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