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Handbook of Philosophical Logic, Volume 1 (Second Edition) by Dov M. Gabbay, F. Guenthner (Kluwer Academic) The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983--1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language, and logic.
The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date, authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc.
The volumes will no longer be as topic-oriented as the first edition because of the way the subject has evolved over the last 15 years or so. However, the volumes will follow some natural groupings of chapters.
This first volume of the second edition contains major contributions on Predicate Logic, First- and Second-order Logic, Higher-order Logic, Algorithms and Decision Problems, and the Mathematics of Logic Programming.

Contents: Editorial Preface; D.M. Gabbay. Elementary Predicate Logic; W. Hodges. Systems Between First- and Second-order Logic; S. Shapiro. Higher-Order Logic; J. van Benthem, K. Doets. Algorithms and Decision Problems: A Crash Course in Recursion Theory; D. van Dalen. Mathematics of Logic Programming; H.D. Ebbinghaus, J. Flum. Index.
Handbook of Philosophical Logic, Volume 2 (Second Edition) by Dov M. Gabbay, F. Guenthner (Kluwer Academic) The second volume of the second edition contains major contributions on Systems of Deduction, Alternatives to Standard First-order Semantics, Algebraic Logic, Basic and Advanced Many-valued Logic. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.
Contents: Editorial Preface; D.M. Gabbay. Systems of Deduction; G. Sundholm. Alternatives to Standard First-order Semantics; H. Leblanc. Algebraic Logic; H. Andreka, et al. Basic Many-valued Logic; A. Urquhart. Advanced Many-valued Logics; R. Hahnle. Index.

Handbook of Philosophical Logic, Volume 3 (Second Edition) by Dov M. Gabbay, F. Guenthner (Kluwer Academic) The third volume of the second edition contains major contributions on Basic and Advanced Modal Logic, Quantification in Modal Logic and Correspondence Theory. Audience: Students and researchers whose work or interests involve philosophical logic and its applications.

Contents: Editorial Preface; D.M. Gabbay. Basic Modal Logic; R.A. Bull, K. Segerberg. Advanced Modal Logic; M. Zakharyaschev, F. Wolter, A. Chagrov. Quantification in Modal Logic; J. Garson. Correspondence Theory; J. van Benthem. Index.
Handbook of Philosophical Logic, Volume 4 (Second Edition) by Dov M. Gabbay, F. Guenthner (Kluwer Academic) This fourth volume of the second edition contains major contributions on Conditional Logic, Dynamic Logic, Logics for Defeasible Argumentation, Preference Logic and Diagrammatic Logic.

Contents: Editorial Preface; D.M. Gabbay. Conditional Logic; D. Nute, C.B. Cross. Dynamic Logic; D. Harel. Logics for Defeasible Argumentation; H. Prakken, G. Vreeswijk. Preference Logic; S.O. Hansson. Diagrammatic Logic; E. Hammer. Index.
Handbook of Philosophical Logic, Volume 5 (Second Edition) by Dov M. Gabbay, F. Guenthner (Kluwer Academic) Editorial Preface; D.M. Gabbay. Intuitionistic Logic; D. van Dalen. Dialogues as a Foundation for Intuitionistic Logic; W. Felscher. Free Logics; E. Bencivenga. Advanced Free Logic; S. Lehmann. Partial Logic; S. Blamey. Index.

It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then.

The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as `the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good.!

The first edition was the second handbook published for the logic commu­nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983‑1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles.

These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa­tion on the one hand and to provide the theoretical basis for the computer program constructs on the other. The result was that the Handbook of Philosophical Logic, which covered most of the areas needed from logic for these active communities, became their bible.

The increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the devel­opment of the subject directly and indirectly. It directly pushed research forward, stimulated by the needs of applications. New logic areas became established and old areas were enriched and expanded. At the same time, it socially provided employment for`generations of logicians residing in com­puter science, linguistics and electrical engineering departments which of course helped keep the logic community thriving. In addition to that, it so happens (perhaps not by accident) that many of the Handbook contributors became active in these application areas and took their place as time passed on, among the most famous leading figures of applied philosophical logic of our times. Today`we have a handbook with a most extraordinary collection of famous people as authors!

The table below will give our readers an idea of the landscape of logic and its relation to computer science and formal language and artificial in­telligence. It shows that the first edition is very close to the mark of what was needed. Two topics were not included in the first edition, even though they were extensively discussed by all authors in a 3‑day Handbook meeting. These are:

• a chapter on non‑monotonic logic

• a chapter on combinatory logic and a‑calculus

We felt at the time (1979) that non‑monotonic logic was not, ready for a chapter yet and that combinatory logic and a‑calculus was too far re­moved.' Non‑monotonic logic is now a very major area of philosophi­cal logic, alongside default logics, labelled deductive systems, fibring log­ics, multi‑dimensional, multimodal and substructural logics. Intensive re­examinations of fragments of classical logic have produced fresh insights, including at time decision procedures and equivalence with non‑classical systems.

Perhaps the most impressive achievement of philosophical logic as arising in the past decade has been the effective negotiation of research partnerships with fallacy theory, informal logic and argumentation theory, attested to by the Amsterdam Conference in Logic and Argumentation in 1995, and the two Bonn Conferences in Practical Reasoning in 1996 and 1997.

These subjects are becoming more and more useful in agent theory and intelligent and reactive databases.

Finally, fifteen years after the start of the Handbook project, I would like to take this opportunity to put forward my current views about logic in computer science, computational linguistics and artificial intelligence. In the early 1980s the perception of the role of logic in computer science was that of a specification and reasoning tool and that of a basis for possibly neat computer languages. The computer scientist was manipulating data structures and the use of logic was one of his options.

My own view at the time was that there was an opportunity for logic to play a key role in computer science and to exchange benefits with this rich and important application area and thus enhance its own evolution. The relationship between logic and computer science was perceived as very much like the relationship of applied mathematics to physics and engineering. Ap­plied mathematics evolves through its use as an essential tool, and so we hoped for logic. Today my view has changed. As computer science and artificial intelligence deal more and more with distributed and interactive systems, processes, concurrency, agents, causes, transitions, communication and control (to name a few), the researcher in this area is having more and more in common with the traditional philosopher who has been analyzing such questions for centuries (unrestricted by the capabilities of any hard­ware).

The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid bureaucracy is very much similar to a complex computer program handling and manipulating data. My guess is that the principles underlying one are very much the same as those underlying the other.

I believe the day is not far away in the future when the computer scientist will wake up one morning with the realisation that he is actually a kind of formal philosopher!

The projected number of volumes for this Handbook is about 18. The subject has evolved and its areas have become interrelated to such an extent that it no longer makes sense to dedicate volumes to topics. However, the volumes do follow some natural groupings of chapters.

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