# Publications

### Preprints

- M. Abbadini, V. Marra and —. Stone-Gelfand duality, for groups: Topological duality and equational axiomatisation for metrically complete lattice-groups. In preparation, 2019.
- A. Di Nola, G. Lenzi, and —, Sheaf representations and locality of Riesz spaces with order unit. In preparation, 2019.
- A. Di Nola, G. Lenzi, V. Marra and —, The algebras of piecewise-linear maps. In preparation, 2019.
- Olivia Caramello, Vincenzo Marra, and Luca Spada. General affine adjunctions, Nullstellensätze, and dualities. Preprint available on ArXiv.org.
- José Gil-Férez, Luca Spada, Constantine Tsinakis, and Hongjun Zhou, Join-completions of ordered algebras.
- 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,**3, 321–343**,**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**. Volume 21(1) 29–37. 2017 doi:10.1007/s00500-016-2344-2. (Preprint page)*in memoriam*Franco Montagna - 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

**Kakutani duality, for groups.**Duality in Algebra and Logic. 14 – 17 September 2018.**Kakutani duality for groups.**Topological Methods in Logic (To Lo VI). Tbilisi, Georgia July 2018.**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

**An overview of MV-algebras.**Melbourne University, 19 April 2018. [Sorry, no slides: blackboard presentation.]**General affine adjunctions, Nullstellensätze, and dualities**. La Trobe University, 19th March 2018. [Sorry, no slides: blackboard presentation.]**Canonical formulas for k-potent commutative, integral, residuated lattices**. La Trobe University, 12th March 2018.**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. [See the course webpage]**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

**An algebraic study of Łukasiewicz logic with hedges**. TbiLLC XIII Batumi, 16-20 September 2019.**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.**Norm complete abelian l-groups: topological duality**. TACL IX. Nice, 17 – 21 June 2019.**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]