TY - GEN A1 - Beim Graben, Peter A1 - Huber, Markus A1 - Meyer, Werner A1 - Römer, Ronald A1 - Wolff, Matthias T1 - Vector Symbolic Architectures for Context-Free Grammars T2 - Cognitive Computation N2 - Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. We present a rigorous mathematical framework for the representation of phrase structure trees and parse trees of context-free grammars (CFG) in Fock space, i.e. infinite-dimensional Hilbert space as being used in quantum field theory. We define a novel normal form for CFG by means of term algebras. Using a recently developed software toolbox, called FockBox, we construct Fock space representations for the trees built up by a CFG left-corner (LC) parser. We prove a universal representation theorem for CFG term algebras in Fock space and illustrate our findings through a low-dimensional principal component projection of the LC parser state. Our approach could leverage the development of VSA for explainable artificial intelligence (XAI) by means of hyperdimensional deep neural computation. Y1 - 2022 UR - https://opus4.kobv.de/opus4-UBICO/frontdoor/index/index/docId/28471 SN - 1866-9964 VL - 14 IS - 2 SP - 733 EP - 748 ER -