Introduction
The Kitchen Sink System consists of a sink, the tap that supplies the water to sink and the drain which drains the water. The water starts to drain from the sink as soon as some water(amount) is filled in the sink i.e height and pressure of the water in the sink is non zero. When the sink is filled up to the brink the height, pressure of water in the sink at maximum and hence, outflow is also maximum. The pressure magnitudes depends only the height of the water in the sink and is independent of the width or shape of the sink.
Quantities and quantity spaces
To describe the Kitchen Sink System, we will be using five quantities namely inflow(IF), volume(V), height(H), pressure(P) and outflow(OF) and their derivatives. Inflow cannot be negative and can either be zero or some value. The quantity space chosen for Height is {zero, plus, max}. Analogous to Height, the Pressure and Volume of water can be zero, or have some value, or be maximal. For that reason, the same quantity spaces are chosen for Pressure and Outflow. Derivatives of all the quantities have a quantity space of {minus,zero,plus}.
Causal Model
Here, the amount of inflow(IF) causes the volume(V) of the water in the sink to increase and hence is modeled by a positive influence. The change in volume of water in the sink causes change in height and pressure of water present in the sink, therefore it is modeled by positive proportionality. And also change in the pressure of water in the sink results in similar change in outflow and hence it is modeled by positive proportionality as well. The increased outflow of water causes the volume of water to decrease and is modeled by a negative influence.
Reasoning
Our QR system takes in inflow(IF), volume(V) as inputs. Also, we take rate of inflow(dIF) as an exogenous input and then give the state graph as the output. Along with it, we highlight the shortest path and give a text file which logs all the transitions between the states and possible cause for the transition.