FRIL++ and Its Applications

We introduce a deductive probabilistic and fuzzy object-oriented database language, called FRIL++, which can deal with both probability and fuzziness. Its foundation is a logic-based probabilistic and fuzzy object-oriented model where a class property (i.e., an attribute or a method) can contain fuzzy set values, and uncertain class membership and property applicability are measured by lower and upper bounds on probability. Each uncertainly applicable property is interpreted as a default probabilistic logic rule, which is defeasible, and probabilistic default reasoning on fuzzy events is proposed for uncertain property inheritance and class recognition. The design, implementation, and basic features of FRIL++ are presented. FRIL++ can be used as both a modeling and a programming language, as demonstrated by its applications to machine learning, user modeling, and modeling with words herein.