On categorical semantics for (the exponential modality in) linear logic:
Valeria de Paiva, §2 of: The Dialectica Categories, in Categories in Computer Science and Logic, Contemporary Mathematics 92 (1989) [ISBN:978-0-8218-5100-5, doi:10.1090/conm/092]
Valeria de Paiva, The Dialectica Categories, PhD thesis, technical report 213, Computer Laboratory, University of Cambridge (1991) [pdf, pdf]
Nick Benton, Gavin Bierman, Valeria de Paiva, Term assignment for intuitionistic linear logic, Technical report 262, Computer Laboratory, University of Cambridge (August 1992) [pdf, pdf]
(published abridged as BBPH92)
Nick Benton, Gavin Bierman, Valeria de Paiva, Martin Hyland, Linear -Calculus and Categorical Models Revisited, in Computer Science Logic. CSL 1992, Lecture Notes in Computer Science 702, Springer (1993) [doi:10.1007/3-540-56992-8_6]
Martin Hyland, Valeria de Paiva, Full Intuitionistic Linear Logic (extended abstract). Annals of Pure and Applied Logic, 64(3), pp.273-291, 1993. (pdf)
A natural deduction-formulation of modal logic (S4/S5) and making explicit the necessity modal operator as a comonad:
Gavin M. Bierman, Valeria de Paiva, Intuitionistic necessity revisited, School of Computer Science research reports-University of Birmingham CSR (1996) [researchgate, pdf]
Gavin M. Bierman, Valeria de Paiva, On an Intuitionistic Modal Logic Studia Logica 65 (2000) 383–416 [doi:10.1023/A:1005291931660, pdf]
Natasha Alechina, Michael Mendler, Valeria de Paiva, Eike Ritter: Categorical and Kripke Semantics for Constructive S4 Modal Logic, in Computer Science Logic. CSL 2001 Lecture Notes in Computer Science 2142, Springer (2001) 292 [doi:10.1007/3-540-44802-0_21]
See also:
On Natural Language Inference:
Gödel’s Dialectica interpretation
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