TACL 2019 --------------- ABSTRACTS TACL 2019 Preface Preface This volume contains the papers presented at TACL 2019: Topology, Algebra, and Categories in Logic held June 17{21, 2019 in Nice. The volume includes the abstracts of 91 accepted contributed talks and of 10 invited talks (a few contributions were rejected after a light refereeing process and a couple of papers were withdrawn by the authors themselves due to the impossibility of their attendance at the con- ference). We thank all Program Committee members for their precious work in reading the submitted abstracts and giving useful suggestions to the authors. TACL 2019 is the ninth conference in the series Topology, Algebra, and Categories in Logic (TACL, formerly TANCL). Earlier instalments of the series have been held in Tbilisi (2003), Barcelona (2015), Oxford (2007), Amsterdam (2009), Marseille (2011), Nashville (2013), Ischia (2015), and Prague (2017). The program of the conference TACL 2019 focuses on three interconnecting mathematical themes central to the semantic study of logic and its applications: topological, algebraic, and categorical methods. Our main sponsors are the European Research Council, the CNRS, and the Universit´eC^ote d'Azur. In particular, the conference has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation program through the DuaLL project (grant agreement No. 670624); from the CNRS, which is supporting the TACL 2019 school as one of its Ecoles´ Th´ematiques;from the Universit´eC^oted'Azur through its Inter- national Conferences program, its International Schools program, through support from the interdisciplinary academies R´eseaux,Information, et Soci´et´eNum´erique and Syst`emesCom- plexes, respectively, and finally through the Laboratoire J. A. Dieudonn´eand the Laboratoire I3S, both of the Universit´eC^oted'Azur. We thank the EasyChair development team for providing their conference management platform. May 6, 2019 Silvio Ghilardi Nice Ramon Jansana Mai Gehrke i TACL 2019 Table of Contents Table of Contents Invited talks Simulations of quantum resources and the degrees of contextuality. 1 Samson Abramsky, Rui Soares Barbosa, Martti Karvonen and Shane Mansfield Generalized continuous closure spaces: a topological approach to domain theory . 3 Marcel Erné Possibility Semantics . 5 Wesley Holliday Non-finitely axiomatisable canonical varieties of BAOs with infinite canonical axiomatisations . 6 Agi Kurucz The poset of all logics . 7 Tommaso Moraschini Some Applications of Stone Duality to Automata Theory . 8 Daniela Petrisan Snapshots of duality theory, from 2019 and fifty years earlier . 9 H. A. Priestley Modal Logics of Dependence . 11 Johan van Benthem Logic, Automata, and Model Companions . 13 Samuel J. van Gool Anabelian geometry in model theory setting. 15 Boris Zilber Contributed talks Norm complete abelian `-groups: topological duality . 17 Marco Abbadini, Vincenzo Marra and Luca Spada Norm complete Abelian `-groups: equational axiomatization. 19 Marco Abbadini, Vincenzo Marra and Luca Spada Polyhedral Completeness of Intermediate and Modal Logics . 21 Sam Adam-Day, Nick Bezhanishvili, David Gabelaia and Vincenzo Marra Product of neighborhood frames with additional common modality.. 23 Rajab Aghamov and Andrey Kudinov Predicative Implications: A Topological Approach . 25 Amirhossein Akbar Tabatabai Ranges of functors and elementary classes via topos theory . 27 Peter Arndt ii TACL 2019 Table of Contents When is the frame of nuclei spatial: A new approach . 29 Francisco Avila, Guram Bezhanishvili, Patrick Morandi and Angel Zaldivar 1 Analysis of the Σ1-Fragment of First Order Gödel Logic extended with Propositional Quantifiers . 31 Matthias Baaz and Norbert Preining Enriched Lawvere Theories for Operational Semantics . 33 John Baez and Christian Williams Enriched distributivity over finite commutative residuated lattices . 35 Adriana Balan, Peter Jipsen and Alexander Kurz Proofs and surfaces . 37 Ðorđe Baralić, Pierre-Louis Curien, Marina Milićević, Jovana Obradović, Zoran Petrić, Mladen Zekić and Rade Živaljević A new logic arising from a scattered Stone space . 39 Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan and Jan van Mill A generalization of Gelfand-Naimark-Stone duality to completely regular spaces . 41 Guram Bezhanishvili, Patrick Morandi and Bruce Olberding The van Benthem characterisation theorem for descriptive models . 43 Nick Bezhanishvili and Tim Henke Nearness Posets . 45 Tristan Bice Towards completeness of logics of information and common belief. 47 Marta Bilkova Counting finite involutive bisemilattices . 49 Stefano Bonzio, Michele Pra Baldi and Diego Valota Difference hierarchies over lattices . 51 Célia Borlido Time-reversal homotopical properties of concurrent systems . 53 Cameron Calk, Eric Goubault and Philippe Malbos A temporal interpretation of intuitionistic quantifiers . 55 Luca Carai and Guram Bezhanishvili Semantic analysis and proof theory for monotone modal logic. 57 Jinsheng Chen, Giuseppe Greco, Alessandra Palmigiano and Apostolos Tzimoulis Completeness properties in abstract algebraic logic . 59 Petr Cintula and Carles Noguera Orders on Groups: an Approach through Spectral Spaces. 61 Almudena Colacito The logic of categories and informational entropy. 63 Willem Conradie, Andrew Craig, Alessandra Palmigiano and Nachoem Wijnberg iii TACL 2019 Table of Contents Goldblatt-Thomason for LE-logics. 65 Willem Conradie, Alessandra Palmigiano and Apostolos Tzimoulis Intuitionistic and classical non-normal modal logics: An embedding. 67 Tiziano Dalmonte, Charles Grellois and Nicola Olivetti Lifting functors from Pos to Pries . 69 Jim de Groot A Sahlqvist theorem for subordination algebras. 71 Laurent De Rudder and Georges Hansoul Extensions of the Stone Duality to the category of zero-dimensional Hausdorff spaces . 73 Georgi Dimov and Elza Ivanova-Dimova Semi-reflective Extensions of Dualities and a New Approach to the Fedorchuk Duality . 74 Georgi Dimov, Elza Ivanova-Dimova and Walter Tholen Extensions of dualities and a new approach to de Vries’ Duality Theorem. 76 Georgi Dimov, Elza Ivanova-Dimova and Walter Tholen Resource Reasoning in Duality-theoretic Form: Stone-type Dualities for Bunched and Separation Logics . 77 Simon Docherty and David Pym Amalgamating poset extensions . 79 Rob Egrot Artin glueings as semidirect products. 81 Peter Faul and Graham Manuell Generic Models for Topological Evidence Logics . 82 Saul Fernandez Gonzalez, Alexandru Baltag and Nick Bezhanishvili On non-distributive lattices with involution . 84 Wesley Fussner Characterization of flat polygonal logics . 86 David Gabelaia, Levan Uridia, Mamuka Jibladze and Evgeny Kuznetsov Undecidabilty methods for residuated lattices . 88 Nikolaos Galatos and Gavin St. John A Glivenko theorem for lattice-ordered groups . 90 José Gil-Férez, Frederik Lauridsen and George Metcalfe Nonclassical first order logics: semantics and proof theory . 92 Giuseppe Greco, Peter Jipsen, Alexander Kurz, M. Andrew Moshier, Alessandra Palmigiano and Apostolos Tzimoulis Algebraic proof theory for LE-logics . 94 Giuseppe Greco, Peter Jipsen, Fei Liang, Alessandra Palmigiano and Apostolos Tzimoulis Proof theory and semantics for structural control . 96 Giuseppe Greco, Apostolos Tzimoulis and Michael Moortgat iv TACL 2019 Table of Contents On the variety of Goedel-MV-algebras. 98 Revaz Grigolia, Antonio Di Nola and Gaetano Vitale Some theorems concerning Grzegorczyk contact lattices . 100 Rafal Gruszczynski and Andrzej Pietruszczak Computing the validity degree in Łukasiewicz logic . 102 Zuzana Hanikova Remarks on the Topos Approach to Quantum Mechanics . 104 John Harding and Chris Heunen Hyper-MacNeille completions of Heyting algebras . 106 John Harding and Frederik Lauridsen Comprehension bicategories and fibrations of toposes . 108 Sina Hazratpour and Steve Vickers Twist products arising from residuated bimodules . 110 Pengfei He, Adam Přenosil and Constantine Tsinakis Relational semantics for extended contact algebras . 112 Tatyana Ivanova Colimits of effect algebras via a reflection . ..