@misc{BeimGrabenHuberMeyeretal., author = {Beim Graben, Peter and Huber, Markus and Meyer, Werner and R{\"o}mer, Ronald and Wolff, Matthias}, title = {Vector Symbolic Architectures for Context-Free Grammars}, series = {Cognitive Computation}, volume = {14}, journal = {Cognitive Computation}, number = {2}, issn = {1866-9964}, doi = {10.1007/s12559-021-09974-y}, pages = {733 -- 748}, abstract = {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.}, language = {en} } @misc{HuberLieblRoemerWirschingetal., author = {Huber-Liebl, Markus and R{\"o}mer, Ronald and Wirsching, G{\"u}nther and Schmitt, Ingo and beim Graben, Peter and Wolff, Matthias}, title = {Quantum-inspired Cognitive Agents}, series = {Frontiers in Applied Mathematics and Statistics}, journal = {Frontiers in Applied Mathematics and Statistics}, number = {8}, issn = {2297-4687}, doi = {10.3389/fams.2022.909873}, pages = {1 -- 31}, abstract = {The concept of intelligent agents is—roughly speaking—based on an architecture and a set of behavioral programs that primarily serve to solve problems autonomously. Increasing the degree of autonomy and improving cognitive performance, which can be assessed using cognitive and behavioral tests, are two important research trends. The degree of autonomy can be increased using higher-level psychological modules with which needs and motives are taken into account. In our approach we integrate these modules in architecture for an embodied, enactive multi-agent system, such that distributed problem solutions can be achieved. Furthermore, after uncovering some weaknesses in the cognitive performance of traditionally designed agents, we focus on two major aspects. On the one hand, the knowledge processing of cognitive agents is based on logical formalisms, which have deficiencies in the representation and processing of incomplete or uncertain knowledge. On the other hand, in order to fully understand the performance of cognitive agents, explanations at the symbolic and subsymbolic levels are required. Both aspects can be addressed by quantum-inspired cognitive agents. To investigate this approach, we consider two tasks in the sphere of Shannon's famous mouse-maze problem: namely classifying target objects and ontology inference. First, the classification of an unknown target object in the mouse-maze, such as cheese, water, and bacon, is based on sensory data that measure characteristics such as odor, color, shape, or nature. For an intelligent agent, we need a classifier with good prediction accuracy and explanatory power on a symbolic level. Boolean logic classifiers do work on a symbolic level but are not adequate for dealing with continuous data. Therefore, we demonstrate and evaluate a quantum-logic-inspired classifier in comparison to Boolean-logic-based classifiers. Second, ontology inference is iteratively achieved by a quantum-inspired agent through maze exploration. This requires the agent to be able to manipulate its own state by performing actions and by collecting sensory data during perception. We suggest an algebraic approach where both kinds of behaviors are uniquely described by quantum operators. The agent's state space is then iteratively constructed by carrying out unitary action operators, while Hermitian perception operators act as observables on quantum eigenstates. As a result, an ontology emerges as the simultaneous solution of the respective eigenvalue equations. Tags: btuktqiai; btuktcogsys; btukttheseus; btuktqtheseus}, language = {en} } @misc{RoemerbeimGrabenHuberLiebletal., author = {R{\"o}mer, Ronald and beim Graben, Peter and Huber-Liebl, Markus and Wolff, Matthias}, title = {(Pre-)linguistic Problem Solving based on Dynamic Semantics}, series = {14th IEEE International Conference on Cognitive Infocommunications - CogInfoCom 2023, September 22-23, Budapest, Hungary}, journal = {14th IEEE International Conference on Cognitive Infocommunications - CogInfoCom 2023, September 22-23, Budapest, Hungary}, isbn = {979-8-3503-2565-2}, issn = {2473-5671}, doi = {10.1109/CogInfoCom59411.2023.10397487}, pages = {147 -- 152}, language = {en} }