# A Decidable Confluence Test for Cognitive Models in ACT-R

## TL;DR

This paper introduces a decidable confluence test for ACT-R cognitive models by translating them into CHR, enabling modelers to verify if their models produce consistent results regardless of rule application.

## Contribution

It presents the first decidable confluence criterion for ACT-R models using translation to CHR, facilitating analysis of model behavior.

## Key findings

- Decidable confluence criterion for ACT-R models established.
- Translation from ACT-R to CHR is sound and complete.
- Modelers can verify confluence to ensure consistent cognitive process outcomes.

## Abstract

Computational cognitive modeling investigates human cognition by building detailed computational models for cognitive processes. Adaptive Control of Thought - Rational (ACT-R) is a rule-based cognitive architecture that offers a widely employed framework to build such models. There is a sound and complete embedding of ACT-R in Constraint Handling Rules (CHR). Therefore analysis techniques from CHR can be used to reason about computational properties of ACT-R models. For example, confluence is the property that a program yields the same result for the same input regardless of the rules that are applied. In ACT-R models, there are often cognitive processes that should always yield the same result while others e.g. implement strategies to solve a problem that could yield different results. In this paper, a decidable confluence criterion for ACT-R is presented. It allows to identify ACT-R rules that are not confluent. Thereby, the modeler can check if his model has the desired behavior. The sound and complete translation of ACT-R to CHR from prior work is used to come up with a suitable invariant-based confluence criterion from the CHR literature. Proper invariants for translated ACT-R models are identified and proven to be decidable. The presented method coincides with confluence of the original ACT-R models.