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# Program

## Preliminary schedule

Invited talks will be 1 hour, contributed talks 30 minutes, both including discussion.

[ Monday | Tuesday | Wednesday | Thursday | Friday | Saturday ]

 Monday 10.9. 09:00- Registration 09:20-09:30 Opening 09:30-10:30 Invited: Daniele Mundici When every principal congruence is an intersection of maximal congruences PDF In their seminal paper recently appeared in the Annals of Pure and Applied Logic, Dubuc and Poveda call an algebra strongly semisimple if it satisfies the condition in the title. For any structure S equipped with a notion of congruence one may ask whether S is strongly semisimple. Dubuc and Poveda were mainly interested in MV-algebras: they observed that strong semisimplicity holds for hyperarchimedean as well as for finitely presented MV-algebras, despite these two classes have so little in common (their intersection is the class of finite MV-algebras). We will discuss further properties of any strongly semisimple n-generator MV-algebra A, with particular reference to the Bouligand-Severi tangent space of the maximal spectral space of A as a closed subset of the unit n-cube. 10:30-11:00 Nikolaos GalatosThe finite embeddability property for varieties of distributive, integral residuated lattices 11:00-11:15 Break 11:15-11:45 Oliver Fasching and Matthias BaazAn analytic calculus for Gödel logics with an operator that shifts truth values 11:45-12:15 Michał KozakStrong Negation in Intuitionistic Style Sequent Systems for Residuated Lattices PDF 12:15-14:00 Lunch Break 14:00-15:00 Tutorial: Felix Bou (Un)Decidability in Monadic Fuzzy Predicate Logics ScreenPDF PrintPDF The decidability of the monadic fragment of (standard) Lukasiewicz predicate logic has been a long-open problem in the realm of mathematical fuzzy logic. Recently, this problem has been settled in a negative way. The aim of this tutorial is explaining how the classical computability notion of "finite inseparable first-order theory" (closely related to hereditary undecidability) can be used to prove this undecidability result. Indeed, the methodology of this new undecidability proof is general enough to deal with most monadic fuzzy predicate logics (BL, Gödel, etc.), and it is able to cope both with standard and general semantics. This new methodology will also be used to write down explicit monadic formulas which are standard Lukasiewicz tautologies but not general tautologies. 15:00-15:30 Nobu-Yuki SuzukiRemarks on Ono's Two Problems: Existence and Disjunction Properties in Super-Intuitionistic Predicate Logics 15:30-15:45 Break 15:45-16:15 Majid Alizadeh, Mohammad Ardeshir and Wim RuitenburgModal Basic Propositional Logic 16:15-16:45 Marjon Blondeel, Tommaso Flaminio and Lluís GodoRelating fuzzy autoepistemic logic and Łukasiewicz KD45 modal logic PDF 16:45-17:15 Felix Bou, Francesc Esteva and Lluis GodoOn possibilistic modal logics over Gödel logic PDF 17:15-17:45 Petr Cintula, Rostislav Horcík and Carles NogueraA basic fuzzy logic which is really basic and fuzzy PDF 18:30-20:30 Opening Reception Tuesday 11.9. 09:00-10:00 Invited: Greg Restall Exotic Sequent Calculi for Truth Degrees PDF In this talk I'll explain how novel “sequent calculi” can be motivated for a wide range of logics of truth degrees, such as Łukasiewicz’s infinitely valued logic. 10:00-10:30 Paolo Baldi, Agata Ciabattoni and Lara SpendierStandard completeness for extensions of MTL: an automated approach PDF 10:30-11:00 Vincenzo Marra and Stefano AguzzoliBetting on events observed over an interval of time: de Finetti's Dutch-Book argument for Gödel logic PDF 11:00-11:15 Break 11:15-11:45 Tomas Kroupa and Ondrej MajerNash Equilibria in a Class of Zero-Sum Games Represented by McNaughton Functions PDF 11:45-12:15 Christian Fermüller and Christoph RoschgerExtending Giles's Game for Lukasiewicz Logic to Fuzzy Quantification PDF 12:15-14:00 Lunch Break 14:00-15:00 Tutorial: Felix Bou (Un)Decidability in Monadic Fuzzy Predicate Logics ScreenPDF PrintPDF The decidability of the monadic fragment of (standard) Lukasiewicz predicate logic has been a long-open problem in the realm of mathematical fuzzy logic. Recently, this problem has been settled in a negative way. The aim of this tutorial is explaining how the classical computability notion of "finite inseparable first-order theory" (closely related to hereditary undecidability) can be used to prove this undecidability result. Indeed, the methodology of this new undecidability proof is general enough to deal with most monadic fuzzy predicate logics (BL, Gödel, etc.), and it is able to cope both with standard and general semantics. This new methodology will also be used to write down explicit monadic formulas which are standard Lukasiewicz tautologies but not general tautologies. 15:00-15:30 Conrad AsmusTowards Many Valued Dependence Logics 15:30-15:45 Break 15:45-16:15 Yoshihiro MaruyamaDiagonals, Paradoxes, and the Edge of Consistency: classical, quantum, and fuzzy 16:15-16:45 Petra MurinováStructure of generalized intermediate syllogisms PDF 16:45-17:15 Shawn StandeferRevision theory and Field's theory of truth 17:15-17:45 Shunsuke YatabeA constructive naive set theory and the $\omega$-rule PDF Wednesday 12.9. 09:00-10:00 Invited: Rostislav Horčík Quasiequational Theory of Square-increasing Residuated Lattices is Undecidable PDF Given an algebraizable logic represented by a consequence relation, there are two natural decision problems. The first one is the set of its theorems. The second problem is the provability of a given formula from a given finite theory. Having an equivalent algebraic semantics for the logic, the first problem is equivalent to decidability of its equational theory and the second one to decidability of its quasiequational theory. Among the basic substructural logics (i.e., logics obtained from Full Lambek Calculus FL by adding any combination of structural rules of exchange, contraction and weakening), the only logic where the above-mentioned problems are not solved, is FL together with contraction. Its equivalent algebraic semantics is the variety of square-increasing residuated lattices. The aim of this talk is to show how to prove that the quasiequational theory of square-increasing residuated lattices is undecidable. To this end we employ two techniques. The first one shows how to encode a string rewriting system preserving square-free words into our logic. The preservation of square-free words here is necessary in order to deal with contraction. The proof that this encoding is faithful is based on the construction of a suitable residuated frame in the sense of Galatos-Jipsen and was inspired by Lafont's idea. The second technique shows how to encode a Minsky (2-counter) machine into a string rewriting system preserving square-free words. This is based on the generation of an arbitrarily long square-free word using a square-free morphism. The idea comes from semigroup theory. 10:00-10:30 Jan KührBCK-algebras and triple construction 10:30-11:00 Félix Bou, Marco Cerami and Francesc EstevaConcept Satisfiability in finite-valued Fuzzy Description Logics is PSPACE-complete PDF 11:00-11:15 Break 11:15-11:45 Libor BehounekFeasibility of program runs in fuzzified Propositional Dynamic Logic PDF 11:45-12:15 Liu Doing Ning and Zhe LinProof Theoretical Investigations on Substructure Modal Logic PDF 12:15-14:00 Lunch Break 14:00- Excursion 19:00-21:00 Conference Dinner Thursday 13.9. 09:30-10:30 Invited: Emil Jeřábek Admissibility and unification with parameters PDF A unifier of a propositional formula with designated parameter variables is a substitution which leaves the parameters unchanged; a rule with parameters is admissible if every unifier of its assumptions unifies its conclusion. In this talk, we will discuss various aspects of unification and admissibility with parameters in nonclassical logics, such as their computational complexity and bases of admissible rules. 10:30-11:00 Stefano Aguzzoli, Tommaso Flaminio and Enrico MarchioniFinite Forests. Their Algebras and Logics PDF 11:00-11:15 Break 11:15-11:45 Jan Paseka and Michal BoturTense MV-algebras and related operators 11:45-12:15 Antonio Ledda, Tomasz Kowalski and Francesco PaoliOn independent varieties and some related notions PDF 12:15-14:00 Lunch Break 14:00-14:30 Sándor JeneiRecent results on involute FLe-monoids PDF 14:30-15:00 Matthias Baaz and Agata CiabattoniProof theory for non-classical logics: negative results 15:00-15:30 James RafteryInconsistency lemmas in algebraic logic 15:30-15:45 Break 15:45-16:15 Milan PetríkAlgebraic webs on more general structures PDF 16:15-16:45 William YoungFree MV-algebras inside Free Abelian l-groups PDF 16:45-17:15 Hitoshi Omori and Katsuhiko SanoGeneralizing Functional Completeness in Belnap-Dunn's Four Valued System PDF 17:15-18:00 Meeting of the Mathematical Fuzzy Logic Group, Steering Committee for LATD Friday 14.9. 09:00-10:00 Invited: Luca Spada The multifarious representations of MV-algebras During the ample fifty years since their inception by Chang, the studies on MV-algebras have unvailed a remarkable number of strong connections (categorical equivalences, in fact) with other more classical mathematical structures. Often to establish these correspondences some restriction on the MV-algebras involved must be required. This is the case, for instance, for Abelian lattice-ordered groups, that are categorical equivalent to perfect MV-algebras, or for rational polyhedra, where only finitely presented MV-algebras have to be considered in order to obtain an equivalence. Notwithstanding the importance of such equivalences, it is often the case that a deeper comprehension of algebras is unlocked by concrete representations generally holding for the full class of structures. Also in this case, results abound in the theory of MV-algebras, for the most part relaying on sheaves. The time-honoured Keimel's representation for lattice-ordered Abelian groups can be converted in the language of MV-algebras, Boolean representations have also been studied quite intensively by Cignoli et al.. Nevertheless in the last years new and quite powerful representation theorems (categorical dualities, in fact) have been discovered. Among the others two stand out for their strong geometrical character. The first is Filipiou and Goergescu's result, affording a representation of any MV-algebra as algebras of global sections of sheaves of local MV-algebras on a compact Hausdorff space; the second is Dubuc and Poveda's result that affords a representation of the full class of MV-algebras as algebras of global sections of particular sheaves of linearly ordered MV-algebras over some special spectral space. Both representations have pro et contra. Filipoiu and Georgescu's representation has the advantage of being defined on a perfectly known base space: any compact Hausdorff space would suit. On the other hand local MV-algebras seem not enough simple to ensure a decomposition down to the basic brics. Dubuc and Poveda's representation has the advantage of involving simpler structures such as linearly ordered ones, but it is more of an adjunction rather then an equivalence. Indeed the base spaces are not characterised, being strongly related to MV-spaces, whose characterisation is quite wriggling. As a matter of fact, even if granting a topological characterisation of the base space, it is still not clear which properties a sheaf must enjoy to be a fixed point of the adjunction. During the talk I will offer a bird-eye view on the numerous representations of MV-algebras, trying to, sometimes formally and sometimes intuitively, link one with the other. 10:00-10:30 Rodica CeterchiThe Decomposition of Linearly Ordered Pseudo-Hoops PDF 10:30-11:00 Umberto RivieccioImplicative twist-structures PDF 11:00-11:15 Break 11:15-11:45 Takahiro SekiDisjunction Property of Non-Associative Substructural Logics PDF 11:45-12:15 Yuri Movsisyan and Diana DavidovaRepresentation theorem for interlaced q-bilattices PDF 12:15-14:00 Lunch Break 14:00-14:30 Thomas VetterleinConstruction methods for finite commutative tomonoids PDF 14:30-15:00 Tomasz KowalskiBCK is not structurally complete PDF 15:00-16:30 Geisha performanceClosing

## Invited speakers

(click on the title to see the abstract)

• Quasiequational Theory of Square-increasing Residuated Lattices is Undecidable PDF

• Admissibility and unification with parameters PDF

• When every principal congruence is an intersection of maximal congruences PDF

• Exotic Sequent Calculi for Truth Degrees PDF

• The multifarious representations of MV-algebras

## Tutorial speaker

(click on the title to see the abstract)

• (Un)Decidability in Monadic Fuzzy Predicate Logics ScreenPDF PrintPDF

## Contributed talks

• Stefano Aguzzoli, Tommaso Flaminio and Enrico Marchioni
Finite Forests. Their Algebras and Logics PDF
Modal Basic Propositional Logic
Towards Many Valued Dependence Logics
• Matthias Baaz and Agata Ciabattoni
Proof theory for non-classical logics: negative results
• Paolo Baldi, Agata Ciabattoni and Lara Spendier
Standard completeness for extensions of MTL: an automated approach PDF
• Libor Behounek
Feasibility of program runs in fuzzified Propositional Dynamic Logic PDF
• Marjon Blondeel, Tommaso Flaminio and Lluís Godo
Relating fuzzy autoepistemic logic and Łukasiewicz KD45 modal logic PDF
• Felix Bou, Francesc Esteva and Lluis Godo
On possibilistic modal logics over Gödel logic
• Félix Bou, Marco Cerami and Francesc Esteva
Concept Satisfiability in finite-valued Fuzzy Description Logics is PSPACE-complete
• Rodica Ceterchi
The Decomposition of Linearly Ordered Pseudo-Hoops PDF
• Petr Cintula, Rostislav Horcík and Carles Noguera
A basic fuzzy logic which is really basic and fuzzy PDF
• Oliver Fasching and Matthias Baaz
An analytic calculus for Gödel logics with an operator that shifts truth values
• Christian Fermüller and Christoph Roschger
Extending Giles's Game for Lukasiewicz Logic to Fuzzy Quantification PDF
• Nikolaos Galatos
The finite embeddability property for varieties of distributive, integral residuated lattices
• Sándor Jenei
Recent results on involute FLe-monoids PDF
• Michiro Kondo
States on bounded commutative residuated lattices
• Tomasz Kowalski
BCK is not structurally complete PDF
• Michał Kozak
Strong Negation in Intuitionistic Style Sequent Systems for Residuated Lattices PDF
• Tomas Kroupa and Ondrej Majer
Nash Equilibria in a Class of Zero-Sum Games Represented by McNaughton Functions PDF
• Jan Kühr
BCK-algebras and triple construction
• Antonio Ledda, Tomasz Kowalski and Francesco Paoli
On independent varieties and some related notions PDF
• Leonardo Manuel Cabrer and Vincenzo Marra
• Vincenzo Marra and Stefano Aguzzoli
Betting on events observed over an interval of time: de Finetti's Dutch-Book argument for Goedel logic PDF
• Yoshihiro Maruyama
Diagonals, Paradoxes, and the Edge of Consistency: classical, quantum, and fuzzy
• Yuri Movsisyan and Diana Davidova
Representation theorem for interlaced q-bilattices PDF
• Petra Murinová
Structure of generalized intermediate syllogisms PDF
• Liu Doing Ning and Zhe Lin
Proof Theoretical Investigations on Substructure Modal Logic PDF
• Hitoshi Omori and Katsuhiko Sano
Generalizing Functional Completeness in Belnap-Dunn's Four Valued System PDF
• Jan Paseka and Michal Botur
Tense MV-algebras and related operators
• Milan Petrík
Algebraic webs on more general structures PDF
• James Raftery
Inconsistency lemmas in algebraic logic
• Umberto Rivieccio
Implicative twist-structures PDF
• Takahiro Seki
Disjunction Property of Non-Associative Substructural Logics PDF
• Shawn Standefer
Revision theory and Field's theory of truth
• Nobu-Yuki Suzuki
Remarks on Ono's Two Problems: Existence and Disjunction Properties in Super-Intuitionistic Predicate Logics
• Thomas Vetterlein
Construction methods for finite commutative tomonoids PDF
• Shunsuke Yatabe
A constructive naive set theory and the $\omega$-rule PDF
• William Young
Free MV-algebras inside Free Abelian l-groups PDF