Logic building & elementary programming Innovation

COURTESY :- vrindawan.in

Wikipedia

Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem 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:

H :- B₁, …, B_n.

and are read declaratively as logical implications:

H if B₁ and … and B_n.

H is called the head of the rule and B₁, …, B_n is called the body. Facts are rules that have no body, and are written in the simplified form:

H.

In the simplest case in which H, B₁, …, B_n are all atomic formulae, these clauses are called definite clauses or Horn clauses. However, there are many extensions of this simple case, the most important one being the case in which conditions in the body of a clause can also be negations of atomic formulas. Logic programming languages that include this extension 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:

to solve H, solve B₁, and … and solve B_n.

Consider the following clause as an example:

fallible(X) :- human(X).

based on an example used by Terry Winograd to illustrate the programming language Planner. As a clause in a logic program, it can be used both as a procedure to test whether X is fallible by testing whether X is human, and as a procedure to find an X which is fallible by finding an X which is human. Even facts have a procedural interpretation. For example, the clause:

human(socrates).

can be used both as a procedure to show that socrates is human, and as a procedure to find an X that is human by “assigning” socrates to X.

The declarative reading of logic programs can be used by a programmer to verify their correctness. Moreover, logic-based program transformation techniques can also be used to transform logic programs into logically equivalent programs that are more efficient. In the Prolog family of logic programming languages, the programmer can also use the known problem-solving behaviour of the execution mechanism to improve the efficiency of programs.

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 in its present form 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 Minskym ,yhu and Seymour Papert.

Although it was based on the proof methods of logic, Planner, developed 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. It was used to implement Winograd’s natural-language understanding program SHRDLU, which was a landmark at that time. To cope with the very limited memory systems at the time, 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 QA-4, 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. Kowalski, on the other hand, developed SLD resolution, a variant of SL-resolution, and showed how it 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.

The Association for Logic Programming was founded to promote Logic Programming in 1986.

Prolog gave rise to the programming languages ALF, Fril, Gödel, Mercury, Oz, Ciao, Visual Prolog, XSB, and λProlog, as well as a variety of concurrent logic programming languages, constraint logic programming languages and Datalog.

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”.

Any search strategy can be used to search this space. Prolog uses a sequential, last-in-first-out, backtracking strategy, in which only one alternative and one sub-goal is considered at a time. Other search strategies, such as parallel search, intelligent backtracking, or best-first search to find an optimal solution, are also possible.

In the more general case, where sub-goals share variables, other strategies can be used, such as choosing the subgoal that is most highly instantiated or that is sufficiently instantiated so that only one procedure applies. Such strategies are used, for example, in concurrent logic programming.