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The frame problem occurs even in very simple domains. A scenario with a door, which can be open or closed, and a light, which can be on or off, is statically represented by two propositions and .
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.
Concise Microsoft O.S. Timeline – a color-coded concise timeline for various Microsoft operating systems (1981–present) Bitsavers – an effort to capture, salvage, and archive historical computer software and manuals from minicomputers and mainframes of the 1950s, 1960s, 1970s, and 1980s
The frame problem shows in this example as the problem that is not a consequence of the above formulae, while the door is supposed to stay closed until the action of opening it is performed. Circumscription can be used to this aim by defining new variables c h a n g e _ o p e n t {\displaystyle change\_open_{t}} to model changes and then ...
The event calculus was developed in part as an alternative to the situation calculus, [6] [7] as a solution to the frame problem, of representing and reasoning about the way in which actions and other events change the state of some world. There are many variants of the event calculus.
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point used to indicate more generally the problem of "formalizing domains with actions in logic", but I think this use is obsolete now.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.