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Posts by Collection
portfolio
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publications
Hereditary Structural Completeness over K4: Rybakov's Theorem Revisited
Published in Master of Logic Institute of Logic, Language and Computation, 2022
Investigation into hereditary structurally complete transitive modal logics via algebraic logic and duality
Recommended citation: Carr, James. (2022). "HSC over K4: Rybakov's Theorem Revisited." Institute of Logic, Language and Computation.
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Homomorphism Preservation Theorems for Many-Valued Structures
Published in ACM Transactions on Computational Logic, 2026
We show how one can extend Rossman's proof of a finite homomorphism preservation theorem to a wide collection of many-valued predicate logics
Recommended citation: Carr, J. (2026). "Homomorphism Preservation Theorems for Many-Valued Structures." ACM Transactions on Computational Logic (to appear). 1(1).
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Locality in Residuated Lattice Structures
Published in Logical Methods in Computer Science, 2026
We study the extent to which the classical locality theorems from Hanf and Gaifman hold true in the residuated lattice setting
Recommended citation: Carr, J. (2026). "Locality in Residuated Structures." Logical Methods in Computer Science (under review) 1. 1(1).
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talks
Hereditary Structural Completeness over K4
Published:
Presentation on investigation into hereditary structurally complete transitive modal logics via algebraic logic and duality. Also presented at LATD 2022, AAC 2022 and Logic Colloqium 2023.
Homomorphism Preservation in the Finite for Many-Valued Logics
Published:
Presentation on extension of Rossman's proof of a classical finite homomorphism preservation theorem to a wide collection of many-valued predicate logics. Also presented at AAL 2023, TACL 2024.
Locality in Residuated Lattice Models
Published:
Presentation summarising investigation into status of classical locality theorems from Hanf and Gaifman to the residuated lattice setting.
Preservation Theorems for Many-Valued Logics via Categorical Methods
Published:
Presentation on using categorical methods to establish morphism preservation results for residuated lattice models.
teaching
Set Theory & Mathematical Logic
Undergraduate course, University of Queensland, School of Mathematics and Physics, 2023
As tutor. Undergraduate course introducing formal computation, set theory and model theory.
Category Theory Reading Group
Reading Group, University of Queensland, School of Mathematics and Physics, 2024
Organiser for a reading group introducing undergraduate students to category theory.
Theory & Practice in Science - Philosophy Component
Undergraduate course, University of Queensland, School of Historical & Philosophical Inquiry, 2025
Tutor for philosophy component of undergraduate introductory science course. Running workshops and essay consultations on philosophy of science.