Stack(OBJ1, OBJ2)

![0_image_0.png](0_image_0.png)

![0_image_2.png](0_image_2.png)

![0_image_1.png](0_image_1.png)

igure Temporal dependencies in the definition of the Stack action.

owever, note that Boil-Spaghetti does not subsume Prepare-Spaghetti, even if it is a con unct in the definition of the latter. This could be better explained observing how the definition of Prepare-Spaghetti plan is expanded

## Prepare-Spaghetti

b  . Make-Spaghetti@  ПВоі1@  П

Make-Sauce@
Then, the Boil action occurs at the interval

$$\begin{array}{r l}{\Delta\mathbf{T}\cong}&{{}\cap\mathbf{D}\cup\mathbf{T}\cup\mathbf{T}}\end{array}$$

which can be di erent from the occurring time of Prepare-Spaghetti as the ect of binding Boil-Spaghetti to the temporal variable . n the contrary, in the definition of Boil-Spaghetti the Boil action takes place necessarily at the same time.   ubsumption between Prepare-Spaghetti and Boil-Spaghetti fails since di  erent temporal relations between the actions describing the two plans and the plans themselves are specified. In particular, observe that the Boil-Spaghetti plan denotes a narrower class than the plan expression

## Bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

which subsumes both Prepare-Spaghetti and Boil-Spaghetti itself.

## 5.2  The Blocks World Domain

As a further example of the expressive power of the temporal language, it is now shown how to represent the Stack action in the blocks world, in a more detailed way than the previous simple Basic-Stack action used as a clarifying example. Thus a stacking action involves two blocks, which should be both clear at the beginning the central part of the action consists of grasping one block  at the end, the blocks are one on top of another, and the bottom one is no longer clear    igure ur representation borrows from the Rat escription ogic einsohn, udenko, Nebel, the intuition of representing action parameters by means of partial rofitlich, functions mapping from the action itself to the involved action parameter see ection . In the language, these functions are called parametric features.   or example, the action Stack has the parameters   OBJECT1 and   OBJECT2, representing in some sense the ob ects that are involved in the action independently from time. 0, in the assertion 0 
- denotes the first ob ect involved in the action at any interval. n the other hand, an assertion involving a  non-parametric  feature, e.g.,  ON
- ", does not
-
imply anything about the truth value at intervals other than .

The concept expression, which defines the Stack action, makes use of temporal   ualified concept expressions, including feature selections and agreements the expression    OBJECT2 Clear-Block @  means that the second parameter of the action should be a Clear-Block