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It is argued that a broad class of AGI-relevant algorithms can be expressedin a common formal framework, via specifying Galois connections linking searchand optimization processes on directed metagraphs whose edge targets arelabeled with probabilistic dependent types, and then showing these connectionsare fulfilled by processes involving metagraph chronomorphisms. Examples aredrawn 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 attentionallocation.  The analysis presented involves representing these cognitive algorithms asrecursive discrete decision processes involving optimizing functions definedover metagraphs, in which the key decisions involve sampling from probabilitydistributions over metagraphs and enacting sets of combinatory operations onselected sub-metagraphs. The mutual associativity of the combinatory operationsinvolved in a cognitive process is shown to often play a key role in enablingthe decomposition of the process into folding and unfolding operations; aconclusion that has some practical implications for the particulars ofcognitive processes, e.g. militating toward use of reversible logic andreversible program execution. It is also observed that where this mutualassociativity holds, there is an alignment between the hierarchy of subgoalsused in recursive decision process execution and a hierarchy of subpatternsdefinable in terms of formal pattern theory.

Patterns of Cognition: Cognitive Algorithms as Galois Connections Fulfilled by Chronomorphisms On Probabilistically Typed Metagraphs