Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications

@article{Correia2021PuttingAS,
  title={Putting a Spin on Language: A Quantum Interpretation of Unary Connectives for Linguistic Applications},
  author={A. D. Correia and H. T. C. Stoof and Michael Moortgat},
  journal={ArXiv},
  year={2021},
  volume={abs/2004.04128}
}
Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural operations give rise to derivational ambiguities that are missed by the original Lambek Calculus or its pregroup simplification. Proposals for compositional interpretation of extended Lambek Calculus in the compact closed category of FVect and linear maps… 
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References

SHOWING 1-10 OF 20 REFERENCES

Density Matrices with Metric for Derivational Ambiguity

This work replaces the pregroup front end by a Lambek categorial grammar with directional implications expressing a word's selectional requirements, and introduces a symmetric, nondegenerate bilinear form called a "metric" that defines a canonical isomorphism between a vector space and its dual, allowing to keep a distinction between left and right implication.

Lexical and Derivational Meaning in Vector-Based Models of Relativisation

A compositional distributional framework is presented that allows us to give a single meaning recipe for the relative pronoun reconciling the Frobenius semantics with the demands of Dutch derivational syntax.

A Frobenius Algebraic Analysis for Parasitic Gaps

This work identifies two types of parasitic gapping where the duplication of semantic content can be confined to the lexicon and proposes a polymorphic type schema for the head of the adjunct phrase that introduces the primary gap.

Meaning updating of density matrices

This work underpins implementation of text-level natural language processing on quantum hardware (a.k.a. QNLP), for which exponential space-gain and quadratic speed-up have previously been identified.

Universal Grammar

  • L. Dezsö
  • Computer Science
    Certainty in Action
  • 2021

Vector spaces as Kripke frames

Applying results and insights from duality and representation theory for the algebraic semantics of nonclassical logics, the complex algebras of the Lambek calculus are regarded as `Kripke frames' the complete residuated lattices, making it possible to establish a systematic connection between vector space semantics and the standard Routley-Meyer semantics of (modal) substructural logics.

Current Research in Operational Quantum Logic

Introduction to Quantum Mechanics

I. THEORY. 1. The Wave Function. 2. The Time-Independent Schrodinger Equation. 3. Formalism. 4. Quantum Mechanics in Three Dimensions. 5. Identical Particles. II. APPLICATIONS. 6. Time-Independent

Structure of Language and Its Mathematical Aspects

Linear Algebra Done Right

-Preface for the Instructor-Preface for the Student-Acknowledgments-1. Vector Spaces- 2. Finite-Dimensional Vector Spaces- 3. Linear Maps- 4. Polynomials- 5. Eigenvalues, Eigenvectors, and Invariant