Dear Cheerful Logicians and Friends of Logic, Supergroup announcement time! Brief Summary: On Tuesday, Pilar Terrés will give a talk on different senses of `and'. On Wednesday, Valeria de Paiva will give a talk about Dialectica categories for the Lambek calculus. Details below.
Supergroup Talk: *Speaker: *Valeria de Paiva (Topos Institute) *Title: *Dialectica categories for the Lambek calculus *Time and Date: *Thursday, June 25, 8pm GMT-5 *Link: * https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09. *Abstract: *Dialectica categorical models of the Lambek Calculus were first presented in the Amsterdam Colloquium a long time ago. Following Lambek's lead, we approached the Lambek Calculus from the perspective of Linear Logic and adapted the Dialectica categorical models for Linear Logic to Lambek's non-commutative calculus. The old work took for granted the syntax of the Lambek calculus and only discussed the exciting possibilities of new models for the modalities that Linear Logic introduced. Many years later we find that the work on dialectica models of the Lambek calculus is still interesting and that it might inform some of the most recent work on the relationship between Categorial Grammars and notions of Distributional Semantics. Thus we revisited the old work, making sure that the syntax details that were sketchy on the first version got completed and verified, using automated tools such as Agda and Ott. Ultimately we are interested in the applicability of the original systems to their intended uses in the construction of semantics of Natural Language. But before we can discuss it, we need to make sure that the mathematical properties that make the Lambek calculus attractive are all properly modeled and this is the main aim of this paper. We recall the Lambek calculus with its Curry-Howard isomorphic term assignment system. We extend it with a $\kappa$ modality, inspired by Yetter's work, which makes the calculus commutative. Then we add the of-course modality $!$, as Girard did, re-introducing weakening and contraction for all formulas and get back the full power of intuitionistic and classical logic. We also present algebraic semantics and categorical semantics, proved sound and complete for the whole system. Finally, we show the traditional properties of type systems, like subject reduction, the Church-Rosser theorem and normalization for the calculi of extended modalities, which we did not have before. Talks by Member Groups *SeLoI* *Speaker: *Pilar Terrés (Barcelona) *Title: *The different senses of ‘and’: a pragmatic solution to Free Choice and Preface Paradoxes *Time and Date: *Tuesday June 23, 10am GMT-5 *Link: * https://us02web.zoom.us/j/86305141780?pwd=K0NiWkxRaW5hcnM0MjJvYzg4d3R1QT09 *Abstract: *In this talk, I aim to explore the behaviour of conjunction under the scope of certain modal operator (such as possibility or permission). I argue that in certain modal contexts, classical logic fails to capture the behaviour of “and”, giving rise to certain paradoxes (such as the lottery, the preface and the free choice paradoxes), and that a logic without contraction can better formalize it (following and reinterpreting the work of Paoli, Zardini and Barker). Moreover, I argue that this deviation in the behaviour of conjunction can be explained pragmatically. Other Notes and Announcements: - The Web School on Logic, Language, and Information is happening July 11-19. More information at https://www.brandeis.edu/nasslli2020/. Of particular interest to our members might be the workshop called Natural Logic Meets Machine Learning; more info at https://typo.uni-konstanz.de/naloma20/. - To access the supergroup calendar, please follow this link: https://calendar.google.com/calendar?cid=ZGhoanNoanF1bGhmaG9xam5scDJlc2o0bDhAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ - To access the member groups joint calendar, please follow this link: https://calendar.google.com/calendar?cid=aG8wNWljaGxkNXI2N2oyMnZvY3BzdmRoMWNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ - If you represent a member group and would like your events to appear on the joint calendar, be sure to add them! Contact me if you need permission to do so. Yay for logic! -- Você está recebendo esta mensagem porque se inscreveu no grupo "LOGICA-L" dos Grupos do Google. Para cancelar inscrição nesse grupo e parar de receber e-mails dele, envie um e-mail para [email protected]. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAMTR990eE33FXUTV1vfVVXGxOhnEz-kxjhXAEPnh%2Bfyet%2B5-mw%40mail.gmail.com.
