On a Fuzzy Logic Satisfying the Boolean Properties as a Fundamental Theory for Dealing with Intelligence of Robots

Abstract

This article, as a fundamental theory for dealing with intelligence of robots, discusses a fuzzy logic satisfying Boolean properties. This article shows the following: General construction of Boolean logics, and significance of each property that should be satisfied so that a whole set of well-formed formulas may form a Boolean algebra; Outline how to process fuzzy inference through an intuitively-understandable example that implies why usual fuzzy logics are not suitable for “deep inference” and what effect Boolean properties have on inference processes; Definition of the extended fuzzy subsets modified from usual fuzzy subsets such that membership functions take binary sequences instead of truth values; Construction of a Boolean fuzzy logic based on extended fuzzy subsets that is one of fuzzy logics satisfying all of the Boolean properties; Process of updating inference when a new knowledge is supplemented; Techniques of calculating membership values in extended fuzzy subsets on condition that some truth values are given; Boolean properties concerning extended fuzzy subsets; How to advance fuzzy inference on the Boolean fuzzy logic.