A computer program that interacts with the real world must be able to reason about things like time, space, and materials. As fundamental and commonsense as these concept may be modeling them turns out to present some problems. and commonsense as these concept may be modeling them turns out to present some problems.
Time: While physicists and philosophers still debate the true nature of time, we all manage to get by on a few basic commonsense motions. These notions help us to decide when to initiate actions how to reason about others actions and how to determine relationships between events.
For Instance: A is preceded by B and C is after B then we can easily infer C is after A. A commonsense theory of time must account for reasoning of this kind. The most basic notation of time is that it is occupied by events. These events occur during intervals, continues spaces of time. What kinds of thins might we want to say about an interval?
An interval has a starting point and an ending point and a duration defined by these points. Intervals can be related to other intervals. The following diagram shows that there are exactly thirteen ways in which two-non-empty time intervals can relate to one another. There are actually only seven distinct relationships. As is clear from the figures. The relationship of equality plus six other relationships that have their own inverses.
Thirteen possible relationships between two time intervals.
Eg: Blocks word problem: Primitives in this include block names, action like PICKUP & STACK and predicates like ON(x,y). If want a real robot to achieve ON(x,y), then that robot had better know what on really means, where x and y are located, how big they are, how they are shaped, how to align x on top of y so that x want fall off and so forth. These requirements become more apparent if we want to issue commands like “Place block x near block y”. Commansense notations of space are critical for living in the real world.
Object have spatial extent, while events have temporal extent. We might therefore try to expand our commonsense theory of time into a commonsense theory of space. Because space is three-dimensional, there are far more than thirteen possible special relationships between two objects.
For instance consider one block top of another. The objects are equal in the length and width dimensions while they meet in height dimension, but we must use the special equivalent of IS-DURING to describe the length and width relationships. The main problems with this approach is that it generates a vast number of relations (namely 133 = 2197), many of which are not commonsensical.
In our discussion of Qualitative Physics we saw how to build abstract models by transforming real valued variables into discrete quantity spaces. We can also view objects and spaces at various levels of abstraction. Choosing a set of relevant properties amounts to viewing the world at a particular level of granularity. Since, different granularities are systematically related to each other.
Materials: Why can’t you walk on water? What happens if you turn a glass of water upside down? What happens when you pour water into the soil of a potted plant?
Liquid present a particular interesting and challenging domain to formalize. “Hayers”(1985) presented one attempt to describe them before we write down any properties of liquids, we must decide what kinds of objects those properties will describe. We defined special relations in terms of the spaces occupied by the objects, not in terms of objects themselves. It is particularly useful to take this point of view with liquids, since liquid “objects” can be split and merged easily.
Ex: We consider a river to be a piece of liquid, then what happens to the river when the liquid flows out into ocean? Instead of continually changing out characterization of river, it is more convenient to view the river as a fixed shape occupied by the water.
Containers play an important role in the world of liquids. Since we do not want to refer to liquid objects, we must have another way of starting how much liquid is in a container. We can define a CAPACITY function to bound the amount of liquid that a space S can hold. The space is FULL when the AMOUNT equals the CAPACITY.
CAPACITY(S) ≥ AMOUNT(L,S) > none
FULL(S) Ξ AMOUNT (L,S) = CAPACITY(S)
We can also define an amount function.
AMOUNT(water,glass) > none.
This statement means “There is water in the Glass”. Hence water refers to the generic concept of water and Glass refers to the space enclosed by a particular Glass.
Suppose, our robot encounters a room with 6 inches of water on floor. What will happen if the robot touches the floor, by the definition of TOUCHING we have
£ d1: OUTER (d1,Robot) ^ OUTER (d1, Floor)
Since the floor has only one face d1. We can conclude
OUTER (d, Robot) ^ OUTER (d, Floor)
Combining first class with the fact WET-BY (d, water) gives us IS-WET(Robot). Recall that at the end, our robot was about to try crossing a river without using a bridge. It might find this fact useful.
INSIDE(S1,S2) ^ FREE(S1) ^ FULL(S2,L) FULL(S1,L)
It is straight forward to show that if the robot is submerged in the first place requires some envisionment.
We also need general rules describing how liquids themselves over time.
The following diagram shows five enivisonment for lazy, bulk liquids. A containment even can become a falling even if the container tips. The falling event becomes a wetting even and then a spreading one. Depending on where the spreading takes place, further falling flowing events may ensure. When all the liquid has left the container, the spreading will stop, and some time afterward, a drying event will begin.
Other material behave differently. Solids can be rigid or flexible. A string can be used to pull an object but not to push it. We can see that common sense knowledge representation has a strongly taxonomic flavor.