Overview
Background
I am a Senior Lecturer in Logic (continuing position) at the University of Queensland (Australia). Before this, I was a postdoc in mathematical logic in the Department of Knowledge-Based Mathematical Systems at Johannes Kepler University Linz (Austria) on an FWF project on residuated structures. Overlapping with this, I also worked on a GACR project on predicate graded logics in computer science. I received my PhD from the University of Otago (New Zealand) in 2017. From 2022-2025, my research is supported by an ARC Discovery Early Career Researcher Award (DE220100544). There was a workshop to kick off the project in 10-12 November 2022. I serve as an editor for Archive for Mathematical Logic and Journal of Multiple-Valued Logic and Soft Computing.
Availability
- Dr Guillermo Badia is:
- Available for supervision
- Media expert
Fields of research
Qualifications
- Doctor of Philosophy, University of Otago
Research interests
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Many-valued logics and related algebras
fuzzy logics, residuated lattices, model theory of fuzzy logics
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Computational logic
modal logic, hybrid logic, weighted logic
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Substructural logics
intuitionistic logic, relevant logic, bi-intuitionistic logic
Works
Search Professor Guillermo Badia’s works on UQ eSpace
2022
Journal Article
Axiomatization via translation: Hiz's warning for predicate logic
Badia, Guillermo, Crossley, John and Humberstone, Lloyd (2022). Axiomatization via translation: Hiz's warning for predicate logic. Logique et Analyse, 257 (257), 39-56. doi: 10.2143/LEA.257.0.3291070
2021
Journal Article
Maximality of bi-intuitionistic propositional logic
Olkhovikov, Grigory and Badia, Guillermo (2021). Maximality of bi-intuitionistic propositional logic. Journal of Logic and Computation, 32 (1) exab058, 1-31. doi: 10.1093/logcom/exab058
2021
Journal Article
A general omitting types theorem in mathematical fuzzy logic
Badia, Guillermo and Noguera, Carles (2021). A general omitting types theorem in mathematical fuzzy logic. IEEE Transactions on Fuzzy Systems, 29 (6) 9003263, 1386-1394. doi: 10.1109/TFUZZ.2020.2975146
2021
Journal Article
Lindström theorems in graded model theory
Badia, Guillermo and Noguera, Carles (2021). Lindström theorems in graded model theory. Annals of Pure and Applied Logic, 172 (3) 102916, 102916. doi: 10.1016/j.apal.2020.102916
2020
Journal Article
Saturated models in first-order many-valued logics
Badia, Guillermo and Noguera, Carles (2020). Saturated models in first-order many-valued logics. Logic Journal of the IGPL, 30 (1), 1-20. doi: 10.1093/jigpal/jzaa027
2020
Journal Article
How much propositional logic suffices for Rosser’s essential undecidability theorem?
Badia, Guillermo, Cintula, Petr, Hajek, Petr and Tedder, Andrew (2020). How much propositional logic suffices for Rosser’s essential undecidability theorem?. Review of Symbolic Logic, 15 (2), 1-18. doi: 10.1017/S175502032000012X
2020
Journal Article
A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain
Badia, Guillermo and Olkhovikov, Grigory (2020). A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain. Fuzzy Sets and Systems, 388, 26-37. doi: 10.1016/j.fss.2019.03.002
2020
Journal Article
A Lindström theorem for intuitionistic propositional logic
Badia, Guillermo and Olkhovikov, Grigory (2020). A Lindström theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1), 11-30. doi: 10.1215/00294527-2019-0030
2019
Journal Article
Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic
Badia, Guillermo, Costa, Vicent, Dellunde, Pilar and Noguera, Carles (2019). Syntactic characterizations of classes of first-order structures in mathematical fuzzy logic. Soft Computing, 23 (7), 2177-2186. doi: 10.1007/s00500-019-03850-6
2019
Journal Article
Incompactness of the A1 fragment of basic second order propositional relevant logic
Badia, Guillermo (2019). Incompactness of the A1 fragment of basic second order propositional relevant logic. Australasian Journal of Logic, 16 (1), 1-8. doi: 10.26686/ajl.v16i1.3925
2019
Book Chapter
A substructural logic for inconsistent mathematics
Badia, Guillermo and Weber, Zach (2019). A substructural logic for inconsistent mathematics. Dialetheism and its applications. (pp. 155-176) edited by Adam Reiger and Gareth Young. Cham, Switzerland: Springer. doi: 10.1007/978-3-030-30221-4_9
2018
Journal Article
Fraisse classes of graded relational structures
Badia, Guillermo and Noguera, Carles (2018). Fraisse classes of graded relational structures. Theoretical Computer Science, 737, 81-90. doi: 10.1016/j.tcs.2018.05.010
2018
Journal Article
On Sahlqvist formulas in relevant logic
Badia, Guillermo (2018). On Sahlqvist formulas in relevant logic. Journal of Philosophical Logic, 47 (4), 673-691. doi: 10.1007/s10992-017-9445-y
2018
Journal Article
On elimination of quantifiers in some non-classical mathematical theories
Badia, Guillermo and Tedder, Andrew (2018). On elimination of quantifiers in some non-classical mathematical theories. Mathematical Logic Quarterly, 64 (3), 140-154. doi: 10.1002/malq.201600078
2018
Journal Article
Currying omnipotence (a reply to Beall and Cotnoir)
Tedder, Andrew and Badia, Guillermo (2018). Currying omnipotence (a reply to Beall and Cotnoir). Thought: A Journal of Philosophy, 7 (2), 119-121. doi: 10.1002/tht3.376
2018
Journal Article
On classes of structures axiomatizable by universal d-Horn sentences and universal positive disjunctions
Badia, Guillermo and Marcos, Joao (2018). On classes of structures axiomatizable by universal d-Horn sentences and universal positive disjunctions. Algebra Universalis, 79 (2) 41, 41. doi: 10.1007/s00012-018-0522-z
2018
Conference Publication
Saturated models in mathematical fuzzy logic
Badia, Guillermo and Noguera, Carles (2018). Saturated models in mathematical fuzzy logic. 2018 IEEE 48th International Symposium on Multiple-Valued Logic (ISMVL), Linz, Austria, 16-18 May 2018. Piscataway, NJ United States: Institute of Electrical and Electronics Engineers. doi: 10.1109/ismvl.2018.00034
2018
Journal Article
Variable sharing in substructural logics: an algebraic characterization
Badia, Guillermo (2018). Variable sharing in substructural logics: an algebraic characterization. Bulletin of the Section of Logic, 47 (2), 107-115. doi: 10.18778/0138-0680.47.2.03
2017
Journal Article
Infinitary propositional relevant languages with absurdity
Badia, Guillermo (2017). Infinitary propositional relevant languages with absurdity. Review of Symbolic Logic, 10 (4), 663-681. doi: 10.1017/S1755020317000132
2017
Journal Article
Model definability in relevant logic
Badia, Guillermo (2017). Model definability in relevant logic. The IfCoLog Journal of Logics and their Applications, 4 (3), 623-645.
Supervision
Availability
- Dr Guillermo Badia is:
- Available for supervision
Before you email them, read our advice on how to contact a supervisor.
Supervision history
Current supervision
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Doctor Philosophy
Algebraic Properties of Bi-intuitionistic Equivalence
Principal Advisor
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Doctor Philosophy
Complexity and definability in many-valued finite model theory
Principal Advisor
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Doctor Philosophy
Model-theoretic aspects of infinitary modal logics
Principal Advisor
Completed supervision
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2023
Doctor Philosophy
A Naturalistic Framework for Metaphysics
Associate Advisor
Other advisors: Associate Professor Joel Katzav
Media
Enquiries
Contact Dr Guillermo Badia directly for media enquiries about:
- logic
- mathematical logic
- philosophy of mathematics
- truth
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