern questions about general properties of modal systems and which have, we believe, led to a genuine deepening of our understanding of modal logic. Most of the relevant material is, however, at present available only in journal articles, and then often in a form which is accessible only to a fairly experienced worker in the field. We have tried to make these important developments accessible to all students of modal logic,as we believe they should be.