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

02/21/2021
by   Ben Goertzel, et al.
5

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/28/2021

The General Theory of General Intelligence: A Pragmatic Patternist Perspective

A multi-decade exploration into the theoretical foundations of artificia...
research
12/03/2020

Folding and Unfolding on Metagraphs

Typed metagraphs are defined as hypergraphs with types assigned to hyper...
research
02/18/2021

Interleaving classical and reversible

Given a simple recursive function, we show how to extract two interactin...
research
04/17/2022

Cognitive Architecture for Decision-Making Based on Brain Principles Programming

We describe a cognitive architecture intended to solve a wide range of p...
research
02/18/2023

Cognitive Architecture for Decision-Making Based on Brain Principles Programming (in Russian)

We describe a cognitive architecture intended to solve a wide range of p...
research
02/07/2018

"How to squash a mathematical tomato", Rubic's cube-like surfaces and their connection to reversible computation

Here we show how reversible computation processes, like Margolus diffusi...
research
09/18/2019

BigData Applications from Graph Analytics to Machine Learning by Aggregates in Recursion

In the past, the semantic issues raised by the non-monotonic nature of a...

Please sign up or login with your details

Forgot password? Click here to reset