Since January 2019, I'm a Lecturer (continuing position) in Logic 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. I received my PhD from the University of Otago (New Zealand) in May 2017. My current research focuses on mathematical fuzzy logic. In particular, I bring methods from model theory into the area of fuzzy logic. More broadly, I'm interested in non-classical logics (in particular semantical analysis by both algebraic and model-theoretic methods), non-classical mathematics, and philosophy of logic/mathematics. Since 2020, I'll be 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). My website is here.
Journal Article: A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain
Badia, Guillermo and Olkhovikov, Grigory (2019). A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain. Fuzzy Sets and Systems, Forthcoming26-37. doi:10.1016/j.fss.2019.03.002
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
Journal Article: Fraisse classes of graded relational structures
Badia, Guillermo and Noguera, Carles (2018). Fraisse classes of graded relational structures. Theoretical Computer Science, 73781-90. doi:10.1016/j.tcs.2018.05.010
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, doi:10.1007/s00012-018-0522-z
Logics for graded reasoning in applied contexts
(2020) UQ Early Career Researcher
A Naturalistic Framework for Ontic Structural Realism
Doctor Philosophy
Richard Sylvan's actual world pluralism
Doctor Philosophy
A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain
Badia, Guillermo and Olkhovikov, Grigory (2019). A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain. Fuzzy Sets and Systems, Forthcoming26-37. doi:10.1016/j.fss.2019.03.002
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, 73781-90. doi:10.1016/j.tcs.2018.05.010
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, 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
A general omitting types theorem in mathematical fuzzy logic
Badia, Guillermo and Noguera, Carles (2020). A general omitting types theorem in mathematical fuzzy logic. IEEE Transactions on Fuzzy Systems1-1. doi:10.1109/TFUZZ.2020.2975146
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
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 doi:10.1017/S175502032000012X
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
A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain
Badia, Guillermo and Olkhovikov, Grigory (2019). A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain. Fuzzy Sets and Systems, Forthcoming26-37. doi:10.1016/j.fss.2019.03.002
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, 73781-90. 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, 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
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
Logics for graded reasoning in applied contexts
(2020) UQ Early Career Researcher
A Naturalistic Framework for Ontic Structural Realism
Doctor Philosophy — Associate Advisor
Other advisors:
Richard Sylvan's actual world pluralism
Doctor Philosophy — Associate Advisor
Other advisors: