Improving Multi-adjoint Logic Programs by Unfolding Fuzzy Connective Definitions

Abstract

Declarative programming has been classically used for solving computational problems regarding AI, knowledge representation and so on. During the last decade, Soft-Computing has emerged as a new application area specially tempting for those new generation declarative languages integrating fuzzy logic into logic programming. In many fuzzy logic programming languages, both program clauses and connective definitions admit a clear declarative, rule-based representation inspired by the well-known logic and functional programming paradigms, respectively. A powerful and promising proposal in this area is represented by the multi-adjoint logic programming approach (for which we have developed the \(\mathcal F \mathcal L \mathcal O \mathcal P \mathcal E \mathcal R\) tool), where a set of (logic) Prolog-like rules are accompanied with a set of (functional) Haskell-like fuzzy connective definitions for manipulating truth degrees beyond the simpler case of {true,false}. Since these definitions can be seen as a particular case of equations and/or rewrite rules typically used in functional programming, in this paper we focus on their optimization by reusing some variants of program transformation techniques based on unfolding with a functional taste, which have been largely exploited in this last crisp (not fuzzy) setting. We also show how our method rebounds in the simplification of some computational cost measures we proposed in the past. Our approach is accompanied with some implementation and practical issues in connection with the \(\mathcal S \mathcal Y \mathcal N \mathcal T \mathcal H\) and \(\mathcal F \mathcal L \mathcal O \mathcal P \mathcal E \mathcal R\) tools and the fuzzyXPath application we have developed in the area of the semantic web.