Hybrid Logic and Uncertain Logic

Probabilistic logic and credibilistic logic are two branches of multi-valued logic for dealing with random knowledge and fuzzy knowledge, respectively. In this paper, a hybrid logic is introduced for dealing with random knowledge and fuzzy knowledge simultaneously. First, a hybrid formula is introduced on the basis of random proposition and fuzzy proposition. Furthermore, a hybrid truth value is defined by chance measure. As a generalization of probabilistic logic, credibilistic logic and hybrid logic, an uncertain logic is proposed to deal with the general uncertain knowledge. Within the framework of uncertainty theory, the uncertain truth value is defined by uncertain measure and some of its basic properties are studied including the law of excluded middle, the law of contradiction and the law of truth conservation. c ©2009 World Academic Press, UK. All rights reserved.