# Program

## Preliminary schedule

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

Monday 10.9. | |

09:00- | Registration |

09:20-09:30 | Opening |

09:30-10:30 | Invited: Daniele MundiciWhen every principal congruence is an intersection of maximal congruences PDFIn 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 PrintPDFThe 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 RestallExotic Sequent Calculi for Truth Degrees PDFIn 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 |

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 HorčíkQuasiequational Theory of Square-increasing Residuated Lattices is Undecidable PDFGiven 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 JeřábekAdmissibility and unification with parameters PDFA 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 SpadaThe multifarious representations of MV-algebrasDuring 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 performance Closing |

## Invited speakers

(click on the title to see the abstract)

- Rostislav Horčík (Academy of Sciences, Czech Republic)

*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.

- Emil Jeřábek (Academy of Sciences, Czech Republic)

*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.

- Daniele Mundici (University of Florence, Italy)

*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. /div>

- Greg Restall (University of Melbourne, Australia)

*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.

- Luca Spada (University of Salerno, Italy)

*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.

## Tutorial speaker

(click on the title to see the abstract)

- Felix Bou (University of Barcelona, Spain)

*(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 - Majid Alizadeh, Mohammad Ardeshir and Wim Ruitenburg
*Modal Basic Propositional Logic* - Conrad Asmus
*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
*Advances on Unification in MV-algebras* - 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