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 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 Galatos The finite embeddability property for varieties of distributive, integral residuated lattices |
| 11:00-11:15 | Break |
| 11:15-11:45 | Oliver Fasching and Matthias Baaz An analytic calculus for Gödel logics with an operator that shifts truth values |
| 11:45-12:15 | Michał Kozak Strong 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 Suzuki Remarks 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 Ruitenburg Modal Basic Propositional Logic |
| 16:15-16:45 | Marjon Blondeel, Tommaso Flaminio and Lluís Godo Relating fuzzy autoepistemic logic and Łukasiewicz KD45 modal logic PDF |
| 16:45-17:15 | Felix Bou, Francesc Esteva and Lluis Godo On possibilistic modal logics over Gödel logic PDF |
| 17:15-17:45 | Petr Cintula, Rostislav Horcík and Carles Noguera A 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 Spendier Standard completeness for extensions of MTL: an automated approach PDF |
| 10:30-11:00 | Vincenzo Marra and Stefano Aguzzoli Betting 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 Majer Nash Equilibria in a Class of Zero-Sum Games Represented by McNaughton Functions PDF |
| 11:45-12:15 | Christian Fermüller and Christoph Roschger Extending 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 Asmus Towards Many Valued Dependence Logics |
| 15:30-15:45 | Break |
| 15:45-16:15 | Yoshihiro Maruyama Diagonals, Paradoxes, and the Edge of Consistency: classical, quantum, and fuzzy |
| 16:15-16:45 | Petra Murinová Structure of generalized intermediate syllogisms PDF |
| 16:45-17:15 | Shawn Standefer Revision theory and Field's theory of truth |
| 17:15-17:45 | Shunsuke Yatabe A 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 Kühr BCK-algebras and triple construction |
| 10:30-11:00 | Félix Bou, Marco Cerami and Francesc Esteva Concept Satisfiability in finite-valued Fuzzy Description Logics is PSPACE-complete PDF |
| 11:00-11:15 | Break |
| 11:15-11:45 | Libor Behounek Feasibility of program runs in fuzzified Propositional Dynamic Logic PDF |
| 11:45-12:15 | Liu Doing Ning and Zhe Lin Proof 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 Marchioni Finite Forests. Their Algebras and Logics PDF |
| 11:00-11:15 | Break |
| 11:15-11:45 | Jan Paseka and Michal Botur Tense MV-algebras and related operators |
| 11:45-12:15 | Antonio Ledda, Tomasz Kowalski and Francesco Paoli On independent varieties and some related notions PDF |
| 12:15-14:00 | Lunch Break |
| 14:00-14:30 | Sándor Jenei Recent results on involute FLe-monoids PDF |
| 14:30-15:00 | Matthias Baaz and Agata Ciabattoni Proof theory for non-classical logics: negative results |
| 15:00-15:30 | James Raftery Inconsistency lemmas in algebraic logic |
| 15:30-15:45 | Break |
| 15:45-16:15 | Milan Petrík Algebraic webs on more general structures PDF |
| 16:15-16:45 | William Young Free MV-algebras inside Free Abelian l-groups PDF |
| 16:45-17:15 | Hitoshi Omori and Katsuhiko Sano Generalizing 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 Ceterchi The Decomposition of Linearly Ordered Pseudo-Hoops PDF |
| 10:30-11:00 | Umberto Rivieccio Implicative twist-structures PDF |
| 11:00-11:15 | Break |
| 11:15-11:45 | Takahiro Seki Disjunction Property of Non-Associative Substructural Logics PDF |
| 11:45-12:15 | Yuri Movsisyan and Diana Davidova Representation theorem for interlaced q-bilattices PDF |
| 12:15-14:00 | Lunch Break |
| 14:00-14:30 | Thomas Vetterlein Construction methods for finite commutative tomonoids PDF |
| 14:30-15:00 | Tomasz Kowalski BCK 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 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.
- 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
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.
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
- Greg Restall (University of Melbourne, Australia)
