It is argued that a broad class of AGI-relevant algorithms can be expressed in a common formal framework, via specifying Galois connections linking search and optimization processes on directed metagraphs whose edge targets are labeled with probabilistic dependent types, and then showing these connections are fulfilled by processes involving metagraph chronomorphisms. Examples are drawn from the core cognitive algorithms used in the OpenCog AGI framework: Probabilistic logical inference, evolutionary program learning, pattern mining, agglomerative clustering, pattern mining and nonlinear-dynamical attention allocation. The analysis presented involves representing these cognitive algorithms as recursive discrete decision processes involving optimizing functions defined over metagraphs, in which the key decisions involve sampling from probability distributions over metagraphs and enacting sets of combinatory operations on selected sub-metagraphs. The mutual associativity of the combinatory operations involved in a cognitive process is shown to often play a key role in enabling the decomposition of the process into folding and unfolding operations; a conclusion that has some practical implications for the particulars of cognitive processes, e.g. militating toward use of reversible logic and reversible program execution. It is also observed that where this mutual associativity holds, there is an alignment between the hierarchy of subgoals used in recursive decision process execution and a hierarchy of subpatterns definable in terms of formal pattern theory.

中文翻译：

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认知模式：作为概率类型元图上的亚纯态实现的伽罗瓦连接的认知算法

有人认为，可以通过指定Galois连接，在有向元图的边缘目标标有概率依赖类型的定向图上链接搜索和优化过程，然后显示满足这些条件，从而在通用的正式框架中表达与AGI相关的各种算法。通过涉及图元变态的过程。示例摘自OpenCog AGI框架中使用的核心认知算法：概率逻辑推理，进化程序学习，模式挖掘，凝聚聚类，模式挖掘和非线性动态注意力分配。提出的分析涉及将这些认知算法表示为递归的离散决策过程，其中包括优化对元图定义的函数，其中的关键决策包括从元图上的概率分布中采样并在选定的子元图上制定组合操作集。研究表明，认知过程中涉及的组合操作之间的相互联系通常在使过程分解为折叠和展开操作中起关键作用。该结论对认知过程的某些细节具有实际意义，例如有助于使用可逆逻辑和可逆程序执行。还观察到，在保持这种相互关联的地方，在递归决策过程执行中使用的子目标层次与根据形式模式理论可定义的子模式层次之间是一致的。