Publications

ArXiv preprints

Badia, G., Kolaitis, P. and Noguera, C. Codd's theorem for databases over semirings, submitted.

Books

 B1. Badia, G. (202+). What is mathematical logic? (2e) (with Crossley, J. N. and Stillwell, J. C.), Oxford University Press, to appear (Published version).

Journal Articles

      All PDFs here are authors preprints. Please always cite the official version.

J38. Badia, G.  Hybrid-Dynamic Ehrenfeucht-Fraïssé Games (with Gaina, D., Knapp, A., Kowalski, T. and Wirsing, M),  ACM Transactions on Computational Logic, to appear (Published version).

J37. Badia, G. A modular bisimulation characterisation for fragments of hybrid logic (with Gaina, D., Knapp, A., Kowalski, T. and Wirsing, M),  Bulletin of Symbolic Logic, to appear (Published version, Open Access).

J36. Badia, G. (202+). New foundations of reasoning via first-order real valued logics (with Fagin, R. and Noguera, C.), Bulletin of Symbolic Logic, to appear (Published version, Open Access).

J35. Badia, G.  (2025). Definable classes of models and frames in Bi-intuitionistic logic (with Kowalski, T. and Olkhovikov, G.). Journal of Applied Logics 12(5):  1125-1152 (Published version, Open Access).

J34. Badia, G. (202+). Asymptotic truth-value laws in many-valued logics (with Caicedo, X. and Noguera, C.), Journal of Symbolic Logic, to appear (Published version, Open Access).

J33. Badia, G. (2024). Maximality of logic without identity (with Caicedo, X. and Noguera, C.), Journal of Symbolic Logic, 89 (1): 147-162 (Published version, Open Access).

J32. Badia, G. (2024). A parametrised axiomatization for a large number of restricted second-order logics (with Bell, J. L.), Journal of Logic and Computation, 34(7): 1295–1304 (Published version, Open Access).

J31. Badia, G. (2024). Relevant Consequence Relations: an invitation (with Behounek, L., Cintula P., and Tedder, A. ), Review of Symbolic Logic, 17(3): 762 -792 (Published version, Open Access).

J30. Badia, G. (2024). First-order friendliness (with and Makinson, D.), Review of Symbolic Logic, 17(4): 1055-1069 (Published version, Open Access).

 J29. Badia, G. (2023). Frame definability in finitely-valued modal logics (with Caicedo, X. and Noguera, C.), Annals of Pure and Applied Logic, 174(7): 103273 (Published version).

J28. Badia, G. (2023). A Lindström Theorem for Intuitionistic First-Order Logic (with Olkhovikov, G. and Zoghifard, R.), Annals of Pure and Applied Logic, 174(10): 103346 (Published version).

J27. Badia, G. (2023).  Omitting Types Theorem in hybrid-dynamic first-order logic with rigid symbols (with Gaina, D. and Kowalski, T.), Annals of Pure and Applied Logic, 174(3):  103212 (Published version).

J26. Badia, G. (202+). Craig Interpolation fails in Bi-Intuitionistic Predicate Logic (with Olkhovikov, G.). Review of Symbolic Logic, to appear (Published version, Open Access).

J25. Badia, G. (2022). Axiomatization via translation: Hiz's warning for predicate logic (with Crossley, J. N. & Humberstone, L.). Logique et Analyse, 65 (257): 39-56 (Published version).

 J24. Badia, G. (2022). Paraconsistent metatheory: new proofs with old tools (with Weber, Z. & Girard, P.). Journal of Philosophical Logic, 51: 825–856 (Published version, Open Access).

J23.  Badia, G. (2022).  A 0-1 law in mathematical fuzzy logic (with Noguera, C.). IEEE Transactions on Fuzzy Systems, 30 (9): 3833-3840 (Published version).

J22.  Badia, G. (2022). Maximality of bi-intuitionistic propositional logic (with Olkhovikov, G.). Journal of Logic and Computation, 32(1): 1-31 (Published version).

J21. Badia, G. (2022). Saturated models of first-order many-valued logics (with Noguera, C.). Logic Journal of the IGPL, 30 (1): 1-20 (Published version).

J20. Badia, G. (2021). Lindström theorems in graded model theory (with Noguera, C.). Annals of Pure and Applied Logic, 172 (3): 102916 (Published version).

J19. Badia, G. (2022). How much propositional logic sufffices for Rosser's undecidability theorem? (with Cintula, P., Hájek, P. and Tedder, A.). Review of Symbolic Logic, 15 (2): 487-504. (Published version).

J18. Badia, G. (2021). A general omitting types theorem in mathematical fuzzy logic (with Noguera, C.). IEEE Transactions on Fuzzy Systems, 29 (6): 1386-1394 (Published version).

J17. Badia, G. (2020). A Lindström Theorem in Many-Valued Modal Logic over a Finite MTL-chain (with  Olkhovikov, G.), Fuzzy Sets and Systems, 388: 26-37 (Published version).

J16. Badia, G. (2020).  A Lindström theorem for intuitionistic propositional logic (with  Olkhovikov, G.), Notre Dame Journal of Formal Logic, 61 (1):  11-30 (Published version).

J15. Badia, G. (2019). Syntactic characterizations of first-order structures in mathematical fuzzy logic (with Costa, V., Dellunde, P. and Noguera, C.), Soft Computing, 23 (7): 2177-2186 (Published version, Open Access).

J14. Badia, G.  (2019). Incompactness of the A1 fragment of basic second order propositional relevant logic. Australasian Journal of Logic, 16 (1): 1-8 (Published version).

J13. Badia, G.  (2018). Fraisse classes of graded relational structures. (with Noguera, C.) Theoretical Computer Science, 737: 81–90 (Published version).

J12. Badia, G. (2018). Currying Omnipotence (A Reply to Beall and Cotnoir). (with Tedder, A.) Thought: A Journal of Philosophy,  7(2): 119-121 (Published version).

J11. Badia, G. (2018). Variable sharing in substructural logics: an algebraic characterization. Bulletin of the Section of Logic, 47(2):  107-115 (Published version).

J10. Badia, G. (2018). On Sahlqvist formulas in relevant logic. Journal of Philosophical Logic, 47(4), 673-691  (Published version, Open Access).

J9. Badia, G. (2018). On elimination of quantifiers in some non-classical mathematical theories. (with Tedder, A.) Mathematical Logic Quarterly, 64 (3): 140-154 (Published version) (The version here fixes some typos from the published version).

J8. Badia, G. (2018). On classes of structures axiomatizable by universal d-Horn sentences and universal positive disjunctions. (with Marcos, J.) Algebra Universalis, 79: 41 (Published version, Open Access).

J7. Badia, G. (2017). Infinitary relevant languages with absurdity. Review of Symbolic Logic, 10 (4): 663-681 (Published version).

J6. Badia, G. (2017). Model definability in relevant logic. IfCoLog Journal of Logics and their Applications, 4 (3): 623-646 (Published version).

J5. Badia, G. (2017). A remark on Maksimova's variable separation property in super-bi-intuitionistic logics. Australasian Journal of Logic, 14 (1): 46-53 (Published version).

J4. Badia, G. (2016). Bi-simulating in bi-intuitionistic logic. Studia Logica, 104 (5): 1037-1050 (Published version).

J3. Badia, G. (2016). What is an inconsistent truth table? (with Weber, Z. & Girard, P.) Australasian Journal of Philosophy,  94 (3): 533-548 (Published version). 

J2. Badia, G.  (2016). A Lindström-style theorem for finitary weak entailment languages with absurdity. Logic Journal of the IGPL, 24 (2): 115-137 (Published version).

J1. Badia, G.  (2016). The relevant fragment of first order logic. Review of Symbolic Logic,  9 (1): 143-166 (Published version). 

                                                                                    Peer-reviewed Conference Proceedings

P5. Badia, G. (202+). Many-Expert Decision Trees  (with C. Noguera, A. Paparella and G. Sciavicco), Proceedings of OVERLAY 2024, 6th International Workshop on Artificial Intelligence and Formal Verification, Logic, Automata, and Synthesis, Bolzano, Italy, November 28–29, 2024,  Daniele Porello, Cosimo Vinci, and Matteo Zavatteri (eds), CEUR Workshop Proceedings, vol. 3904, pp.  97–102. (Published version).

P4. Badia, G. (202+). Fitting's Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation (with Noguera, C., Paparella, A., Sciavicco, G.  and Stan, E. I.), 31st International Symposium on Temporal Representation and Reasoning (TIME 2024), Leibniz International Proceedings in Informatics, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Volume 318, pp. 7:1-7:16 (2024). (Published version).

P3. Badia, G. (2024).  Logical characterizations of weighted complexity classes (with Droste, M., Noguera, C. and Paul, E.), Mathematical Foundations of Computer Science (MFCS 2024), Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) (Published version).

P2. Badia, G. (2022) Robinson consistency in many-sorted hybrid first-order logics (with Gaina, D. and Kowalski, T.) Advances in Modal Logic: Volume 14, David Fernández-Duque, Alessandra Palmigiano and Sophie Pinchinat, eds., College Publications, pp. 407-428. (Published version).

P1. Badia, G. (2018). Saturated Models in Mathematical Fuzzy Logic. (with Noguera, C.)  Proceedings of the IEEE International  Symposium on Multiple-Valued Logic 2018, IEEE Computer Society: 150-155 (Published version).

           Peer-reviewed Book Chapters

C1. Badia, G. (2019).  A substructural logic for inconsistent mathematics (with Weber, Z.). In Dialetheism and its applications, ed. A Reiger and G Young, Springer (Trends in logic), pp.155-176 (Published version). 

                                                                                                               Thesis

The Languages of Relevant Logic: A Model-Theoretic Perspective, University of Otago, 2016.