Possibilistic Residuated Implication Logics and Applications

Abstract

In this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterized by a t-norm operation on [0,1], and we express the degree of implication between the possibilities of two formulas explicitly by using residuated implication with respect to the t-norm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning. Key Words:Possibilistic reasoning, similarity-based reasoning, nonmonotonic reasoning. 1 Introduction Knowledge representation and reasoning is fundamental to knowledge based systems. Due to the imprecision and incompleteness of acquired knowledge, uncertain reasoning is a key issue in knowledge representation. To accommodate different types of incomplete knowledge, many uncertainty reasoning methods have been proposed and extensively studied. Most methods focus e..