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Correspondence Theory on Vector Spaces

  • 2024
  • OriginalPaper
  • Chapter
Published in:
Authors
Alessandra Palmigiano
Mattia Panettiere
Ni Wayan Switrayni
Published in
Logic, Language, Information, and Computation
Publisher
Springer Nature Switzerland

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Abstract

This chapter delves into the application of correspondence theory on vector spaces, extending the semantics for the Lambek calculus enriched with tense modal operators. It introduces a complete semantics for analytic inductive inequalities, which are crucial for structural control in type-logical theory. The paper begins by recalling basic algebraic definitions and facts, then extends correspondence theory to algebras over a field seen as frames. It shows how analytic inductive inequalities can be rewritten into simpler shapes and demonstrates their equivalence to quasi-left primitive inequalities. The work concludes by characterizing the first-order conditions corresponding to these inequalities and discusses potential future research directions in the context of structural control and meaning spaces.
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This summary of the content was generated with the help of AI.

The first author acknowledges the NWO grant KIVI.2019.001.
The third author is supported by the Indonesian Education Scholarship, Ref. Number: 1027/J5.2.3/BPI.LG/VIII/2022.
The authors have received support from the EU’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101007627.

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previous chapter Labelled Sequent Calculi for Inquisitive Modal Logics
next chapter An EXPTIME-Complete Entailment Problem in Separation Logic
Title
Correspondence Theory on Vector Spaces
Authors
Alessandra Palmigiano
Mattia Panettiere
Ni Wayan Switrayni
Copyright Year
2024
Book
Logic, Language, Information, and Computation

Print ISBN: 978-3-031-62686-9

Electronic ISBN: 978-3-031-62687-6

Copyright Year: 2024

DOI
https://doi.org/10.1007/978-3-031-62687-6_10
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