ABSTRACT
Deductive logic provides tools for modeling a variety of applications and for finding solutions to problems involving optimal decisions. Specifically, this chapter will illustrate how logical expressions can be used to model decisions involved in city planning and to model the evolution of a biological system over time. In addition, an extension of deductive logic, called game theory, can be used to model situations of competition or conflict in which we seek a rationally defensible strategy in the face of uncertain actions by an adversary. Certain paradoxes that seem to defy rational behavior are discussed, and we see how reliance on chance mechanisms can actually aid in making optimal decisions in adversarial situations.
In Chapter 10, we discussed some well-known equivalences called the Rules of Replacement. These are listed for easy reference in Table 11.1. Such equivalences can be used to simplify logical expressions that arise in a variety of applications and may thereby result in savings of time or money. We will next discuss how logical expressions can be used to model a particular application that arises in the optimal location of emergency facilities.
