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Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses: A :- B1, ..., Bn. and are read as declarative sentences in logical form: A if B1 and ... and Bn. A is called the head of the rule, B1, ..., Bn is called the body, and the Bi are called literals or conditions. When n = 0, the rule is called a fact and is written in the simplified form: A. Queries (or goals) have the same syntax as the bodies of rules and are commonly written in the form: ?- B1, ..., Bn. In the simplest case of Horn clauses (or "definite" clauses), all of the A, B1, ..., Bn are atomic formulae of the form p(t1 ,..., tm), where p is a predicate symbol naming a relation, like "motherhood", and the ti are terms naming objects (or individuals). Terms include both constant symbols, like "charles", and variables, such as X, which start with an upper case letter. Consider, for example, the following Horn clause program: Given a query, the program produces answers. For instance for a query ?- parent_child(X, william), the single answer is Various queries can be asked. For instance the program can be queried both to generate grandparents and to generate grandchildren. It can even be used to generate all pairs of grandchildren and grandparents, or simply to check if a given pair is such a pair: Although Horn clause logic programs are Turing complete, for most practical applications, Horn clause programs need to be extended to "normal" logic programs with negative conditions. For example, the definition of sibling uses a negative condition, where the predicate = is defined by the clause X = X: Logic programming languages that include negative conditions have the knowledge representation capabilities of a non-monotonic logic. In ASP and Datalog, logic programs have only a declarative reading, and their execution is performed by means of a proof procedure or model generator whose behaviour is not meant to be controlled by the programmer. However, in the Prolog family of languages, logic programs also have a procedural interpretation as goal-reduction procedures. From this point of view, clause A :- B1,...,Bn is understood as: to solve A, solve B1, and ... and solve Bn. Negative conditions in the bodies of clauses also have a procedural interpretation, known as negation as failure: A negative literal not B is deemed to hold if and only if the positive literal B fails to hold. Much of the research in the field of logic programming has been concerned with trying to develop a logical semantics for negation as failure and with developing other semantics and other implementations for negation. These developments have been important, in turn, for supporting the development of formal methods for logic-based program verification and program transformation. History The use of mathematical logic to represent and execute computer programs is also a feature of the lambda calculus, developed by Alonzo Church in the 1930s. However, the first proposal to use the clausal form of logic for representing computer programs was made by Cordell Green. This used an axiomatization of a subset of LISP, together with a representation of an input-output relation, to compute the relation by simulating the execution of the program in LISP. Foster and Elcock's Absys, on the other hand, employed a combination of equations and lambda calculus in an assertional programming language that places no constraints on the order in which operations are performed. Logic programming, with its current syntax of facts and rules, can be traced back to debates in the late 1960s and early 1970s about declarative versus procedural representations of knowledge in artificial intelligence. Advocates of declarative representations were notably working at Stanford, associated with John McCarthy, Bertram Raphael and Cordell Green, and in Edinburgh, with John Alan Robinson (an academic visitor from Syracuse University), Pat Hayes, and Robert Kowalski. Advocates of procedural representations were mainly centered at MIT, under the leadership of Marvin Minsky and Seymour Papert. Although it was based on the proof methods of logic, Planner, developed by Carl Hewitt at MIT, was the first language to emerge within this proceduralist paradigm. Planner featured pattern-directed invocation of procedural plans from goals (i.e. goal-reduction or backward chaining) and from assertions (i.e. forward chaining). The most influential implementation of Planner was the subset of Planner, called Micro-Planner, implemented by Gerry Sussman, Eugene Charniak and Terry Winograd. Winograd used Micro-Planner to implement the landmark, natural-language understanding program SHRDLU. For the sake of efficiency, Planner used a backtracking control structure so that only one possible computation path had to be stored at a time. Planner gave rise to the programming languages QA4, Popler, Conniver, QLISP, and the concurrent language Ether. 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. In the meanwhile, Alain Colmerauer in Marseille was working on natural-language understanding, using logic to represent semantics and using resolution for question-answering. During the summer of 1971, Colmerauer invited Kowalski to Marseille, and together they discovered that the clausal form of logic could be used to represent formal grammars and that resolution theorem provers could be used for parsing. They observed that some theorem provers, like hyper-resolution, behave as bottom-up parsers and others, like SL resolution (1971) behave as top-down parsers. It was in the following summer of 1972, that Kowalski, again working with Colmerauer, developed the procedural interpretation of implications in clausal form. It also became clear that such clauses could be restricted to definite clauses or Horn clauses, and that SL-resolution could be restricted (and generalised) to SLD resolution. Kowalski's procedural interpretation and SLD were described in a 1973 memo, published in 1974. Colmerauer, with Philippe Roussel, used the procedural interpretation as the basis of Prolog, which was implemented in the summer and autumn of 1972. The first Prolog program, also written in 1972 and implemented in Marseille, was a French question-answering system. The use of Prolog as a practical programming language was given great momentum.... Discover the Prolog Editorial popular books. Find the top 100 most popular Prolog Editorial books.