Logic is one of the oldest intellectual disciplines in human history. It dates back to Aristotle. It has been studied through the centuries by people like Leibniz, Boole, Russell, Turing, and many others. And it is still a subject of active investigation today.
We use Logic in just about everything we do. We use it in our professional discussions. We use it in our personal conversations.
We use the language of Logic to state observations, to define concepts, and to formalize theories.
Abby likes Bess but Bess does not like Abby.
A triangle is a polygon with three sides.
Pressure times volume is proportional to temperature.
We use logical reasoning to derive conclusions from these bits of information.
We use logical proofs to convince others of our conclusions.
And we are not alone! Logic is increasingly being used by computers - to prove mathematical theorems, to validate engineering designs, to encode and analyze laws and regulations and business rules.
This lesson is an overview of Logic as presented in this course. We start with a discussion of possible worlds and illustrate the notion in an application area known as Sorority World. We then give an informal introduction to the key elements of Logic - logical sentences, logical entailment, and logical proofs. We talk about the value of using a formal language for expressing logical information instead of natural language. Finally, we discuss the automation of logical reasoning and some of the computer applications that this makes possible.