[Paper Review] Towards a Semantic Information Theory (Introducing Quantum Corollas)

Philip Tetlow, Dinesh Garg+5 more|arXiv (Cornell University)|Jan 14, 2022

Neural Networks and Applications4 citations

TL;DR

This paper introduces 'Quantum Corollas'—a novel framework that extends Quantum Information Theory by modeling semantic meaning through quantum-entangled, directed semantic triples. By combining denotational semantics with distributional vector representations and entanglement, it enables a finitely quantifiable, entropy-compliant theory of meaning that integrates semantics into quantum information systems.

ABSTRACT

The field of Information Theory is founded on Claude Shannon's seminal ideas relating to entropy. Nevertheless, his well-known avoidance of meaning (Shannon, 1948) still persists to this day, so that Information Theory remains poorly connected to many fields with clear informational content and a dependence on semantics. Herein we propose an extension to Quantum Information Theory which, subject to constraints, applies quantum entanglement and information entropy as linguistic tools that model semantics through measures of both difference and equivalence. This extension integrates Denotational Semantics with Information Theory via a model based on distributional representation and partial data triples known as Corolla.

Motivation & Objective

• To address the longstanding absence of semantics in Shannon’s Information Theory by integrating denotational semantics into quantum information frameworks.
• To resolve the duality between primitive and non-primitive representations in vector-based systems by introducing axiomatic, derivable semantic primitives.
• To model semantic meaning as a physical, quantifiable construct using quantum entanglement and information entropy, thereby grounding semantics in physical theory.
• To enable formal, graph-theoretic representation of meaning in quantum networks through the Corolla construct, supporting future quantum knowledge representation and information management systems.

Proposed method

• Proposes the Corolla as a partial semantic triple $(n, p_{\text{directed}})$, where $n$ is a semantic node and $p_{\text{directed}}$ is a directed predicate, forming a half-part of a non-directional semantic triple.
• Models semantic relationships using quantum-entangled qusyms, where entanglement encodes both difference and equivalence, enabling semantic coherence across distributed representations.
• Applies density matrices and error density matrices from quantum measurement to encode semantic uncertainty and compress semantic information in Hilbert space.
• Uses distributional vector representations to ground semantic nodes and predicates in a formal ontology, enabling compositional semantics within a quantum framework.
• Introduces a graph-theoretic model of semantic information where Corollas form directed edges in a knowledge graph, with entanglement enforcing semantic consistency.
• Quantifies semantic information via entropy constraints, asserting that only finitely expressible semantic structures are practically useful, analogous to the periodic table’s physical limits.

Experimental results

Research questions

• RQ1 How can semantic meaning be formally integrated into quantum information theory without relying on classical, non-physical models of meaning?
• RQ2 What is the role of quantum entanglement in modeling semantic equivalence and difference between concepts in a formal knowledge representation?
• RQ3 Can semantic primitives be defined axiomatically in vector-based systems using quantum-entangled representations, and if so, how are they derivable from first principles?
• RQ4 To what extent can semantic information be compressed and persisted in quantum networks using entanglement and entropy-based constraints?
• RQ5 What are the physical and theoretical limits of semantic expressiveness in quantum systems, and how do they relate to the laws of entropy and quantum measurement?

Key findings

• The Corolla construct enables a formal, axiomatic representation of semantic primitives by combining a semantic node with a directed predicate, forming a half-part of a non-directional semantic triple.
• Quantum entanglement between qusym pairs provides a physical mechanism to model both semantic difference and equivalence, forming the basis for semantic triples in a quantum network.
• Error density matrices from quantum measurements can be repurposed to encode and compress semantic information, enabling persistent storage of semantic content in quantum systems.
• Semantic information is shown to be finitely quantifiable and complementary to classical information theory, with its expressiveness bounded by entropy and physical constraints.
• The framework extends Quantum Information Theory to include graph-theoretic semantics, enabling the development of quantum knowledge representation and information management systems.
• Theoretical limits on semantic expressiveness are analogous to the periodic table—while infinite semantic forms are logically possible, only a finite, physically realizable set is practically useful.