Judging if a conclusion follows logically from a given set of premises can depend much more on the believability than on the logical validity of the conclusion. This so-called belief bias effect has been replicated repeatedly for many decades now. An interesting observation is, however, that process models for deductive reasoning and models for the belief bias have not much of an overlap - they have largely been developed independently. Models for the belief bias often just implement first order logic for the reasoning part, thereby neglecting a whole research field. This paper aims to change that by presenting a first attempt at substituting the first order logic components of two models for belief, selective scrutiny and misinterpreted necessity, with two state of the art approaches for modeling human syllogistic reasoning, mReasoner and PHM. In addition, we propose an approach for extending the traditionally dichotomous predictions to numerical rating scales thereby enabling more detailed analysis. Evaluating the models on a dataset published with a recent meta-analysis on the belief bias effect, we demonstrate the general success of the augmented models and discuss the implication of our extensions in terms of the limitations of the current focus of research as well as the potential for future investigation of human reasoning.