A New Introduction to Modal Logic

To a generation of philosophers, modal logic was a field with ties to some of the most active areas of research and Hughes and Cresswell was the authoritative text and reference to that field. 'Hughes and Cresswell,' of course, referred to the authors' An Introduction to Modal Logic, published by Methuen in 1968 and reprinted as a University Paperback in 1972. Supposing no prior logic, An Introduction presented, in remarkably readable prose, axiomatic and semantic treatments of the propositional modal systems T, S4 and S5 (including completeness and decidability results), similar treatments of a few basic predicate systems, and an extensive survey of other results. Although this work continues to be widely used and cited, it has become somewhat dated. There are now more streamlined methods of proving completeness and decidability than the normal forms and semantic diagrams it employed. There has been a realization that the modal 'frame' is a more fundamental semantic notion than 'model' and a concomitant investigation of the phenomenon of modal 'incompleteness' (i.e., of systems not characterised by classes of frames). And there has been an explosion of further investigations and applications beyond those contained in the original survey. Several newer texts have appeared, but none combines the lucidity and the encyclopedic perspective of Hughes and Cresswell. Brian Chellas's excellent Modal Logic: An Introduction, for example, treats only the propositional systems. Hughes and Cresswell themselves tried to fill the void with A Companion to Modal Logic (Methuen & Co., 1984). This was a self-contained work in the same style, but at a more advanced level, than the previous. To use both an 'introduction' and 'companion' as texts is somewhat awkward, however, and the Companion itself has become dated. Thus, the New Introduction fills a great need. The relevant parts of An Introduction and A Companion have been rewritten and integrated with a wealth of new material into a worthy successor to the original Hughes and Cresswell.