- 09.30 - 10.00: Constantine Tsinakis -
*Join Completions of Ordered Algebras*(abstract) - 10.10 - 10.40: Tomasz Kowalski -
*Admissibility of an Abelian Rule in BCI and Related Logics*(abstract) - 11.00 - 11.30: Laura Schn�riger -
*Bases for Admissible Rules for Fragments of RMt*(abstract) - 11.40 - 12.10: George Metcalfe -
*Admissibility and Exact Unification Types*(abstract) - 12.10 - 14.00: Lunch
- 14.00 - 14.30: Jan K�hr -
*On a representation of residuated structures by certain triples*(abstract) - 14.40 - 15.10: Michal Botur -
*Operators induced by fuzzy relations*(abstract) - 15.30 - 16.00: Michel Marti -
*Hennessy-Milner Properties for Many-Valued Modal Logics*(abstract) - 16.10 - 16.40: Jonas Rogger -
*Tableaux Systems for G�del Modal Logics*(abstract)

Constantine Tsinakis - Join Completions of Ordered AlgebrasA poset Q is said to be an extension of a poset P provided P is a subset of Q and the order of Q restricts to that of P. In case every element of Q is a join (in Q) of elements of P, we say that Q is a join-extension of P and that P is join-dense in Q. We use the term join-completion for a join-extension that is a complete lattice. Given a partially ordered monoid P, the following question arises: Which join-completions of P are residuated lattices with respect to a, necessarily unique, multiplication that extends the multiplication of P? We provide an answer to this question using the concept of a nucleus. As an application, we present a novel approach for constructing the Dedekind-MacNeille completion of algebras in various subvarieties of residuated lattices and involutive residuated lattices, including semi-simple MV-algebras and Archimedean lattice-ordered groups. |

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Tomasz Kowalski - Admissibility of an Abelian rule in BCI and related logics.The Abelian rule of the title is the rule (A -> B) -> B |- A It is called Abelian because is it derivable in Abelian l-groups, and indeed even in Abelian groups, if A -> B is interpreted as -A+B. I will show that the Abelian rule is admissible (but not derivable) in BCI. Somewhat curiously, in a large class of natural extensions of BCI, including BCK, the Abelian rule is admissible only if it is derivable. However, a weaker form of the Abelian rule, namely (((A -> B) -> B) -> A) -> A |- (A -> B) -> B is admissible, but not derivable in BCK. This is also a weaker form of the rule (B -> A) -> A |- (A -> B) -> B, which I used to prove structural incompleteness of BCK. Time permitting, I will discuss some variations of this theme. |

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George Metcalfe - Admissibility and Exact Unification TypesI will present a new hierarchy of "exact" unification types motivated by the study of admissible rules, where one unifier is more general than another if all identities unified by the first are unified by the second. I will also describe a Ghilardi-style algebraic interpretation of this hierarchy that features exact algebras rather than projective algebras. |

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