A Refined Operational Semantics for ACT-R Investigating the Relations between Different ACT-R Formalizations

The popular cognitive architecture ACT-R is used in many cognitive models to explain cognitive features of human-beings. It has a well-defined psychological theory but lacks a formalization of its underlying computational system. This lack allows for technical ad-hoc artifacts in the original reference implementation. More importantly, formal analysis of cognitive models is not possible without a well-defined semantics. In prior work we have defined an abstract operational semantics for ACT-R's production system that is suitable for model analysis. It abstracts from details like timings and conflict resolution methods. However, to describe the behavior of ACT-R implementations a more refined semantics is needed. In this paper, we first introduce a new very abstract operational semantics for ACT-R that serves as formal base to compare different semantics. We define an improved version of the abstract semantics as an instance of our new very abstract semantics. Furthermore, we present a more refined operational semantics that also captures details from actual ACT-R implementations. We show that the refined semantics is sound w.r.t. the abstract semantics. This makes model analysis with the abstract semantics suitable for real-world ACT-R models.