The Yale shooting problem is one of the most prominent problems in temporal nonmonotonic reasoning. The problem describes the following scenario: initially, a man is alive and a gun is loaded. Then he waits for a while, and then he is shot with the gun. The question is whether the man is still alive after the shooting. Various proposals exist in the literature to solve the shooting problem, but it is not clear at this moment which proposal is “the correct” solution. The two most popular solutions, chronological minimization and causal minimization, have their limitations. For example, the chronological minimization approach in general has difficulty in handling the temporal explanation problem, which requires reasoning backward in time, and the causal minimization approach requires that the domain axioms be written in a restricted form using the “Causes” predicate.

Baker proposes a new approach to avoid these limitations. He uses the original formulation of the shooting problem in the framework of situation calculus. The new approach is based on the idea that since the abnormality predicate takes a situational argument, it is important to hold the meanings of the situations constant across the various models being compared. In other words, we should treat the predicate “hold” (which specifies the meanings of situations) as a parameter and allow the function “Result” (rather than the predicate “hold”) to vary in circumscribing the abnormality predicate “Ab.” To carry out this idea, an additional axiom is asserted to guarantee that every consistent situation is included in the domain of discourse. The nice thing about this approach is that with the simple change in circumscription policy and the additional axiom about the existence of every consistent situation, ordinary circumscription produces the intuitively correct answer to the shooting problem.

This research paper is well written, with nice diagrams and examples. The intended readers of the paper are researchers in nonmonotonic reasoning and knowledge representation.