Publications and presentations



My preprints on

  1. L. Carai, S. Lapenta, and L. Spada. Dualities for abelian l-groups and vector lattices beyond archimedeanity. arXiv:2310.13427 [math.RA].
  2. M. Abbadini, V. Marra and L. Spada. Stone-Gelfand duality for metrically complete lattice-ordered groups. arXiv:2210.15341 [math.FA]
  3. S. Lapenta, G. Metere, L. Spada. Relative ideals in homological categories, with an application to MV-algebras. arXiv:2208.12597 [math.CT]
  4. V. Marra and L. Spada. Two isomorphism criteria for directed colimits. arXiv:1312.0432 [math.CT]

International journals

  1. M. Abbadini, L. Spada. Are locally finite MV algebras a variety? Journal of Pure and Applied Algebra. 266(4) 2022. doi: 10.1016/j.jpaa.2021.106858 Preprint available on
  2. A. Di Nola, G. Lenzi, and Luca Spada, Sheaf representations and locality of Riesz spaces with order unit. Journal of Logic and Analysis 13 2021. doi: 10.4115/jla.2021.13.2 
  3.  Olivia Caramello, Vincenzo Marra, and Luca Spada. General affine adjunctions, Nullstellensätze, and dualities.  Journal of Pure and Applied Algebra. 225(1), 2021. doi: 10.1016/j.jpaa.2020.106470 Preprint available on
  4. José Gil-Férez, Luca Spada, Constantine Tsinakis, and Hongjun Zhou, Join-completions of partially ordered algebras. Annals of Pure and Applied Logic. 171(10) 2020. doi:10.1016/j.apal.2020.102842 Preprint available on
  5. Nick Bezhanishvili, Nick Galatos, and Luca Spada. Canonical formulas for k-potent commutative, integral, residuated latticesAlgebra Universalis, 3, 321–343, 2017 doi:10.1007/s00012-017-0430-7. Preprint available on
  6. Leonardo Cabrer and Luca Spada. MV-algebras, infinite dimensional polyhedra, and natural dualities. Archive for Mathematical Logic, 56(1), 21-42. 2017 doi:10.1007/s00153-016-0512-9. Preprint available on
  7. Luca Spada. An expansion of Basic Logic with fixed points. Special issue of Soft Computing in memoriam Franco Montagna. Volume 21(1) 29–37. 2017 doi:10.1007/s00500-016-2344-2. (Preprint page)
  8. Vincenzo Marra and Luca Spada. Duality, projectivity, and unification in Łukasiewicz logic and MV-algebrasAnnals of Pure and Applied Logic 164:192-210. 2013(Preprint page)
  9. Vincenzo Marra and Luca Spada. The dual adjunction between MV-algebras and Tychonoff spacesStudia Logica 100(1-2):253-278, 2012. Special issue of Studia Logica in memoriam Leo Esakia (L. Beklemishev, G. Bezhanishvili, D. Mundici and Y. Venema Editors).(Preprint page)
  10. Enrico Marchioni and Luca Spada. Advances in the Theory of μŁΠ algebras, Logic Journal of the IGPL, 19(3):476-489, 2011. (Preprint page)
  11. Brunella Gerla, Ciro Russo, and Luca Spada. Representation of Perfect and Local MV-algebras, Mathematica Slovaca 61(3):327–340, 2011. (Available on ArXiv),
  12. Antonio Di Nola, Revaz Grigolia, and Luca Spada. A discrete representation of free MV-algebras. Mathematical Logic Quarterly 56(3):279–288, 2010. (Preprint page)
  13. Antonio Di Nola, Giacomo Lenzi, and Luca Spada. Representation of MV-algebras by regular ultrapowers of [0,1]Archive for Mathematical Logic 49(4):491–500, 2010. (Preprint page)
  14. Antonio Di Nola, George Georgescu, and Luca Spada. Forcing in Łukasiewicz predicate logic. Studia Logica 89(1):111-145, 2008. (Preprint page)
  15. Luca Spada. ŁΠ logic with fixed points. Archive for Mathematical Logic, 47(7-8):741-763, 2008. (Preprint page)
  16. Luca Spada. μMV algebras: an approach to fixed points in Łukasiewicz logic, Fuzzy Sets and Systems, Special Issue: Mathematical and Logical foundations of Soft Computing. 159:1260-1267, 2008. (Preprint page)
  17. Franco Montagna and Luca Spada. Continuous approximations of product implication in MV-algebras with product. Soft Computing 9(3):149-154, 2005. (Preprint page)

Proceeding with referee

  1. Serafina Lapenta, Sebastiano Napolitano, Luca Spada. The Logic FP(Ł, Ł) and Two-Sorted Equational States. In Proceedings of the 13th International Symposium on Imprecise Probabilities: Theories and Applications – ISIPTA 2023. Proceedings of Machine Learning Research 215. 2023.
  2. Serafina Lapenta, Sebastiano Napolitano, Luca Spada. Ideals in the Two-Sorted Variety of Equational States In Fuzzy Logic and Technology, and Aggregation OperatorsLecture Notes in Computer Science 14069, 2023.
  3. Marco Abbadini, Federica Di Stefano, Luca Spada. Unification in Lukasiewicz logic with a finite number of variables. In M.-J. Lesot et al. (Eds.): IPMU 2020, CCIS 1239, pp. 622–633, 2020. doi:10.1007/978-3-030-50153-2_46 (Preprint page)
  4. Luca Spada. Some consequences of compactness in Łukasiewicz logic. In C. Drossos, P. Peppas and C. Tsinakis Eds. Proceeding of the VII Panhellenic Symposium. Patras 2009. ISBN 978-960-530-108-8. (Preprint page)
  5. Luca Spada. μMV algebras : an approach to fixed points in Łukasiewicz logic, in Proceeding of the Intl. Conference on The Logic of Soft Computing, Malaga September 2006. (Preprint page)
  6. Luca Spada. Continuous Approximations of MV-Algebra with Product and Product Residuation: A Cathegory-Theoretic Equivalence, Proceeding of Goedel Society Vol. 8, Vienna 2004. ISBN 3-901546-03-0. (Preprint page)

Book chapters

  1. Vincenzo Marra, Franco Montagna, and Luca Spada. Logiche Polivalenti. in H. Hosni, G. Lolli e C. Toffalori, Le direzioni della ricerca logica in Italia. Edizioni della Normale. 2015. ISBN 978-88-7642-570-7.
  2. Antonio Di Nola and Luca Spada. A short introduction to formal fuzzy logic via t-norms, in Amenta P., D’ambra L., Squillante M., Ventre A.G., Metodi, Modelli e Tecnologie dell’ informazione a Supporto delle Decisioni, Franco Angeli Editore. (pp. 592) 2008. ISBN 9788846483812. (Preprint page)

Invited papers

  1. Luca Spada. Geometrical dualities for Łukasiewicz logicBollettino dell’UMI, VI(9):749-763 2013.
  2. Luca Spada. Punti fissi nelle logiche a più valori, Bollettino U.M.I. La Matematica nella Società e nella Cultura. Serie VIII, Vol. X-A:355-358, 2007.


Invited conferences

  1. The unification type of Lukasiewicz logic with finitely many variables. Order Algebras and Logic. 30 March – 3 April 2022 [Slides]
  2. Some remarks about rigs. Open House on Category Theory 2021 18 – 19 November 2021, Ciudad de México.
  3. Are locally finite MV-algebras a variety? Shanks Workshop on Ordered Algebras and Logic. Vanderbilt University (Nashville, US) 5-7 March 2020.
  4. Kakutani duality, for groups. Duality in Algebra and Logic. Chapman University (California, US) 14-17 September 2018.
  5. Kakutani duality for groups. Topological Methods in Logic (To Lo VI). Tbilisi, Georgia July 2018.
  6. Geometric aspects of MV-algebras . Topology, Algebra and Categories in Logic (TACL). Prague, Czech Republic. 26-30 June 2017. [Slides]
  7. A categorical duality for residuated lattices. Soft Computing Days. Beijing, China. 27-29 November 2016.
  8. A duality for lattices with residuated operations. Topological Methods in Logic (ToLo) V. Tbilisi, Georgia, June 2016.
  9. An extension of Basic Logic with fixed points, Coherence and Truth. In memoriam Franco Montagna. Certosa di Pontignano (Siena), Italy. December 2015.
  10. A(nother) duality for the whole variety of MV-algebras. BEYOND 2014,  Florence, Italy. 3-5 December 2014.
  11. The multifarious representations of MV-algebras, Logic, Algebra and Truth Degrees 2012. Kanazawa, Japan. 14th September, 2012 [Slides page]
  12. Dualities for MV-algebras, Ordered Groups and Lattices in Algebraic Logic – a conference in memoriam Leo Esakia. Tbilisi, Georgia. 22d September, 2011 [Slides page]
  13. Unification for Abelian l-groups. Lattice-Ordered Groups and MV-Algebras: Interaction and Impact on Algebras of Logic. Buenos Aires 12th-15th October 2010. [A small variation of this can be found on this Slides page]
  14. Projectivity and unification in many valued logic, CSL 2010: Workshop on Mathematical Foundations of Fuzzy Logics. Brno 21st-29th August 2010. [Slides page]
  15. The prime spectrum of MV-algebras, Topological Methods is Logic II. Tbilisi, 8th–10th June 2010 [Slides page]
  16. Fixed points in many-valued logic, Logic, Algebra and Foundamentals of Computer Science. Bucharest 16 May 2008. [Slides page]
  17. Fuzzy logic and algebra, 2d MATHLOGAP workshop. Leeds 21-25 August 2006. [Slides page]

Invited seminars

  1. Some remarks about rigs. Nonclassical Logic Webinar. 24 September 2021. Online.
  2. Are locally finite MV-algebras a variety? Algebra|Coalgebra seminar (ILLC, University of Amsterdam) 13 May 2020. [Slides page]
  3. An overview of MV-algebras. Melbourne University, 19 April 2018. [Sorry, no slides: blackboard presentation.]
  4. General affine adjunctions, Nullstellensätze, and dualities. La Trobe University, 19th March 2018. [Sorry, no slides: blackboard presentation.]
  5. Canonical formulas for k-potent commutative, integral, residuated lattices. La Trobe University, 12th March 2018.
  6. A general framework for dualities. Mathematical Institute. Oxford University, 6th November 2014, UK. [Sorry, no slides: blackboard presentation.]
  7. General affine adjunctions, Nullstellensätze, and dualities. Applied Logic Seminars. Delft, The Netherlands. 7th May 2014. [Slides page]
  8. Axiomatisations for all varieties of n-potent residuated latticesPrague seminar on substructural logics.  28th-29th March 2014 Prague, Czech Republic. [Sorry, no slides: blackboard presentation.]
  9. General affine adjunctions, Nullstellensätze, and dualities, Colloquium on Mathematical Logic. Amsterdam, The Netherlands. 16th October 2013. [Sorry, no slides: blackboard presentation.]
  10. Two isomorphism criteria for directed colimits. Algebra|Coalgebra Seminar, 9th October 2013, Amsterdam, The Netherlands. [Sorry, no slides: blackboard presentation.]
  11. Forcing in Many-Valued Logic, Institute of Computer Science Academy of Sciences of the Czech Republic. Prague 10th December 2008. [A small variation of this can be found on this Slides page]
  12. Free MV algebras as direct limit, Slovak Academy of Sciences. Bratislava 25th September 2008. [Slides page]
  13. Fixed points in many-valued logic, University of Tbilisi, 2d June 2008. [Slides page]
  14. Logique Multi-Valeur: une introduction, Institute Camille Jordan, University of Lyon I, 22d September 2005. English and French [Slides page]

Invited courses

  1. Algebra della Logica. Scuola Estiva di Logica.  20 – 26 August 2017. Palazzo Feltrinelli, Gargano, Italy. [See the course webpage]
  2. Dualities. 16th Latin American Symposium on Mathematical Logic. 28th July –  1Sst August 2014. Buenos Aires, Argentina. [Slides page]
  3. Łukasiewicz logic and MV algebras, Philosophy and Mathematics of Uncertainty and Vagueness, 6th-15th August 2012, Campinas (SP), Brazil. [Slides page]
  4. An introduction to many-valued logic and its algebraic semantics, Tbilisi Summer school in Logic, 28th September – 2d October 2009. [A small variation of this can be found on this Slides page]
  5. Introduction to Fuzzy Sets and Fuzzy Logic, REASONPARK. Foligno, 17th-19th September 2009. [Slides page]

Contributed presentations

  1. Ideals in the Two-Sorted Variety of Equational States. EUSFLAT 2023, Palma, Spain. September 2023
  2. The logic FP(L,L) and two-sorted equational states. ISIPTA 2023, Oviedo, Spain. July 2023
  3. The coordinatization of the spectra of ℓ-groups. TACL 2022, Coimbra, 20-24 June 2022
  4. An algebraic study of Łukasiewicz logic with hedges. TbiLLC XIII Batumi, 16-20 September 2019.
  5. Stone-Gelfand duality, for groups: Topological duality and equational axiomatisation for norm-complete lattice-groups. Strutture residuate e strutture quantistiche: logica, algebra e applicazioni. Cagliari, 9-10 September 2019.
  6. Norm complete abelian l-groups: topological duality. TACL IX. Nice, 17 – 21 June 2019.
  7. Denominator respecting maps. XXVI Incontro AILA. Padova, Italia, 25-28 September 2017. [Slides]
  8. Łukasiewicz logic, with coefficients. Logic Colloquium 2017. Stockholm, Sweden, 14-20 August 2017. [Slides]
  9. The Nullstellensatz for varieties, and topological dualities. XX Congresso dell’unione Matematica Italiana. Siena, Italy. 7th-12th September 2015.  [Slides page]
  10. Canonical formulas for k-potent residuated latticesIV Logic, Algebra and Truth Degrees 2014 (LATD 2014). Vienna, Austria. 16th-19th July 2014. [Slides page]
  11. Dualities and GeometryXXV incontro dell’Associazione Italiana di Logica e sue Applicazioni. 14th-17th April 2014, Pisa, Italy. [Slides page]
  12. A general framework for dualities. Workshops on Duality and Probabilistic Systems, 14th – 21st March 2014. Bellairs, Barbados. [Sorry, no slides: (open air!) blackboard presentation]
  13. Canonical Formulas and Residuated Lattices. Shanks Workshop on Ordered Algebras and Logic 22th-23th February 2014, Nashville, US. [Sorry, no slides: blackboard presentation.]
  14. An Isomorphism Criterion for Colimits of Sequences of Finitely Presented ObjectsInternational Workshop on Algebraic Logic in Computer Science (a satellite workshop of  LPAR). 14th-19th December 2013, Stellenbosch, South Africa. [Slides page]
  15. A general framework for geometric dualities for varieties of algebras, TACL VI, 28th July-1st August 2013, Nashville, US. [Sorry, no slides: blackboard presentation.]
  16. Dualità geometriche per la logica di Łukasiewicz, (featured presentation) XIX Congresso dell’Unione Matematica Italiana, Bologna, 15th September 2011.  A small variation of this can be found on this [Slides page]
  17. The unification type of Łukasiewicz logic is nullary, (featured presentation) TACL V, Marseille, 25th-30th July 2011. [Slides page]
  18. Omitting type theorems for Łukasiewicz Logic, ManyVal10: Beyond algebraic semantics: bridging intended and formal interpretations of many-valued logics. Varese 3-5 May 2010. [Slides page]
  19. A uniform version on Di Nola Theorem, Probability, Uncertainty and Rationality, Certosa di Pontignano, Siena 1-3 November 2009. [Slides page]
  20. Advances in the theory of fixed points in many-valued logics, VIII International Tbilisi Symposium on Language, Logic and Computation. Bakuriani, 21-25 September 2009. [Slides page]
  21. Some consequences of compactness in Łukasiewicz Predicate Logic, VII Panhellenic Logic Symposium, Patras 15-19 July 2009. [Slides page]
  22. Small advances in the algebraic proof theory of substructural logicsTACL IV. Amsterdam 7-11 July 2009. [Slides page]
  23. μŁΠ-algebre libere, XVIII Congresso UMI. Bari 24-29 September 2007. [Slides page]
  24. Freedom in μŁΠ algebras, TA(N)CL III, Oxford, 6-9 August 2007. [Slides page]
  25. Finite and infinite forcing in Łukasiewicz logic, 3d MATHLOGAP workshop. Aussois 24-30 June 2007. [Slides page]
  26. μMV algebras: an approach to fixed points in Łukasiewicz logic, The Logic of Soft Computing. Malaga, 13-15 September 2006. [Slides page]
  27. ŁΠ logic with fixed points operator, TA(N)CL II. Barcelona 15-18 June 2005. [Slides page]
  28. ŁΠq algebras and quasifields, Kurt Goedel Colloquium. Vienna 25-30 August 2003. [Slides page]