Modeling Interpretive Steps in Fuzzy Logic Computations

Abstract

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming (LP). In this setting, the multi-adjoint logic approach represents an extremely flexible fuzzy language with a procedural principle structured in two separate phases. During the operational one, admissible steps are systematically applied in a similar way to classical resolution steps in LP, thus returning an expression where all atoms have been exploited. This last expression is then interpreted under a given lattice during the so called interpretive phase. Whereas the operational phase has been successfully formalized in the past, more effort is needed to clarify the notion of interpretive step. In this paper we firstly introduce a refinement of this concept which fairly models at a very low level the computational behaviour of the interpretive phase. Then, we present a simple but powerful cost measure induced from such definition which helps to estimate the computational (interpretive) effort required to solve a goal. The resulting method is much more accurate and realistic than other simpler cost measures (like counting the number or the weights of interpretive steps) that we have proposed in the past for proving efficiency properties in program transformation tasks such as fold/unfold, partial evaluation, and so on.

This work was supported by the EU (FEDER), and the Spanish Science and Education Ministry (MEC) under grants TIN 2004-07943-C04-03 and TIN 2007-65749.