Mathematics of General Intelligence With Homotopy Type Theory and Category Theory

Artificial General Intelligence (AGI) requires a pre-existing mechanism of ‘understanding’, based on powerful abstractions, that enables all learning. The form this abstract structure must necessarily possess is analyzed using Category Theory (CT). Similarly, a pre-existing mechanism of abstract reasoning is required to translate understanding into intelligent responses. Homotopy Type Theory (HoTT) can be leveraged to construct such a mechanism.The above provides a mathematical foundation for designing a framework that must exist before any intelligent learning from experience or training is possible. The abstractions and ideas used in the Subjective Emergence of Objective Minds (SEOM) model, developed earlier by the author, help simplify the design. Philosophical issues related to computing with (ontologically and epistemologically) subjective inputs are considered. The mathematical categories, built from ideas in SEOM, are compared to Kant’s Categories of Understanding. This analysis highlights a fundamental problem with Kant’s categories while bringing out the structure of a system capable of understanding. The discussion also suggests an inversion of Heidegger’s notion of Dasein, as a dynamically computed, changing ‘being-within’, constructed from internal representations, that grounds the entire framework. However, the most important philosophical result of the mathematical and logical analysis presented refutes the general claim that syntax is not semantics and cannot possibly produce semantics. It is argued here that semantics can be generated only through carefully crafted syntactical structures that expand the scope of the computations to include subjective inputs.The paper concludes by observing that the structure of the Categories of Understanding described is a kind of Deep Neural Network (DNN) with enhanced semantics.