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08:45 | Relatively filtral quasivarieties SPEAKER: James Raftery ABSTRACT. Improving a recent result of the author, it is shown here that, when a quasivariety K algebraizes a finitary sentential logic L, then L has a classical inconsistency lemma iff K is relatively filtral and its nontrivial members have only nontrivial subalgebras. In the process, the theory of uniform congruence schemes, ideal varieties and filtrality is extended from varieties to quasivarieties, and it is proved that a quasivariety is relatively filtral iff it is relatively semisimple and has equationally definable principal relative congruences. |

09:15 | On logics of varieties and logics of semilattices SPEAKER: Josep Maria Font ABSTRACT. This contribution addresses a general problem of abstract algebraic logic and its instantiation for the variety of semilattices, which is the underlying structure of a host of non-classical logics, in particular fuzzy logics. The general problem is how to associate a logic with a given variety. Since the general theory of abstract algebraic logic provides three procedures to associate a class of algebras with a given logic, our original problem gives rise to three different questions. We show that one of them cannot be answered affirmatively in general, while the other two always can. We determine and study the weakest solution. This leads to a natural definition of the notion of "the logic of a variety". We obtain some results on the poset of all logics of a variety generated by a primal algebra. In the second part we study the poset of the logics of the variety of semilattices, showing that it has a minimum and two maximals and is atomless, among other results. |

09:45 | Congruential deductive systems associated with equationally orderable varieties SPEAKER: Ramon Jansana ABSTRACT. We introduce the notion of the deductive system of the order of an equationally orderable quasivariety and we prove that for equationally orederable varieties this deductive system is congreuntial (fully selfextensional). We compare the result with previous results on deductive systems with the congruece property (selfextensional)and the deduction-detachment property or the property of conjunction. |

08:45 | Semantial and syntactial charaterisation of some extensions of the class of MV-algebras SPEAKER: Krystyna Mruczek-Nasieniewska |

09:15 | The space of directions of a polyhedron SPEAKER: Andrea Pedrini ABSTRACT. We study the Stone-Priestley dual space The main result we announce here is that If time allows, we discuss selected consequences of our main result, including compactness of the subspace of minimal primes of |

09:45 | Interpreting Lukasiewicz logic into Intuitionistic logic SPEAKER: Daniel Mcneill ABSTRACT. Fixing countable sets of propositional variables X and Y, we write Form(X) for the set of formulæ of Łukasiewicz (infinite-valued propositional) logic |

10:45 | The Range of Realization Which modal logics have explicit counter parts SPEAKER: Melvin Fitting |

11:45 | Tutorial: Fuzzy Description Logics (Part 1) SPEAKER: Franz Baader |

14:30 | First-Order Logics and Truth Degrees SPEAKER: George Metcalfe |

15:30 | Classification of germinal MV-algebras SPEAKER: Leonardo Manuel Cabrer ABSTRACT. The aim of this paper is to give a complete classification of germinal MV-algebras. As an application, we will settle the fifth one of the eleven problems present by Mundici in [D. Mundici, Advanced Łukasiewicz calculus and MV-algebras, Trends in Logic, Studia Logica Library. Vol. 35, Springer, Berlin, 2011]. |

16:30 | Cut-free calculus for second-order {G\"odel} logic SPEAKER: unknown ABSTRACT. We prove that the extension of the known hypersequent calculus for standard first-order {G\"odel} logic with usual rules for second-order quantifiers is sound and (cut-free) complete for Henkin-style semantics for second-order {G\"odel} logic. The proof is semantic, and it is similar in nature to {Sch\"utte} and Tait's proof of Takeuti's conjecture. |

17:00 | Poof Search and Co-NP completeness for Many-Valued Logics SPEAKER: unknown ABSTRACT. We provide a methodology to introduce relational hypersequent calculi for a large class of many-valued logics, and a sufficient condition for their Co-NP completeness. Our results include the most important Co-NP fuzzy logics. |

17:30 | Cut and completion? SPEAKER: Sam van Gool ABSTRACT. During the last decade a connection emerged between proof theory and algebra via which cut-elimination, one of the cornerstones of structural proof theory, can be proved by using completions, in particular, the MacNeille completion. This technique, which has been developed for a wide range of logics, including substructural ones, is far from trivial. Our modest aim in this paper is to establish what the technique of completions boils down to for "strong" logics such as full intuitionistic propositional logic, and what the connection is with other semantical proofs of cut-elimination. |

16:30 | Definability of truth predicates in abstract algebraic logic SPEAKER: Tommaso Moraschini ABSTRACT. One of the main topics of Abstract Algebraic Logic is the study of the Leibniz hierarchy, in which logics are classified by means of properties of the Leibniz operator which determine how nicely the Leibniz congruences and the truth predicates can be described in models of the logic. In this talk we will introduce and characterize logics, whose truth predicates are defined by means of equations with parameters. Then we will go through the consideration of weaker conditions on the truth predicates of a logic. This will give rise to a small hierarchy, in which logics are classified according to the way their truth predicates are defined; this new hierarchy can be thought of as an extension of the Leibniz hierarchy, since almost all the conditions we take into account turn out to be characterised by a property of the Leibniz operator. |

17:00 | Generalizing the Leibniz and Suszko operators SPEAKER: Hugo Albuquerque ABSTRACT. In this paper we study the notion of an S-coherent family of S-compatibility operators, for a sentential logic S. This notion is tailored to be a common generalization of the well-known Leibniz and Suszko operators, which have been fundamental tools in recent developments of Abstract Algebraic Logic. The first main result we prove is a General Correspondence Theorem, which generalizes several results of this kind obtained for either the Leibniz operator (Blok and Pigozzi, 1986; Font and Jansana, 2001) or the Suszko operator (Czelakowski, 2003). We apply the general results to obtain several new characterizations of the main classes of logics in the Leibniz hierarchy in terms of the Leibniz operator or in terms of the Suszko operator. |

17:30 | Church-style type theories over finitary weakly implicative logics SPEAKER: Libor Behounek ABSTRACT. In this paper, Church--Henkin simple type theories are constructed for finitary weakly implicative logics. The resulting type theory TT(L) over a given finitary weakly implicative logic L is the minimal (extensional, substitution-invariant) type theory closed under the rules of lambda-conversion and the intersubstitutivity of equals whose propositional fragment coincides with L and whose sound and complete Henkin semantics consists of Henkin-style general models over a generating class of L-algebras. The soundness and completeness theorem for TT(L) is obtained by a schematic adaptation of the proof for the ground theory TT0 which is a common fragment of all TT(L). |