Computational psychology has the aim to explain human cognition by computational models of cognitive processes. The cognitive architecture Adaptive Control of Thought -Rational (ACT-R) is popular to develop such models. Although ACT-R has a well-defined psychological theory and has been used to explain many cognitive processes, there are two problems that make it hard to reason formally about its cognitive models: First, ACT-R lacks a computational formalization of its underlying production rule system and secondly, there are many different implementations and extensions of ACT-R with many technical artifacts complicating formal reasoning even more.This paper describes a formal operational semantics -the very abstract semantics -that abstracts from as many technical details as possible keeping it open to extensions and different implementations of the ACT-R theory. In a second step, this semantics is refined to define some of its abstract features that are found in many implementations of ACT-R -called the abstract semantics. It concentrates on the procedural core of ACT-R and is suitable for analysis of the general transition system since it still abstracts from details like timing, the sub-symbolic layer of ACT-R or conflict resolution.Furthermore, a translation of ACT-R models to the declarative programming language Constraint Handling Rules (CHR) is defined. This makes the abstract semantics an executable specification of ACT-R. CHR has been used successfully to embed other rule-based formalisms like graph transformation systems or functional programming. There are many theoretical results and practical tools that support formal reasoning about and analysis of CHR programs. The translation of ACT-R models to CHR is proven sound and complete w.r.t. the abstract operational semantics of ACT-R. This paves the way to analysis of ACT-R models through CHR analysis results and tools. Therefore, to the best of our knowledge, our abstract semantics is the first abstract formulation of ACT-R suitable for both analysis and execution.An Operational Semantics for ACT-R and its Translation to CHR 39:3[11] like term rewriting systems [22], graph transformation systems [20,23] and business rules [19]. Such embeddings have been used successfully to make the analysis results of CHR available to other approaches. The sound and complete embedding of ACT-R in CHR enables the use of these results and tools to formally reason about cognitive models.The paper is structured as follows: We first give a short introduction to ACT-R in section 2. The formal definition of the very abstract semantics is given in section 3 and the the abstract semantics is defined as an instance in section 4. The translation scheme of abstract ACT-R models to CHR programs is described in section 5 and proven sound and complete w.r.t. the operational semantics in section 6. Related work is discussed in section 7 with a detailed comparison to prior work.
