Download Logic, Programming and Prolog by Nilsson U., Maluszynski J. PDF
By Nilsson U., Maluszynski J.
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Additional resources for Logic, Programming and Prolog
Sample text
Xn ) = g(f (X0 , X0 ), f (X1 , X1 ), . . , f (Xn−1 , Xn−1 )) where X0 , . . , Xn are distinct. By case 1 this reduces to: . . {X1 = f (X0 , X0 ), X2 = f (X1 , X1 ), . . , Xn = f (Xn−1 , Xn−1 )} Assume that the equation selected in step i is of the form Xi = f (. . , . ). Then in the . k-th iteration the selected equation is of the form Xk = Tk where Ti+1 := f (Ti , Ti ) and T0 := X0 . Hence, |Ti+1 | = 2|Ti | + 1. That is, |Tn | > 2n . This shows the exponential dependency of the unification time on the length of the structures.
However, the transition from experimental theorem proving to applied logic programming requires improved efficiency of the system. This is achieved by introducing restrictions on the language of formulas — restrictions that make it possible to use the relatively simple and powerful inference rule called the SLD-resolution principle. This chapter introduces a restricted language of definite logic programs and in the next chapter their computational principles are discussed. In subsequent chapters a more unrestrictive language of so-called general programs is introduced.
Father (adam, mary). ← newborn(mary). newborn(mary). 1: Refutation of ← proud (Z). atoms obtained in that way. This basic computation step can be seen as an inference rule since it transforms logic formulas. It will be called the resolution principle for definite programs or SLD-resolution principle. As illustrated above it combines in a special way modus ponens with the elimination rule for the universal quantifier. At the last step of reasoning the empty goal, corresponding to falsity, is obtained.