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The frame problem can be thought of as the problem of formalizing the principle that, by default, "everything is presumed to remain in the state in which it is" (Leibniz, "An Introduction to a Secret Encyclopædia", c. 1679).
This representation of fluents is used in the event calculus, in the fluent calculus, and in the features and fluents logics. Some fluents can be represented as functions in a different way. For example, the position of a box can be represented by a function o n ( b o x , t ) {\displaystyle on(box,t)} whose value is the object the box is ...
The frame problem is solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as:
The version of the situation calculus introduced by McCarthy in 1986 differs to the original one by the use of functional fluents (e.g., (,) is a term representing the position of x in the situation s) and for an attempt to use circumscription to replace the frame axioms.
The event calculus is a logical theory for representing and reasoning about events and about the way in which they change the state of some real or artificial world. It deals both with action events, which are performed by agents, and with external events, which are outside the control of any agent.
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The name "frame problem" has been at some point used to indicate more generally the problem of "formalizing domains with actions in logic", but I think this use is obsolete now. Regarding inertia, this was the initial assmption in the original problem; there are however some logics where fluents can be specified not to be inertial.
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 comes from a scenario proposed by its inventors, Steve Hanks and Drew McDermott , working at Yale University when they proposed it.