Thinking stands on two legs.One is information. The other is reason. Reason interprets the information. Reason draws inferences from information.
Knowledge is information in a form that facilitates interpretation and inference.
Reasoning systems based on the physical symbol system model have two parts:
The inference engine knows how to reason with the knowledge base.
A Thinking Machine = A Knowledge Base + An Inference Engine
Putting human knowledge in a form with which computers can reason is a daunting task. Much human knowledge is recorded (encoded) in the form of text on paper. Humans read and reason with this knowledge, but computers cannot do much with this format.
What is needed is to translate from such a 'natural' language form, to some artificial language which an inference engine program can reason with. One such artificial language is the first order predicate calculus, also known as FOL, first order logic.
Logic was first studied in the 4th century B.C. its invention is attributed to the Greek philosopher Aristotle. It was made symbolic in the 19th century by Boole and further developed in the 20th century by Frege, Robinson and others.
First order logic is very well understood, and has a sound mathematical foundation. It combines an expressive language with a sound method of inference in that language. Therefore FOL has been immensely popular in AI's attempt to construct intelligent programs.
FOL comes in two flavours.
This is the simplest form. There are no variables, just statements. Originally, natural language was used to express these statements. For example (These are to logic what 'Hello, World' programs are to CS!)
Propositional calculus is nice to show various aspects of Logic but it is not expressive enough for serious use. You need variables.
This is the main form of FOL. You can make more general statements in predicate calculus than you can in propositional calculus because of the availability of variables.