Publications
Preprints
- Olivia Caramello, Vincenzo Marra, and Luca Spada. General affine adjunctions, Nullstellensätze, and dualities. Preprint available on ArXiv.org. Submitted 2018.
- José Gil-Férez, Luca Spada, Constantine Tsinakis, and Hongjun Zhou, Join-completions of ordered algebras. Preprint available on ArXiv.org. Submitted 2017.
- Vincenzo Marra and Luca Spada. Two isomorphism criteria for directed colimits. Preprint available on ArXiv.org 2013.
International journals
- Nick Bezhanishvili, Nick Galatos, and Luca Spada. Canonical formulas for k-potent commutative, integral, residuated lattices. Algebra Universalis, published online, 2017 doi:10.1007/s00012-017-0430-7. Preprint available on ArXiv.org
- 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 ArXiv.org
- 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)
- Vincenzo Marra and Luca Spada. Duality, projectivity, and unification in Łukasiewicz logic and MV-algebras. Annals of Pure and Applied Logic 164:192-210. 2013. (Preprint page)
- Vincenzo Marra and Luca Spada. The dual adjunction between MV-algebras and Tychonoff spaces, Studia 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)
- Enrico Marchioni and Luca Spada. Advances in the Theory of μŁΠ algebras, Logic Journal of the IGPL, 19(3):476-489, 2011. (Preprint page)
- Brunella Gerla, Ciro Russo, and Luca Spada. Representation of Perfect and Local MV-algebras, Mathematica Slovaca 61(3):327–340, 2011. (Available on ArXiv),
- 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)
- 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)
- Antonio Di Nola, George Georgescu, and Luca Spada. Forcing in Łukasiewicz predicate logic. Studia Logica 89(1):111-145, 2008. (Preprint page)
- Luca Spada. ŁΠ logic with fixed points. Archive for Mathematical Logic, 47(7-8):741-763, 2008. (Preprint page)
- 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)
- 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
- 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)
- 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)
- 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
- 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.
- 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
- Luca Spada. Geometrical dualities for Łukasiewicz logic. Bollettino dell’UMI, VI(9):749-763 2013.
- 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.
Presentations
Invited conferences
- Geometric aspects of MV-algebras . Topology, Algebra and Categories in Logic (TACL). Prague, Czech Republic. 26-30 June 2017. [Slides]
- A categorical duality for residuated lattices. Soft Computing Days. Beijing, China. 27-29 November 2016.
- A duality for lattices with residuated operations. Topological Methods in Logic (ToLo) V. Tbilisi, Georgia, June 2016.
- An extension of Basic Logic with fixed points, Coherence and Truth. In memoriam Franco Montagna. Certosa di Pontignano (Siena), Italy. December 2015.
- A(nother) duality for the whole variety of MV-algebras. BEYOND 2014, Florence, Italy. 3-5 December 2014.
- The multifarious representations of MV-algebras, Logic, Algebra and Truth Degrees 2012. Kanazawa, Japan. 14th September, 2012 [Slides page]
- Dualities for MV-algebras, Ordered Groups and Lattices in Algebraic Logic – a conference in memoriam Leo Esakia. Tbilisi, Georgia. 22d September, 2011 [Slides page]
- 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]
- Projectivity and unification in many valued logic, CSL 2010: Workshop on Mathematical Foundations of Fuzzy Logics. Brno 21st-29th August 2010. [Slides page]
- The prime spectrum of MV-algebras, Topological Methods is Logic II. Tbilisi, 8th–10th June 2010 [Slides page]
- Fixed points in many-valued logic, Logic, Algebra and Foundamentals of Computer Science. Bucharest 16 May 2008. [Slides page]
- Fuzzy logic and algebra, 2d MATHLOGAP workshop. Leeds 21-25 August 2006. [Slides page]
Invited seminars
- A general framework for dualities. Mathematical Institute. Oxford University, 6th November 2014, UK. [Sorry, no slides: blackboard presentation.]
- General affine adjunctions, Nullstellensätze, and dualities. Applied Logic Seminars. Delft, The Netherlands. 7th May 2014. [Slides page]
- Axiomatisations for all varieties of n-potent residuated lattices. Prague seminar on substructural logics. 28th-29th March 2014 Prague, Czech Republic. [Sorry, no slides: blackboard presentation.]
- General affine adjunctions, Nullstellensätze, and dualities, Colloquium on Mathematical Logic. Amsterdam, The Netherlands. 16th October 2013. [Sorry, no slides: blackboard presentation.]
- Two isomorphism criteria for directed colimits. Algebra|Coalgebra Seminar, 9th October 2013, Amsterdam, The Netherlands. [Sorry, no slides: blackboard presentation.]
- 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]
- Free MV algebras as direct limit, Slovak Academy of Sciences. Bratislava 25th September 2008. [Slides page]
- Fixed points in many-valued logic, University of Tbilisi, 2d June 2008. [Slides page]
- Logique Multi-Valeur: une introduction, Institute Camille Jordan, University of Lyon I, 22d September 2005. English and French [Slides page]
Invited courses
- Algebra della Logica. Scuola Estiva di Logica. 20 – 26 August 2017. Palazzo Feltrinelli, Gargano, Italy.
- Dualities. 16th Latin American Symposium on Mathematical Logic. 28th July – 1Sst August 2014. Buenos Aires, Argentina.[Slides page]
- Łukasiewicz logic and MV algebras, Philosophy and Mathematics of Uncertainty and Vagueness, 6th-15th August 2012, Campinas (SP), Brazil. [Slides page]
- 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]
- Introduction to Fuzzy Sets and Fuzzy Logic, REASONPARK. Foligno, 17th-19th September 2009. [Slides page]
Contributed presentations
- Denominator respecting maps. XXVI Incontro AILA. Padova, Italia, 25-28 September 2017. [Slides]
- Łukasiewicz logic, with coefficients. Logic Colloquium 2017. Stockholm, Sweden, 14-20 August 2017. [Slides]
- The Nullstellensatz for varieties, and topological dualities. XX Congresso dell’unione Matematica Italiana. Siena, Italy. 7th-12th September 2015. [Slides page]
- Canonical formulas for k-potent residuated lattices. IV Logic, Algebra and Truth Degrees 2014 (LATD 2014). Vienna, Austria. 16th-19th July 2014. [Slides page]
- Dualities and Geometry. XXV incontro dell’Associazione Italiana di Logica e sue Applicazioni. 14th-17th April 2014, Pisa, Italy. [Slides page]
- A general framework for dualities. Workshops on Duality and Probabilistic Systems, 14th – 21st March 2014. Bellairs, Barbados. [Sorry, no slides: (open air!) blackboard presentation]
- Canonical Formulas and Residuated Lattices. Shanks Workshop on Ordered Algebras and Logic 22th-23th February 2014, Nashville, US. [Sorry, no slides: blackboard presentation.]
- An Isomorphism Criterion for Colimits of Sequences of Finitely Presented Objects, International Workshop on Algebraic Logic in Computer Science (a satellite workshop of LPAR). 14th-19th December 2013, Stellenbosch, South Africa. [Slides page]
- A general framework for geometric dualities for varieties of algebras, TACL VI, 28th July-1st August 2013, Nashville, US. [Sorry, no slides: blackboard presentation.]
- 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]
- The unification type of Łukasiewicz logic is nullary, (featured presentation) TACL V, Marseille, 25th-30th July 2011. [Slides page]
- 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]
- A uniform version on Di Nola Theorem, Probability, Uncertainty and Rationality, Certosa di Pontignano, Siena 1-3 November 2009. [Slides page]
- 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]
- Some consequences of compactness in Łukasiewicz Predicate Logic, VII Panhellenic Logic Symposium, Patras 15-19 July 2009. [Slides page]
- Small advances in the algebraic proof theory of substructural logics, TACL IV. Amsterdam 7-11 July 2009. [Slides page]
- μŁΠ-algebre libere, XVIII Congresso UMI. Bari 24-29 September 2007. [Slides page]
- Freedom in μŁΠ algebras, TA(N)CL III, Oxford, 6-9 August 2007. [Slides page]
- Finite and infinite forcing in Łukasiewicz logic, 3d MATHLOGAP workshop. Aussois 24-30 June 2007. [Slides page]
- μMV algebras: an approach to fixed points in Łukasiewicz logic, The Logic of Soft Computing. Malaga, 13-15 September 2006. [Slides page]
- ŁΠ logic with fixed points operator, TA(N)CL II. Barcelona 15-18 June 2005. [Slides page]
- ŁΠq algebras and quasifields, Kurt Goedel Colloquium. Vienna 25-30 August 2003. [Slides page]