Enumeration of Success Patterns in Logic Programs

Since the proposal of logic programming by Horn clauses [5] and Prolog [7] has been gaining popularity because of the unified treatment of declarative semantics and procedural semantics. It has been successfully applied to natural language processing [3], data base queary [4] and others. Pattern directed invocation and built-in back+racking mechanism of Prolog are suited for symbolic manipulation. A Prolog Irdgram consists of logical formulas called Horn clauses. There are two types of Horn clauses -definite clause and goal clause. The definite clause has the form Ao+A, . . . A, (ma0) where A,&. . . &A,,, implies Ao. A0 is the head and the literal sequence A, . . . A, ic, the body. Erich Ai is a goal. m = 0 is the unit clause, which asserts that A, is true. When m >O, the clause works as a procedure to compute the relation A, by the goals Al . . . A,,. A Prolog program, --hich consists of definite clauses, can be seen as an axiom. For example,