Tuesday, July 27, 2010

Qualitative Physics.

Qualitative Physics:

People know a great deal about the how the physical world works. Consider the above three situations.

a) The ball will probability bounce on the ground several times an comes to rest.

b) The ball will travel to upward right direction then downward.

c) The ball will swing repeatedly from left to right finally comes to rest in middle. How can we build a computer program to do this kind of reasoning?

The obvious answer is to program in the equation governing the physical motion of objects. These equation dates back introduced in classical physics.

Ex: The initial velocity of ball in fig(b) is V0. The angle of its departure from the ground is θ. The balls position ‘t’ seconds after being launched is given by:

Height = V0. t. Sin(θ) – ½ gt2

Distance= V0 .t.Cos(θ).

The goal of qualitative physics is to understand how to build and reason with abstract, number less representations. Once might object to qualitative physics on the grounds that computers are actually well suited to model physics processes. The goal of qualitative physics is not replace the traditional physics, but rather to provide a foundation for programs that can reason about the physical world. One such program might be a physics Expert System.

 Representation Qualitative Information:

Qualitative physics seeks to understand physical processes by building models of them. A model is an abstract representation that eliminates irrelevant details.

Traditional physics models build up from real valued variables, quantity spaces, rates of change expressions, equations and states.

Qualitative physics provides similar building blocks ones which are more abstract and mon-numeric.

Variables: In traditional physics, real valued variables are used to represent features of objects, such as position, velocity, angle, Temperature. Qualitative physics retains this notation but restrict to each variable to a small finite set of possible values.

For example the amount of water in a pot will be represented as on of [Empty, between, full] and its temperatures are [from, between, boiling].

Quantity Space: A small set of discrete values for a variable is called “Quantity Space”;

Rates of Change: Variables take on different values at different times. A real valued Rate of change (dx/dt) can be modeled qualitatively with the quantity space [decreasing, steadily, increasing].

Expressions: Variables can be combined to form expressions. Consider representing volume of water in a glass as [empty, between, full]. If we pour contents of one glass to another how much water will contain in second glass?

Empty + Empty = Empty.

Empty + Between = Between.

Empty + Full = Full.

Between + Between = [Between, Full].

Between +Full = Full + Overflow.

Full + Full = Full + Overflow.

Equations: Expressions and variables can be linked to one another via equations. The simplest equation states that variable x increases as variable y increases. This gives us an abstract representation of the actual functions relating x and y.

States: A state is a single snap shot in which each variable possesses one value. With in qualitative physics there are several different ways of formulating state information.

Reasoning with Qualitative Information:
A common reasoning method in qualitative physics is called “Quantitative Simulation”. The idea is to construct sequence of discrete “Episodes” that occur as qualitative variables change values. States are linked to other states by qualitative rules. Some rules are very general.

For example one simulation rule states that variables reach closer values before reaching further ones, and another rule states that changing from one values to another consumes some finite amount of time. Other rules, such as the rules governing the motion of objects through the air are more specific.

A network of all possible states and transitions for a qualitative system is called an evisionment. The above diagram shows an envisionment of the bouncing ball system. They are often many paths through an envisionment. Each path is called a history. Envisionments are useful in a number of applications. Most importantly, envisionments provide explanations for physical systems and those explanations can be used to predict feature behavior. In addition, if a system is an Artificial one , such as a mechanical device, envisionments can be used to diagnose problems that occur when components fail to behave correctly. Envisionments can also be used to represent and/or repair inaccurate mental models that people may have.

In order to write programs that automatically construct envisionments. We must represent qualitative knowledge about the behavior of particular kinds of processes substances, spaces, devices and so on.