Logic Languages

Programming that uses a form of symbolic logic as a programming language is often called logic programming, and languages based on symbolic logic are called logic programming languages, or declarative languages. The syntax of logic programming languages is remarkably different from that of the imperative and functional languages. The semantics of logic programs also bears little resemblance to that of imperative-language programs. These observations should lead the reader to some curiosity about the nature of logic programming and declarative languages.

Predicate Calculus

A proposition can be thought of as a logical statement that may or may not be true. It consists of objects and the relationships among objects. Formal logic was developed to provide a method for describing propositions, with the goal of allowing those formally stated propositions to be checked for validity. Symbolic logic can be used for the three basic needs of formal logic: to express propositions, to express the relationships between propositions, and to describe how new propositions can be inferred from other propositions that are assumed to be true.

Propositions

The simplest propositions, which are called atomic propositions, consist of compound terms. A compound term is one element of a mathematical relation, written in a form that has the appearance of mathematical function notation.

Causal Form

Clausal form, which is a relatively simple form of propositions, is one such standard form. All propositions can be expressed in clausal form. The right side of a clausal form proposition is called the antecedent. The left side is called the consequent because it is the consequence of the truth of the antecedent.

Predicate Calculus and Proving Theorems

Predicate calculus provides a method of expressing collections of propositions. One use of collections of propositions is to determine whether any interesting or useful facts can be inferred from them. This is exactly analogous to the work of mathematicians, who strive to discover new theorems that can be inferred from known axioms and theorems. Resolution is an inference rule that allows inferred propositions to be computed from given propositions, thus providing a method with potential application to automatic theorem proving. Resolution was devised to be applied to propositions in clausal form. Theorem proving is the basis for logic programming. Much of what is computed can be couched in the form of a list of given facts and relationships as hypotheses, and a goal to be inferred from the hypotheses, using resolution.

Logic Programming

One of the essential characteristics of logic programming languages is their semantics, which is called declarative semantics. The basic concept of this semantics is that there is a simple way to determine the meaning of each statement, and it does not depend on how the statement might be used to solve a problem. Programming in both imperative and functional languages is primarily procedural, which means that the programmer knows what is to be accomplished by a program and instructs the computer on exactly how the computation is to be done. Programming in a logic programming language is nonprocedural. Programs in such languages do not state exactly how a result is to be computed but rather describe the form of the result.

Prolog

Alain Colmerauer and Phillippe Roussel at the University of Aix-Marseille, with some assistance from Robert Kowalski at the University of Edinburgh, developed the fundamental design of Prolog. Colmerauer and Roussel were interested in natural-language processing, and Kowalski was interested in automated theorem proving. The collaboration between the University of Aix-Marseille and the University of Edinburgh continued until the mid-1970s. Since then, research on the development and use of the language has progressed independently at those two locations, resulting in, among other things, two syntactically different dialects of Prolog.

The development of Prolog and other research efforts in logic programming received limited attention outside of Edinburgh and Marseille until the announcement in 1981 that the Japanese government was launching a large research project called the Fifth Generation Computing Systems (FGCS; Fuchi, 1981; Moto-oka, 1981). One of the primary objectives of the project was to develop intelligent machines, and Prolog was chosen as the basis for this effort. The announcement of FGCS aroused in researchers and the governments of the United States and several European countries a sudden strong interest in artificial intelligence and logic programming.

After a decade of effort, the FGCS project was quietly dropped. Despite the great assumed potential of logic programming and Prolog, little of great significance had been discovered. This led to the decline in the interest in and use of Prolog, although it still has its applications and proponents.