Prof. Dr. George Metcalfe Managing Director of the Institute / Member of Institute Management Mathematisches Institut (MAI) Telefon +41 31 684 88 23 E-Mail george.metcalfe@unibe.ch Büro 221b Postadresse Universität Bern Mathematisches Institut (MAI) Sidlerstrasse 5 3012 Bern Schweiz
Publications Books Residuated Structures in Algebra and Logic (with F. Paoli and C. Tsinakis). AMS Mathematical Surveys and Monographs Volume 277 (2023), 265 pages. Proof Theory for Fuzzy Logics (with N. Olivetti and D. Gabbay). Springer Series in Applied Logic Volume 36 (2008), 284 pages. Journal Articles One-Variable Fragments of First-Order Logics (with P. Cintula and N. Tokuda). Bulletin of Symbolic Logic (2024), to appear. Deciding Equations in the Time Warp Algebra (with S. van Gool, A. Guatto, and S. Santschi). Log. Methods Comput. Sci. 20(2) (2024), 22 pages. Transfer Theorems for Finitely Subdirectly Irreducible Algebras (with W. Fussner). J. Algebra 640 (2024), 1-20. Model Completions for Universal Classes: Necessary and Sufficient Conditions (with L. Reggio). J. Symbolic Logic 88(1) (2023), 381-417. One-Variable Fragments of Intermediate logics over Linear Frames (with X. Caicedo, R. Rodriguez, and Ol Tuyt). Inform. and Comput. 287 (2022), 20 pages. From Distributive L-Monoids to L-Groups, and Back Again (with A. Colacito, N. Galatos, and S. Santschi). J. Algebra 601 (2022), 129-148. Integrally Closed Residuated Lattices (with J. Gil-Férez and F. Lauridsen). Studia Logica 108 (2020), 1063-1086. Structure Theorems for Idempotent Residuated Lattices (with J. Gil-Férez and P. Jipsen). Algebra Universalis 81(2) (2020), 25 pages. Ordering Free Groups and Validity in Lattice-Ordered Groups (with A. Colacito). J. Pure Appl. Algebra 223(12) (2019), 5163-5175. Skolemization and Herband Theorems in Lattice-Valued Logics (with P. Cintula and D. Diaconescu). Theoret. Comp. Sci. 768 (2019), 54-75. Uniform Interpolation and Coherence (with T. Kowalski ). Ann. Pure Appl. Logic 170(7) (2019), 825-841. Checking Admissibility using Natural Dualities (with L. Cabrer, B. Freisberg, and H. Priestley). ACM Trans. Comput. Log. 20(1) (2019), 1-19. A Real-Valued Modal Logic (with D. Diaconescu and L. Schnüriger). Log. Methods Comput. Sci. 14(1) (2018), 27 pages. Expressivity of Chain-Based Modal Logics (with M. Marti). Arch. Math. Logic 57(3-4) (2018), 361-380. Uniform Interpolation and Compact Congruences (with S. van Gool and C. Tsinakis). Ann. Pure Appl. Logic 168 (2017), 1927-1948. Decidability in Order-Based Modal Logics (with X. Caicedo, R. Rodriguez, and J. Rogger). J. Comput. Syst. Sci 88 (2017), 53-74. Density Revisited (with C. Tsinakis). Soft Computing 21(1) (2017), 175-189. An Avron Rule for Fragments of R-Mingle. J. Logic Comput. 26(1) (2016), 381-393. Proof Theory for Lattice-Ordered Groups (with N. Galatos). Ann. Pure Appl. Logic 167 (2016), 707-724. Admissibility via Natural Dualities (with L. Cabrer). J. Pure Appl. Algebra 219(9) (2015), 4229-4253. Exact Unification and Admissibility (with L. Cabrer). Log. Methods Comput. Sci 11(3) (2015), 15 pages. Amalgamation and Interpolation in Ordered Algebras (with F. Montagna and C. Tsinakis). J. Algebra 402 (2014), 21-82. Admissibility in Finitely Generated Quasivarieties (with C. Röthlisberger). Log. Methods Comput. Sci. 9(2) (2013), 19 pages. Craig Interpolation for Substructural Semilinear Logics (with E. Marchioni). MLQ Math. Log. Q. 58(6) (2012), 468-481. Admissibility in De Morgan Algebras (with C. Röthlisberger). Soft Computing 16(11) (2012), 1875-1882. Towards a Proof Theory of Gödel Modal Logics (with N. Olivetti). Log. Methods Comput. Sci.7(2) (2011), 27 pages. Admissible Rules in the Implication-Negation Fragment of Intuitionistic Logic (with P. Cintula). Ann. Pure Appl. Logic 162(10) (2010), 162-171. Herbrand's Theorem, Skolemization, and Proof Systems for First-Order Lukasiewicz Logic (with M. Baaz). J. Logic Comput. 20(1) (2010), 35-54. Algebraic and Proof-theoretic Characterizations of Truth Stressers for MTL and its Extensions (with A. Ciabattoni and F. Montagna). Fuzzy Set. Syst. 161(3) (2010), 369-389. A Sequent Calculus for Constructive logic with Strong Negation as a Substructural Logic. Bull. Sect. Log., 38(1) (2009), 1-7. Giles's Game and Proof Theory for Lukasiewicz Logic (with C. G. Fermuller). Studia Logica, 92(1) (2009), 27-61. Structural Completeness for Fuzzy Logics (with P. Cintula). Notre Dame J. Formal Logic 50(2) (2009), 153-183. Proof Theory for Admissible Rules (with R. Iemhoff). Ann. Pure Appl. Logic 159(1-2) (2009), 171-186. Density Elimination (with A. Ciabattoni). Theoret. Comp. Sci. 403 (2008), 328-346. Substructural Fuzzy Logics (with F. Montagna). J. Symbolic Logic 72(3) (2007), 834-864. Fuzzy Logics Based on [0,1)-Continuous Uninorms (with D. Gabbay). Arch. Math. Logic 46(6) (2007), 425-469. Normal Forms for Fuzzy Logics: a Proof-Theoretic Approach (with P. Cintula). Arch. Math. Logic 46(5) (2007), 347-363. Proof Calculi for Casari's Comparative Logics. J. Logic Comput. 16(4) (2006), 405-422. Sequent and Hypersequent Calculi for Abelian and Lukasiewicz logics (with N. Olivetti and D. Gabbay). ACM Trans. Comput. Log. 6(3) (2005), 578-613. Lukasiewicz Logic: From Proof Systems to Logic Programming (with N. Olivetti and D. Gabbay). Log. J. IGPL 13 (2005), 561-585. Hypersequents and Fuzzy Logic (with N. Olivetti and D. Gabbay). Rev. R. Acad. Cienc. Exactas 98(1) (2004), 113-126. Analytic Proof Calculi for Product Logics (with N. Olivetti and D. Gabbay). Arch. Math. Logic 43(7) (2004), 859-889. Book Chapters Deciding Dependence in Logic and Algebra (with N. Tokuda). Dick de Jongh on Intuitionistic and Provability Logics, Outstanding Contributions to Logic 28, Springer (2024), 155-173. Theorems of Alternatives for Substructural Logics (with A. Colacito and N. Galatos). Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer (2021). Proof Theory of Mathematical Fuzzy Logic. Studies in Logic Vol. 37, College Publications (2011), 209-282. Ordered Algebras and Logic (with F. Paoli and C. Tsinakis). In Probability, Uncertainty and Rationality. CRM Series Vol. 10, Edizioni della Scuola Normale Superiore, Pisa (2010), 3-83. Goal-Directed Methods for Fuzzy Logics (with N. Olivetti). We Will Show Them! (2): Festschrift in honour of Dov Gabbay's 60th birthday. King's College Publications (2005), 307-330. Conference Papers Towards an Algebraic Theory of KD45-Like Logics (with L. van den Berg, M. Busaniche, and M. Marcos). Proc. AiML 2024, College Publications (2024), 171–186. Algebraic Semantics for One-Variable Lattice-Valued Logics (with P. Cintula and N. Tokuda). Proc. AiML 2022, College Publications (2022), 237-257. Time Warps, from Algebra to Algorithms (with S. van Gool, A. Guatto, and S. Santschi). Proc. RAMICS 2021, LNCS 13027, Springer (2021), 309-324. A Monadic Logic of Ordered Abelian Groups (with O. Tuyt). Proc. AiML 2020, College Publications (2020), 441-457. The One-Variable Fragment of Corsi Logic (with X. Caicedo, R. Rodriguez, and O. Tuyt). Proc. WoLLIC 2019, LNCS 11541, Springer (2019), 70-83. Coherence in Modal Logic (with T. Kowalski). Proc. AiML 2018, College Publications (2018), 236-251. Proof Theory and Ordered Groups (with A. Colacito). Proc. WoLLIC 2017, LNCS 10388, Springer (2017), 80-91. Axiomatizing a Real-Valued Modal Logic (with D. Diaconescu and L. Schnüriger). Proc. AiML 2016, College Publications (2016), 236-251. Skolemization for Substructural Logics (with P. Cintula and D. Diaconescu). Proc. LPAR 2015, LNCS 9450, Springer (2015), 1-15. A Hennessy-Milner Property for Many-Valued Modal Logics (with M. Marti). Proc. AiML 2014, College Publications (2014), 407-420. A Finite Model Property for Gödel Modal Logics (with X. Caicedo, R. Rodríguez, and J. Rogger). Proc. WoLLIC 2013, LNCS 8071, Springer (2013), 226–237. Herbrand Theorems for Substructural Logics (with P. Cintula). Proc. LPAR 2013, LNCS 8312, Springer (2013), 584-600. Admissible Rules: From Characterizations to Applications. Proc. WoLLIC 2012, LNCS 7456, Springer (2012), 56-69. Unifiability and Admissibility in Finite Algebras (with C. Röthlisberger). Proc. CiE 2012, LNCS 7318, Springer (2012), 485-495. Interpolation Properties for Uninorm Based Logics (with E. Marchioni). Proc. ISMVL 2010, IEEE Computer Society Press (2010), 205-210. Proof Systems for a Godel Modal Logic (with N. Olivetti). Proc. TABLEAUX 2009, LNAI 5607, Springer (2009), 265-279. Hypersequent Systems for the Admissible Rules of Modal and Intermediate Logics (with R. Iemhoff ). Proc. LFCS 2009, LNCS 5407, Springer (2009), 230-245. Herbrand Theorems and Skolemization for Fuzzy Logics (with M. Baaz). Proc. CiE 2008, LNCS 5028, Springer (2008), 22-31. Density Elimination and Rational Completeness for First Order Logics (with A. Ciabattoni). Proc. LFCS 2007, LNCS 4514, Springer (2007), 132-146. Proof Theory for First Order Lukasiewicz Logic (with M. Baaz). Proc. TABLEAUX 2007, LNAI 4548, Springer (2007), 28-42. Uniform Rules and Dialogue Games for Fuzzy Logics (with A. Ciabattoni and C. G. Fermuller). Proc. LPAR 2004, LNAI 3452, Springer (2005), 496-510. Goal-Directed Methods for Lukasiewicz Logic (with N. Olivetti and D. Gabbay). Proc. CSL 2004, LNCS 3210, Springer (2004), 85-99. Goal-Directed Calculi for Godel-Dummett Logics (with N. Olivetti and D. Gabbay). Proc. CSL 2003, LNCS 2803, Springer (2003), 413-426. Bounded Lukasiewicz Logics (with A. Ciabattoni). Proc. TABLEAUX 2003, LNCS 2796, Springer (2003), 32-47. Analytic Sequent Calculi for Abelian and Lukasiewicz logics (with N. Olivetti and D. Gabbay). Proc. TABLEAUX 2002, LNCS 2381, Springer (2002), 191-205.
Biography Education PhD, Computer Science. King's College London, UK, 2004. MSc, Artificial Intelligence. Edinburgh University, UK, 1998. BA, Mathematics and Philosophy. St. Anne's College, Oxford, UK, 1996. Positions Full Professor. University of Bern, Switzerland, since 2019. Associate Professor. University of Bern, Switzerland, 2013-2019. Assistant Professor (Tenure-Track). University of Bern, Switzerland, 2009-2013. Assistant Professor (NTT). Vanderbilt University, USA, 2006-2009. Marie Curie Fellow. Vienna University of Technology, Austria, 2004-2006.
Research Group Members of the Research Group Name / Titel Jim de Groot Funktion Early Postdoc Mail jim.degroot@unibe.ch Telefon +41 31 684 88 30 Name / Titel Michael Heusser Funktion Hilfsassistent Mail michael.heusser@unibe.ch Telefon +41 31 684 88 27 Name / Titel Isabel Hortelano Martín Funktion Doktorandin Mail isabel.hortelanomartin@unibe.ch Telefon +41 31 684 88 33 Name / Titel Simon Santschi Funktion Doktorand Mail simon.santschi@unibe.ch Telefon +41 31 684 88 30 Name / Titel Niels Vooijs Funktion Doktorand Mail niels.vooijs@unibe.ch Telefon +41 31 684 88 33 Former Members of the Research Group Dr. Line van den Berg (Postdoc) Dr. Leonardo Cabrer (Postdoc) Dr. Almudena Colacito (PhD Student) Dr. Denisa Diaconescu (Postdoc) Dr. José Gil-Férez (Postdoc) Dr. Wesley Fussner (Postdoc) Dr. Sam van Gool (Postdoc) Dr. Luca Reggio (Postdoc) Dr. Jonas Rogger (PhD Student) Dr. Christoph Röthlisberger (PhD Student) Dr. Laura Schnüriger (PhD Student) Dr. Naomi Tokuda (PhD Student) Dr. Olim Tuyt (PhD Student)
Name / Titel Michael Heusser Funktion Hilfsassistent Mail michael.heusser@unibe.ch Telefon +41 31 684 88 27
Name / Titel Isabel Hortelano Martín Funktion Doktorandin Mail isabel.hortelanomartin@unibe.ch Telefon +41 31 684 88 33
Current Lectures Current Lectures Algebra (HS 2024) Seminar on Gödel's Incompleteness Theorems (HS 2024)
