Symbol Grounding via Chaining of Morphisms
  A new model of symbol grounding is presented, in which the structures of
natural language, logical semantics, perception and action are represented
categorically, and symbol grounding is modeled via the composition of morphisms
between the relevant categories. This model gives conceptual insight into the
fundamentally systematic nature of symbol grounding, and also connects
naturally to practical real-world AI systems in current research and commercial
use. Specifically, it is argued that the structure of linguistic syntax can be
modeled as a certain asymmetric monoidal category, as e.g. implicit in the link
grammar formalism; the structure of spatiotemporal relationships and action
plans can be modeled similarly using "image grammars" and "action grammars";
and common-sense logical semantic structure can be modeled using
dependently-typed lambda calculus with uncertain truth values. Given these
formalisms, the grounding of linguistic descriptions in spatiotemporal
perceptions and coordinated actions consists of following morphisms from
language to logic through to spacetime and body (for comprehension), and vice
versa (for generation). The mapping is indicated between the spatial
relationships in the Region Connection Calculus and Allen Interval Algebra and
corresponding entries in the link grammar syntax parsing dictionary. Further,
the abstractions introduced here are shown to naturally model the structures
and systems currently being deployed in the context of using the OpenCog
cognitive architecture to control Hanson Robotics humanoid robots.
