Each of our theories of mental representation provides some insight into how the mind works. However, these insights often seem incompatible, as the debates between symbolic, dynamical, emergentist, sub-symbolic, and grounded approaches to cognition attest. Mental representations—whatever they are—must share many features with each of our theories of representation, and yet there are few hypotheses about how a synthesis could be possible. Here, I develop a theory of the underpinnings of symbolic cognition that shows how sub-symbolic dynamics may give rise to higher-level cognitive representations of structures, systems of knowledge, and algorithmic processes. This theory implements a version of conceptual role semantics by positing an internal universal representation language in which learners may create mental models to capture dynamics they observe in the world. The theory formalizes one account of how truly novel conceptual content may arise, allowing us to explain how even elementary logical and computational operations may be learned from a more primitive basis. I provide an implementation that learns to represent a variety of structures, including logic, number, kinship trees, regular languages, context-free languages, domains of theories like magnetism, dominance hierarchies, list structures, quantification, and computational primitives like repetition, reversal, and recursion. This account is based on simple discrete dynamical processes that could be implemented in a variety of different physical or biological systems. In particular, I describe how the required dynamics can be directly implemented in a connectionist framework. The resulting theory provides an “assembly language” for cognition, where high-level theories of symbolic computation can be implemented in simple dynamics that themselves could be encoded in biologically plausible systems.

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表示的计算起源

我们的每一种心理表征理论都提供了一些关于思维如何运作的见解。然而，这些见解往往看起来互不相容，正如象征性、动力性、涌现论、次象征性和扎根认知方法之间的争论所证明的那样。心理表征——无论它们是什么——必须与我们的每种表征理论共享许多特征，但关于如何进行综合的假设却很少。在这里，我发展了一种关于符号认知基础的理论，该理论展示了子符号动力学如何产生结构、知识系统和算法过程的更高层次的认知表征。该理论通过提出一种内部通用表示语言来实现概念角色语义学的一个版本，学习者可以在其中创建心理模型来捕捉他们在世界中观察到的动态。该理论形式化地描述了真正新颖的概念内容如何出现，使我们能够解释如何从更原始的基础学习基本的逻辑和计算操作。我提供了一个学习表示各种结构的实现，包括逻辑、数字、亲属关系树、常规语言、上下文无关语言、磁性、支配层次结构、列表结构、量化和计算原语（如重复、反转）等理论领域和递归。该解释基于简单的离散动态过程，可以在各种不同的物理或生物系统中实现。我特别描述了如何在联结主义框架中直接实现所需的动态。由此产生的理论为认知提供了一种“汇编语言”，其中高级符号计算理论可以在简单的动力学中实现，而这些动力学本身可以在生物学上合理的系统中进行编码。