On fuzzy unfolding: A multi-adjoint approach

Pascual Juli an a Gin es Moreno b Jaime Penabad c aDepartment of Computer Science ESI, Univ. of Castilla{La Mancha Paseo de la Universidad, 4; 13071 Ciudad Real, Spain bDepartment of Computer Science cDepartment of Mathematics EPSA, Univ. of Castilla{La Mancha Campus Universitario, s/n; 02071 Albacete, Spain Abstract In the context of (fuzzy) logic programs, `unfolding' means to transform a program rule by replacing an atom call of the body (of that rule) by its de nition. Unfolding is a semantics{preserving program transformation technique that is able to improve programs, generating more e cient code, since it anticipates computation steps. Unfolding is the basis for developing sophisticated and powerful programming tools, such as fold/unfold transformation systems or partial evaluators. In this paper we address the problem of extending the classical de nition of the unfolding rule (for pure logic programs) to the setting of multi{adjoint logic programming, where a fuzzy computed answer is a pair htruth degree; substitutioni computed by a fuzzy generalization of the modus ponens inference rule. Our main contributions can be summarized as follows: We proved the independence of the computation rule for multi{adjoint admissible computations. Moreover, we de ned a fuzzy unfolding rule and we demonstrated its strong correctness properties, that is, original and unfolded programs compute the same fuzzy computed answers for a given goal. We also proved that unfolding transformations increase the e ciency of the residual programs, by reducing the length of fuzzy admissible derivations when solving goals.