Dr Guillermo Badia

ARC DECRA Research Fellow

School of Historical and Philosophical Inquiry
Faculty of Humanities, Arts and Social Sciences
+61 7 336 56402


I am a 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.

Research Interests

  • Many-valued logics and related algebras
    fuzzy logics, residuated lattices, model theory of fuzzy logics
  • Computational logic
    modal logic, hybrid logic, weighted logic
  • Substructural logics
    intuitionistic logic, relevant logic, bi-intuitionistic logic


  • Doctor of Philosophy, University of Otago


  • Badia, Guillermo, Caicedo, Xavier and Noguera, Carles (2023). Frame definability in finitely-valued modal logics. Annals of Pure and Applied Logic, 174 (7) 103273, 103273. doi: 10.1016/j.apal.2023.103273

  • Gaina, Daniel, Badia, Guillermo and Kowalski, Tomasz (2023). Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols. Annals of Pure and Applied Logic, 174 (3) 103212, 1-41. doi: 10.1016/j.apal.2022.103212

  • Badia, Guillermo, Caicedo, Xavier and Noguera, Carles (2023). Maximality of logic without identity. The Journal of Symbolic Logic, 89 (1), 1-16. doi: 10.1017/jsl.2023.2

  • 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

View all Publications


View all Grants


  • Doctor Philosophy

  • Doctor Philosophy

  • Doctor Philosophy

View all Supervision


Featured Publications

Book Chapter

  • 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

Journal Article

Conference Publication

  • Badia, Guillermo, Droste, Manfred, Noguera, Carles and Paul, Erik (2024). Logical characterizations of weighted complexity classes. Mathematical Foundations of Computer Science (MFCS 2024), Bratislava, Slovakia, 26-30 August 2024. Schloss Dagstuhl, Germany: Leibniz Center for Informatics.

  • 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.

  • 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

Other Outputs

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

  • Doctor Philosophy — Principal Advisor

  • Doctor Philosophy — Principal Advisor

  • Doctor Philosophy — Principal Advisor

Completed Supervision