# 3. Logic Programming and Prolog¶

In the previous chapters we have seen how logic can be used to represent knowledge about a particular domain, and to derive new knowledge by means of logical inference. A distinct feature of logical reasoning is the separation between model theory and proof theory: a set of logical formulas determines the set of its models, but also the set of formulas that can be derived by applying inference rules. Another way to say the same thing is: logical formulas have both a declarative meaning and a procedural meaning. For instance, declaratively the order of the atoms in the body of a clause is irrelevant, but procedurally it may determine the order in which different answers to a query are found.

Because of this procedural meaning of logical formulas, logic can be used as a programming language. If we want to solve a problem in a particular domain, we write down the required knowledge and apply the inference rules built into the logic programming language. Declaratively, this knowledge specifies what the problem is, rather than how it should be solved. The distinction between declarative and procedural aspects of problem solving is succinctly expressed by Kowalski’s equation

algorithm = logic + control

Here, logic refers to declarative knowledge, and control refers to procedural knowledge. The equation expresses that both components are needed to solve a problem algorithmically.

In a purely declarative programming language, the programmer would have no means to express procedural knowledge, because logically equivalent programs would behave identical. However, Prolog is not a purely declarative language, and therefore the procedural meaning of Prolog programs cannot be ignored. For instance, the order of the literals in the body of a clause usually influences the efficiency of the program to a large degree. Similarly, the order of clauses in a program often determines whether a program will give an answer at all. Therefore, in this chapter we will take a closer look at Prolog’s inference engine and its built-in features (some of which are non-declarative). Also, we will discuss some common programming techniques.