Thresholded Tabulation in a Fuzzy Logic Setting

Abstract

Fuzzy logic programming represents a flexible and powerful declarative paradigm amalgamating fuzzy logic and logic programming, for which there exists different promising approaches described in the literature. In this paper we propose an improved fuzzy query answering procedure for the so called multi-adjoint logic programming approach, which avoids the re-evaluation of goals and the generation of useless computations thanks to the combined use of tabulation with thresholding techniques. The general idea is that, when trying to perform a computation step by using a given program rule R, we firstly analyze if such step might contribute to reach further significant solutions (non tabulated yet). When it is the case, it is possible to avoid a useless computation step via a rule R by using thresholds and filters based on the truth degree of R, as well as a safe, accurate and dynamic estimation of the maximum truth degree associated to its body.

Beyond multi-adjoint logic programming

“…We start this section by providing some conventions followed too in [18,41] for describing the operational principle of MALP:…”

“…Following [18,19], after evaluating with admissible steps all the atoms appearing on a given expression, the resulting goal is ready for being reduced and interpreted w.r.t. lattice L in the following way.…”

“…Focusing on this setting, in [1,17,18,21,[43][44][45] we describe some fundamental and practical issues regarding the design of declarative languages, programming environments and real-world applications with a fuzzy taste 1 developed in our research group during the last years. In essence, our research on MALP follows the fruitful path initiated by Lee [26], where the classical inference mechanism of selective linear definite clause resolution (SLD-resolution) used in LP, has been replaced by a fuzzy variant able to handle partial truth and uncertainty in a comfortable way.…”