## Analysis of Cognitive Models in Constraint Handling RulesComputational cognitive modeling explores cognition by building computational models for cognitive processes, mechanisms and representations. Currently, implementations of cognitive models lack a formal foundation. This inhibits analysis. In this thesis, the cognitive architecture Adaptive Control of Thought - Rational (ACT-R) is formalized and embedded into the rule-based programming language Constraint Handling Rules (CHR). The powerful analytical methods of CHR, particularly confluence analysis, are extended by reasoning modulo equivalence relations. The results are applied to the domain of cognitive modeling. |

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### Contents

introduction | 1 |

basic notions | 15 |

constraint handling rules | 21 |

adaptive control of thought rational | 61 |

ii | 69 |

analysis of actr models | 147 |

embedding actr models into chr | 181 |

confluence criterion for actr | 207 |

conclusion | 227 |

future work | 233 |

list of figures | 251 |

list of publications | 257 |

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### Common terms and phrases

abstract semantics ACT-R ACT-R models action actual additional information allows analysis appear applicable approach architecture B-property buffer built-in constraints called Chapter CHR program chunk store clear cognitive models combination computation confluence modulo equivalence congruence relation considered consists contains corresponding criterion decidable defined definition denote derivation described directly discussed effects elements embedding example exists final formal function global goal ground Hence holds idea implementations instance interface interpretation introduced invariant invariant-based confluence joinable language leads Lemma logical maintain matching means methods minimal extensions monotonicity necessary Note object operational equivalence operational semantics overlap pairs partial possible program analysis Proof reasoning reduced reference representation represented request respect restriction rule rule application satisfy shown slot split substitution symbols term terminating Theorem theory thesis transition system translation user-defined equivalence relations values variables