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Prime Numbers and Implication Free Reducts of Mvn-Chains.Pdf SYSMICS2019 Syntax Meets Semantics Amsterdam, The Netherlands 21-25 January 2019 Institute for Logic, Language and Computation University of Amsterdam SYSMICS 2019 The international conference “Syntax meet Semantics 2019” (SYSMICS 2019) will take place from 21 to 25 January 2019 at the University of Amsterdam, The Nether- lands. This is the closing conference of the European Marie Sk lodowska-Curie Rise project Syntax meets Semantics – Methods, Interactions, and Connections in Sub- structural logics, which unites more than twenty universities from Europe, USA, Brazil, Argentina, South Africa, Australia, Japan, and Singapore. Substructural logics are formal reasoning systems that refine classical logic by weakening structural rules in a Gentzen-style sequent calculus. Traditionally, non- classical logics have been investigated using proof-theoretic and algebraic methods. In recent years, combined approaches have started to emerge, thus establishing new links with various branches of non-classical logic. The program of the SYSMICS conference focuses on interactions between syntactic and semantic methods in substructural and other non-classical logics. The scope of the conference includes but is not limited to algebraic, proof-theoretic and relational approaches towards the study of non-classical logics. This booklet consists of the abstracts of SYSMICS 2019 invited lectures and contributed talks. In addition, it also features the abstract of the SYSMICS 2019 Public Lecture, on the interaction of logic and artificial intelligence. We thank all authors, members of the Programme and Organising Committees and reviewers of SYSMICS 2019 for their contribution. Apart from the generous financial support by the SYSMICS project, we would like to acknowledge the sponsorship by the Evert Willem Beth Foundation and the Association for Symbolic Logic. Finally, we are grateful for the support of the Institute for Logic, Language and Computation of the University of Amsterdam, which hosts this event. Nick Bezhanishvili (Organizing Committee Chair) YdeVenema(ProgrammeCommitteeChair) 13December,2019 1 Committees Program Committee StefanoAguzzoli (UniversityofMilan) Nick Bezhanishvili (University of Amsterdam) AgataCiabattoni (ViennaUniversityofTechnology) PetrCintula (CzechAcademyofSciences) PilarDellunde (AutonomousUniversityofBarcelona) BrunellaGerla (UniversityofInsubria) Llu´ısGodo (IIIA -CSIC, Barcelona) RamonJansana (UniversityofBarcelona) Jan K¨uhr (University of Olomouci) AntonioLedda (UniversityofCagliari) GeorgeMetcalfe (UniversityofBern) CarlesNoguera (CzechAcademyofSciences) LucaSpada (UniversityofSalerno) Yde Venema (University of Amsterdam, Chair) Organizing Committee NickBezhanishvili (UniversityofAmsterdam,Chair) AlmudenaColacito (UniversityofBern) GianlucaGrilletti (UniversityofAmsterdam) FrederikM¨ollerstr¨omLauridsen (UniversityofAmsterdam) Peter van Ormondt (University of Amsterdam) Ayb¨uke Ozg¨un¨ (University of Amsterdam) 2 Contents SYSMICS 2019 1 Invited Talks 6 Bahareh Afshari, An infinitary treatment of full mu-calculus ....... 7 Miguel Campercholi, Algebraic Functions .................. 8 Silvio Ghilardi, Free algebras endomorphisms: Ruitenburg’s Theorem and Beyond ................................. 9 Sam van Gool, Pro-aperiodic monoids via Stone duality .......... 10 Wesley Holliday, Inquisitive Intuitionistic Logic: An Application of Nu- clear Semantics ............................. 11 Tom´aˇs Kroupa, Positive Subreducts in Finitely Generated Varieties of MV-algebras ............................... 12 Valeria de Paiva, A Dialectica Model of Relevant Type Theory ...... 15 Amanda Vidal, On the axiomatizability of modal many-valued logics ... 16 Public Lecture 17 Frank van Harmelen, AI? That’s logical! .................. 18 Contributed Talks 19 Matteo Acclavio and Lutz Straßburger, Combinatorial Proofs for the Modal Logic K ............................. 20 Federico Aschieri, Agata Ciabattoni and Francesco A. Genco, Intermedi- ate Logic Proofs as Concurrent Programs ............... 23 Guillermo Badia, Vicent Costa, Pilar Dellunde and Carles Noguera, Preser- vation theorems in graded model theory ................ 26 Zeinab Bakhtiari, Helle Hvid Hansen and Alexander Kurz, A (Co)algebraic Approach to Hennessy-Milner Theorems for Weakly Expressive Logics 30 Alexandru Baltag, Nick Bezhanishvili and Sa´ul Fern´andez Gonz´alez, Multi- Agent Topological Evidence Logics ................... 34 Alexandru Baltag, Nick Bezhanishvili and Sa´ul Fern´andez Gonz´alez, The McKinsey-Tarski Theorem for Topological Evidence Models ..... 38 Guram Bezhanishvili, Nick Bezhanishvili, Joel Lucero-Bryan and Jan van Mill, Trees and Topological Semantics of Modal Logic ........ 42 3 Guram Bezhanishvili and Luca Carai, Characterization of metrizable Esakia spaces via some forbidden configurations ........... 46 Xavier Caicedo, George Metcalfe, Ricardo Rodr´ıguez and Olim Tuyt, The One-Variable Fragment of Corsi Logic ................ 50 Almudena Colacito, Universal Objects for Orders on Groups, and their Dual Spaces ............................... 54 Almudena Colacito, Nikolaos Galatos and George Metcalfe, Theorems of Alternatives: An Application to Densifiability ............ 58 Marcelo E. Coniglio, Aldo Figallo-Orellano and Ana Claudia Golzio, Mul- tialgebraic First-Order Structures for QmbC ............. 62 Marcelo E. Coniglio, Frances¸cEsteva, Tommaso Flaminio and Llu´ıs Godo, Prime numbers and implication free reducts of MVn-chains ..... 66 Antonio Di Nola, Serafina Lapenta and Ioana Leu¸stean, Infinitary con- nectives and Borel functions in Lukasiewicz logic ........... 70 Frank M. V. Feys, Helle Hvid Hansen and Lawrence S. Moss, (Co)Algebraic Techniques for Markov Decision Processes .............. 73 Aldo Figallo-Orellano and Juan Sebasti´an Slagter, An algebraic study of First Order intuitionistic fragment of 3-valued Lukasiewicz logic .. 77 Didier Galmiche, Michel Marti and Daniel M´ery, From Bunches to Labels and Back in BI Logic (extended abstract) ............... 81 Davide Grossi and Simon Rey, Credulous Acceptability, Poison Games and Modal Logic ............................ 84 Rafa l Gruszczy´nski and Andrzej Pietruszczak, Representation theorems for Grzegorczyk contact algebras .................... 88 Willem B. Heijltjes, Dominic J. D. Hughes and Lutz Straßburger, On Intuitionistic Combinatorial Proofs .................. 92 Tomasz Jarmu˙zek and Mateusz Klonowski, From Tableaux to Axiomatic Proofs. A Case of Relating Logic ................... 95 Dick de Jongh and Fatemeh Shirmohammadzadeh Maleki, Below G¨odel- Dummett ................................ 99 Tom´aˇsL´aviˇcka and Adam Pˇrenosil, Syntactical approach to Glivenko-like theorems .................................103 Bj¨ornLellmann, Countermodels for non-normal modal logics via nested sequents .................................107 Benedikt L¨owe, Robert Passmann and Sourav Tarafder, Constructing illoyal algebra-valued models of set theory ...............111 Tommaso Moraschini and Jamie J. Wannenburg, Epimorphisms in vari- eties of Heyting algebras ........................115 Claudia Mure¸san, Roberto Giuntini and Francesco Paoli, Generators and Axiomatizations for Varietes of PBZ*-lattices ............117 Ricardo Rodr´ıguez,Olim Tuyt, Frances¸cEsteva and Llu´ısGodo, Simpli- fied Kripke semantics for a generalized possibilistic G¨odellogic ...121 4 Igor Sedl´ar, Substructural PDL .......................125 Valentin Shekhtman and Dmitry Shkatov, On one-variable fragments of modal predicate logics ..........................129 Ana Sokolova and Harald Woracek, Proper Convex Functors .......133 Amir Akbar Tabatabai and Raheleh Jalali, Semi-analytic Rules and Craig Interpolation ..............................136 Fan Yang, Propositional Union Closed Team Logics: Expressive Power and Axiomatizations ..........................139 Authors Index 143 5 Prime numbers and implication free reducts of MVn-chains Marcelo E. Coniglio1, Francesc Esteva2, Tommaso Flaminio2, and Lluis Godo2 1 Dept. of Philosophy - IFCH and CLE University of Campinas, Campinas, Brazil [email protected] 2 IIIA - CSIC, Bellaterra, Barcelona, Spain esteva,tommaso,godo @iiia.csic.es { } Abstract Let L be the MV-chain on the n +1elementssetL = 0, 1/n, 2/n, . , (n 1)/n, 1 n+1 n+1 { − } in the algebraic language , [3]. As usual, further operations on L n+1 are definable by the following stipulations:{! 1 =¬}x x,0= 1, x y = x y, x y = ( x y), x y = x (x y), x y = ( x! y). Moreover,¬ ⊕ we will¬ pay! special attention ¬ to¬ the⊕ ¬ also ^ ! _ ¬ ¬ ^ ¬ definable unary operator ⇤x = x x. In fact, the aim of this paper is to continue the study initiated in [4] of the ⇤, , - { ¬ _} reducts of the MV-chains L n+1, denoted L n⇤+1. In fact L n⇤+1 is the algebra on L n+1 obtained by replacing the implication operator by the unary operation ⇤ which represents the square ! operator ⇤x = x x and which has been recently used in [5] to provide, among other things, an alternative axiomatization for the four-valued matrix logic J = L , 1/3, 2/3, 1 .Inthis 4 h 4 { }i contribution we make a step further in studying the expressive power of the ⇤ operation, in particular our main result provides a full characterization of those prime numbers n for which the structures L n+1 and L n⇤+1 are term-equivalent. In other words, we characterize for which n the Lukasiewicz implication is definable in L ⇤ , or equivalenty, for which n L ⇤ is in ! n+1 n+1 fact an MV-algebra. We also recall that, in any case, the matrix logics L n⇤+1,F ,whereF is an order filter,
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