I'm a Lecturer in Philosophy (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 will be supported by an ARC Discovery Early Career Researcher Award (DE220100544). There is a workshop to kick off the project in 10-12 November 2022. I'm an editor of the Journal of Multiple-Valued Logic and Soft Computing (so please get in touch if you want me to handle your manuscript).
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
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
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
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
Fuzzy logics for graded reasoning in applied contexts
(2022–2025) ARC Discovery Early Career Researcher Award
MOSAIC-Modalities in Substructural Logics: Theory, Methods and Applications (EU H2020 MSCA RISE)
(2021–2025) Spanish National Research Council (Agencia Estatal Consejo Superior de Investigaciones Científicas)
Logics for graded reasoning in applied contexts
(2020–2021) UQ Early Career Researcher
Algebraic Properties of Bi-intuitionistic Equivalence
Doctor Philosophy
Complexity and definability in many-valued finite model theory
Doctor Philosophy
Simulation as Argument: Towards a computational approach of philosophy
Doctor Philosophy
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
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
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
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
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
Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols
Gaina, Daniel, Badia, Guillermo and Kowalski, Tomasz (2022). Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols. Annals of Pure and Applied Logic 103212. doi: 10.1016/j.apal.2022.103212
Paraconsistent metatheory: new proofs with old tools
Badia, Guillermo, Weber, Zach and Girard, Patrick (2022). Paraconsistent metatheory: new proofs with old tools. Journal of Philosophical Logic, 51 (4), 825-856. doi: 10.1007/s10992-022-09651-x
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, 39-56. doi: 10.2143/LEA.257.0.3291070
Craig Interpolation fails in Bi-Intuitionistic Predicate Logic
Olkhovikov, Grigory and Badia, Guillermo (2022). Craig Interpolation fails in Bi-Intuitionistic Predicate Logic. Review of Symbolic Logic, 1-27. doi: 10.1017/S1755020322000296
A 0-1 law in mathematical fuzzy logic
Badia, Guillermo and Noguera, Carles (2021). A 0-1 law in mathematical fuzzy logic. IEEE Transactions on Fuzzy Systems, 30 (9), 1-1. doi: 10.1109/TFUZZ.2021.3131200
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
A remark on Maksimova's variable separation property in super-bi-intuitionistic logics
Badia, Guillermo (2017). A remark on Maksimova's variable separation property in super-bi-intuitionistic logics. Australasian Journal of Logic, 14 (1), 46-53. doi: 10.26686/ajl.v14i1.4027
Bi-simulating in bi-intuitionistic logic
Badia, Guillermo (2016). Bi-simulating in bi-intuitionistic logic. Studia Logica, 104 (5), 1037-1050. doi: 10.1007/s11225-016-9664-1
A Lindström-style theorem for finitary propositional weak entailment languages with absurdity
Badia, Guillermo (2016). A Lindström-style theorem for finitary propositional weak entailment languages with absurdity. Logic Journal of the IGPL, 24 (2), 115-137. doi: 10.1093/jigpal/jzv054
The relevant fragment of first order logic
Badia, Guillermo (2016). The relevant fragment of first order logic. Review of Symbolic Logic, 9 (1), 143-166. doi: 10.1017/S1755020315000313
What is an inconsistent truth table?
Weber, Zach, Badia, Guillermo and Girard, Patrick (2016). What is an inconsistent truth table?. Australasian Journal of Philosophy, 94 (3), 533-548. doi: 10.1080/00048402.2015.1093010
Possible worlds and paradoxes Mundos posibles y paradojas
Badía, Guillermo (2013). Possible worlds and paradoxes Mundos posibles y paradojas. Arete, 25 (2), 219-229.
Robinson consistency in many-sorted hybrid first-order logics
Gaina, Daniel, Badia, Guillermo and Kowalski, Tomasz (2022). Robinson consistency in many-sorted hybrid first-order logics. 2022 Advances in Modal Logic (AiML), Rennes, France, 22-25 August 2022. London, United Kingdom: College Publications.
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
Badia, Guillermo and Makinson, David (2022). First-order friendliness.
Relevant consequence relations: an invitation
Badia, Guillermo, Cintula, Petr, Behounek, Libor and Tedder, Andrew (2022). Relevant consequence relations: an invitation.
New foundations of reasoning via real-valued first-order logics
Badia, Guillermo, Fagin, Ronald and Noguera, Carles (2022). New foundations of reasoning via real-valued first-order logics.
Frame definability in finitely-valued modal logics
Badia, Guillermo, Caicedo, Xavier and Noguera, Carles (2022). Frame definability in finitely-valued modal logics.
A Lindström theorem for intuitionistic first-order logic
Olkhovikov, Grigory, Badia, Guillermo and Zoghifard, Reihane (2022). A Lindström theorem for intuitionistic first-order logic.
A parametrised axiomatization for a large number of restricted second-order logics
Badia, Guillermo and Bell, John Lane (2022). A parametrised axiomatization for a large number of restricted second-order logics.
Maximality of logic without identity
Badia, Guillermo, Caicedo, Xavier and Noguera, Carles (2022). Maximality of logic without identity.
Fuzzy logics for graded reasoning in applied contexts
(2022–2025) ARC Discovery Early Career Researcher Award
MOSAIC-Modalities in Substructural Logics: Theory, Methods and Applications (EU H2020 MSCA RISE)
(2021–2025) Spanish National Research Council (Agencia Estatal Consejo Superior de Investigaciones Científicas)
Logics for graded reasoning in applied contexts
(2020–2021) UQ Early Career Researcher
Algebraic Properties of Bi-intuitionistic Equivalence
Doctor Philosophy — Principal Advisor
Complexity and definability in many-valued finite model theory
Doctor Philosophy — Principal Advisor
Simulation as Argument: Towards a computational approach of philosophy
Doctor Philosophy — Principal Advisor
Other advisors:
Richard Sylvan's actual world pluralism
Doctor Philosophy — Associate Advisor
Other advisors:
A Naturalistic Framework for Ontic Structural Realism
Doctor Philosophy — Associate Advisor
Other advisors: