Proto logic and neural subsymbolic reasoning

Abstract

The sub-symbolic 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 sub-symbolic 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 sub-symbols. Our goal is to form a sequence of associations, which lead to a desired state represented by sub-symbols, from an initial state represented by sub-symbols. 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 sub-symbols is described by a simple proto logic, which verifies if a subset of sub-symbols is present in a set of sub-symbols.

The Quantum Binding Problem in the Context of Associative Memory

“…We represent the 7 objects at various positions in the scene by the symbols A , B , C , D , E , F , G . The task is the identification of a category that is formed by the objects represented by the set B , C , G [ 11 , 12 , 14 ]. We determine whether each of the symbols B , C , G is present in the set that represents the scene.…”

“…We also verify whether a set representing a category is a subset of the set representing a scene. This task is described by proto logic sets [ 14 ]. Proto logic operates on sets; it verifies whether a subset is present in a certain set.…”

“…According to [ 11 , 12 , 14 , 27 ] the identity of an object can be represented by a binary pattern which is normalized for size and orientation. Its location in the x -axis is represented by a binary vector of the size of the abscissa of the pictogram representing the object.…”

“…The three vectors that compose the cognitive entity are called associative fields. Each associative field is represented by a binary vector of a fixed dimension; each cognitive entity is formed by the concatenation of the associative fields [ 11 , 12 , 14 ]. A cognitive entity is represented by a binary vector formed by the concatenation of binary vectors which represent the three associative fields [ 11 , 12 , 14 , 27 ].…”

“…This paper comprises a classical section that reviews previously published work [ 11 , 12 , 14 ] related to the sub-symbolic variable binding approach and an integration section that describes the new quantum computational approach.…”