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Logic programming (which might better be called logical programming by analogy with mathematical programming and linear programming) is, in its broadest sense, the use of mathematical logic for computer programming. In this view of logic programming, which can be traced at least as far back as John McCarthy's [1958] advice-taker proposal, logic is used as a purely declarative representation language, and a theorem-prover or model-generator is used as the problem-solver. The problem-solving task is split between the programmer, who is responsible only for ensuring the truth of programs expressed in logical form, and the theorem-prover or model-generator, which is responsible for solving problems efficiently.

The programmer is responsible, not only for ensuring the truth of programs, but also for ensuring their efficiency. In many cases, to achieve efficiency, the programmer needs to be aware of and to exploit the problem-solving behavior of the theorem-prover.

Moreover, such programs, being declarative, are at a higher conceptual level than purely imperative programs; and their program executers, being theorem-provers, operate at a higher conceptual level than conventional compilers and interpreters.
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Logic programming in the first and wider sense gave rise to a number of implementations, such as those by Fischer Black (1964), James Slagle (1965) and Cordell Green (1969), which were question-answering systems in the spirit of McCarthy's advice-taker. Foster and Elcock's Absys (1969), on the other hand, was probably the first language to be explicitly developed as an assertional programming language.

Hayes and Kowalski in Edinburgh tried to reconcile the logic-based declarative approach to knowledge representation with Planner's procedural approach. Hayes (1973) developed an equational language, Golux, in which different procedures could be obtained by altering the behavior of the theorem prover. Kowalski, on the other hand, showed how SL-resolution treats implications as goal-reduction procedures. Kowalski collaborated with Colmerauer in Marseille, who developed these ideas in the design and implementation of the programming language Prolog.

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The programming language Prolog was developed in 1972 by Alain Colmerauer. It emerged from a collaboration between Colmerauer in Marseille and Robert Kowalski in Edinburgh. Colmerauer was working on natural language understanding, using logic to represent semantics and using resolution for question-answering. During the summer of 1971, Colmerauer and Kowalski discovered that the clausal form of logic could be used to represent formal grammars and that resolution theorem provers could be used for parsing.

In the simplified, propositional case in which a logic program and a top-level atomic goal contain no variables, backward reasoning determines an and-or tree, which constitutes the search space for solving the goal. The top-level goal is the root of the tree. Given any node in the tree and any clause whose head matches the node, there exists a set of child nodes corresponding to the sub-goals in the body of the clause. These child nodes are grouped together by an "and". The alternative sets of children corresponding to alternative ways of solving the node are grouped together by an "or".