Yale shooting problem

The Yale shooting problem is a conundrum or scenario in formal situational logic on which early logical solutions to the frame problem fail. The name of this problem derives from its inventors, Steve Hanks and Drew McDermott, working at Yale University when they proposed it. In this scenario, Fred (later identified as a turkey) is initially alive and a gun is initially unloaded. Loading the gun, waiting for a moment, and then shooting the gun at Fred is expected to kill Fred. However, if inertia is formalized in logic by minimizing the changes in this situation, then it cannot be uniquely proved that Fred is dead after loading, waiting, and shooting. In one solution, Fred indeed dies; in another (also logically correct) solution, the gun becomes mysteriously unloaded and Fred survives.

Technically, this scenario is described by two fluents (a fluent is a condition that can change truth value over time): ${\displaystyle alive}$ and ${\displaystyle loaded}$. Initially, the first condition is true and the second is false. Then, the gun is loaded, some time passes, and the gun is fired. Such problems can be formalized in logic by considering four time points ${\displaystyle 0}$, ${\displaystyle 1}$, ${\displaystyle 2}$, and ${\displaystyle 3}$, and turning every fluent such as ${\displaystyle alive}$ into a predicate ${\displaystyle alive(t)}$ depending on time. A direct formalization of the statement of the Yale shooting problem in logic is the following one:

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