Sequential merging and construction of rankings as cognitive logic

Abstract

We introduce and evaluate a cognitively inspired formal reasoning approach that sequentially applies a combination of a belief merging operator and a ranking construction operator. The approach is inspired by human propositional reasoning, which is understood here as a sequential process in which the agent constructs a new epistemic state in each task step according to newly acquired information. Formally, we model epistemic states by Spohn's ranking functions. The posterior representation of the epistemic state is obtained by merging the prior ranking function and a ranking function constructed from the new piece of information. We denote this setup as the sequential merging approach. The approach abstracts from the concrete merging operation and abstracts from the concrete way of constructing a ranking function according to new information. We formally show that sequential merging is capable of predicting with theoretical maximum achievable accuracy. Various instantiations of our approach are benchmarked on data from a psychological experiment, demonstrating that sequential merging provides formal reasoning methods that are cognitively more adequate than classical logic.