Proto logic and neural subsymbolic reasoning

The subsymbolic representation of the world often corresponds to a pattern that mirrors the world as described by the biological sense organs. Sparse binary vectors can describe subsymbolic representations, which can be efficiently stored in associative memories. According to the production system theory, a geometrically based problem-solving model can be defined as a production system operating on subsymbols. Our goal is to form a sequence of associations, which lead to a desired state represented by subsymbols, from an initial state represented by subsymbols. A simple and universal heuristic function can be defined, which takes into account the relationship between the vector and the corresponding similarity of the represented object or state in the real world. The manipulation of the subsymbols is described by a simple proto logic, which verifies if a subset of subsymbols is present in a set of subsymbols.