Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

M Eugenia Cornejo,Jesús Medina,David Lobo

doi:10.3390/math8060881

Abstract

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs.

Highlights

Multi-adjoint logic programming (MALP) was introduced in [1] in order to generalize different non-classical logic programming approaches [2,3]
We have presented a methodology to simulate an arbitrary multi-adjoint normal logic programming (MANLP) by means of a semantically equivalent Core fuzzy answer set programming (CFASP)
In its body, by using the residuated pair, which defines the rule. This procedure allows us to complete the labour initiated in [15], that is, extended multi-adjoint logic programs can be translated into CFASPs with the goal of handling compact simple programs, which are semantically equivalent

Summary

Introduction

Multi-adjoint logic programming (MALP) was introduced in [1] in order to generalize different non-classical logic programming approaches [2,3]. A method for translating an arbitrary CFASP into a semantically equivalent MANLP has been shown Among others, this method entails the possibility of using current theorems in MALP and MANLP in CFASP, such as the existence theorem for stable models given in the multi-adjoint framework [14], to provide a sufficient condition for the existence of answer sets.

Preliminaries

Multi-Adjoint Normal Logic Programming

Core Fuzzy Answer Set Programming

From MANLP to CFASP

From Core Fuzzy Answer Set Programs to Multi-Adjoint Normal Logic Programs

Conclusions and Future Work