Ignorance, inconsistency, nonsense and similar phenomena are omnipresent in everyday reasoning. They have been intensively studied, especially in the area of multiple-valued logics. Therefore we develop a framework for belief bases, combining multiple-valued and probabilistic reasoning, with the main focus on the way belief bases are actually used and accessed through queries.

As an implementation tool we use a probabilistic programming language PROBLOG. Though based on distribution semantics with the independence assumption, we show how its constructs can successfully be used in implementing the considered logics and belief bases. In particular, we develop a technique for shifting probabilistic dependencies to the level of symbolic parts of belief bases.

We also discuss applications of the framework in reasoning with Likert-type scales, widely exploited in questionnaire-based experimental research in psychology, economics, sociology, politics, public opinion measurements, and related areas.