ACM CR categories:
I.2.3 Deduction and theorem proving - nonmonotonic reasoning and belief revision
F.3.1 Logics of programs
The first volume in a series by Springer on logicians, this book is on the contributions of Krister Segerberg. Segerberg is an outstanding practitioner of logic in the treatment of philosophical problems, many of them dealing with events, processes, programs and routines, in which he includes recipes, selecting the options on a washing machine and turning on the computer.
After an introduction by the editor of the volume, there are six chapters in the area of logics of actions, including two in the area of deontic logic, which deals with permissions and obligations. There are then seven chapters in the area of doxastic logic and belief change. Alchourrón, Gärdenfors and Makinson (known as AGM) came up with an axiomatic treatment in 1985. In 1991 two papers by Katsuno and Mendelson, and by Grahne, had a different approach that they called belief update, and which Segerberg christened KGM. Segerberg pioneered the idea of using a logic of actions (he called it dynamic doxastic logic) as a way of dealing with belief revision, tying it up with the field of logics of programs.
A graduate student in the area of logic or in artificial intelligence will find a wealth of material here. Unfortunately, the book does not have an index. The authors forcefully argue the merits and demerits of different approaches. Can you imagine revising your current beliefs with the new belief b and finding that as soon as you revise, you do not believe b ? A clue: the belief b can be about beliefs, such statements were studied by the philosopher G.E.Moore. In this book, you will encounter the layered models which handle such beliefs under the delightful name of onions. What I find remarkable is how Segerberg's approach of handling many different things under the rubric of action and program logics makes them mathematically simple to handle, so simple that difficulties like the Moore statements become easy to spot. Even the first chapter by Richmond Thomason takes a critical stance, pointing out that for the requirements of artificial intelligence, Segerberg's notion of routine is too simple. As Johan van Benthem says in his chapter, it is hard to roam for long in modal logic without finding traces of Segerberg's work.
There are an autobiographical and a philosophical chapter by Segerberg, who went all the way from Sweden to New Zealand and back during his career. I was surprised to read about the conditions under which he studied in school north of the Arctic circle. He also writes about his attempts to deal with academic isolation in Sweden. I was pleased that he remembers a short visit meeting students from all over India at a logic summer school in Jaipur, arranged by Biswambhar Pahi.
Several moving sentences remained in my mind. One is Segerberg's comment when a publisher suggested converting his doctoral thesis into a book. Segerberg says, "I was not a student of Dana Scott for nothing [whose] papers were always extremely well-written: brilliant of content and elegant of style." He declined to put something done in a hurry into print. Later, when he thought he had a publishable version, publishers were no longer interested. There is also the story of the now-famous Segerberg induction axiom for dynamic (and temporal) logic, and his feelings on discovering that his completeness proof for the logic had a gap. As he says, the matter does not seem so important today, but it was the humiliating experience of a mistake being found and then corrected by someone else (it took logicians of the calibre of Rohit Parikh and Dov Gabbay) that rankled him. At the end, Segerberg comments on the professional hazards of being a quasi-itinerant scholar: "We go some place, and for a limited time we develop an intense relationship with colleagues who feel like friends for life; and then we may never see them again."