Thomas Müller (ed).
Nuel Belnap on indeterminism and free action.
Springer Publishing Company, Incorporated, 2014.

ACM CR categories:
I.2.0 Artificial intelligence - philosophical foundations
F.4.1 Mathematical logic - temporal logic

This open access book of papers on the work of Nuel Belnap includes one by Belnap himself. The editor and contributors are distinguished philosophers, a handful of people from computing, and one or two from other disciplines. If you thought philosophers shy away from mathematics, you can revise your opinion based on this volume. In an interview carried out by the editor, Belnap says he really enjoyed programming in octal (and later decimal), on punch cards, on an IBM 701.

Any computing scientist who thinks about his subject philosophically should find something to read in this book. For example, if you work in artificial intelligence, there is a striking paper by Robert Kane who applies the parallel distributed processing (PDP) approach to the problem of free will. If you work in robotics, you may want to see Marek Sergot's questions about when an agent is responsible for an action. If you work in decision theory, you will find much of interest in Paul Bartha's article.

Belnap is known to logicians, along with Alan Anderson, for outstanding contributions to relevance logic and entailment. None of them find a place in this book. Reading it is to understand that in the three areas of branching time, branching space-time and a logic with the operator "agent i sees to it that P holds" (written [i stit]P), Belnap and his coauthors made another outstanding contribution [1]. And already in his paper in this volume, Belnap is moving on to new work in logic based on an idea of "cases".

There are three papers on the nature of branching time (two of them contest whether there is a single "real" future [2]) and three on its relativistic extension to branching space-time (on which I confess ignorance), which is finding applications in biological ancestry.

Most of the remaining articles deal with STIT logic. For example, van Benthem and Pacuit analyze STIT from the standpoint of dynamic epistemic and game logics, which deal with actions and agents, which bring about a proposition P. They give an embedding of STIT logic into a logic of matrix games when there is a fixed vocabulary of actions and agents.

Consider the European Space Agency (ESA) that is to "see to it that" its craft Rosetta (actually its lander Philae) lands on comet Churyumov-Gerasimenko. Abbreviating by r the program of Rosetta reaching the neighbourhood of the comet and by R the proposition that it has done so (this was achieved early in August 2014), and by l the program of Philae landing on the comet and by L the proposition that it has done so (this is set to happen in November 2014), one mission objective can be stated as follows: [esa stit](R and [esa stit]L), which in an action-based syntax becomes [r](R and [l]L). But what precisely is this program l ? ESA scientists are presently working on determining it. The reason they could not do so earlier was that l, the program for Philae to land on the comet, depends on the data about the comet sent by Rosetta in its state satisfying R. It seems that by refraining from mentioning actions, STIT logic may be at an advantage in modelling situations like these, at the cost of expressiveness in reasoning in more restricted situations.

[1] Belnap, N., M. Perloff and M. Xu, Facing the future, OUP, 2001.
[2] Belnap, N. and M. Green, Indeterminism and the thin red line, Phil. Persp. 8, 1994, pp 365-388.