Dear Cheerful Logicians and Friends of Logic, Some announcements before we get to the talks for the week:
1. The supergroup finally has its own official website! Woohoo! Here's a link <https://sites.google.com/view/logicsupergroup/the-logic-supergroup>. You can find the calendar of talks, the calendar of member group talks, and the Black Lives Matter statement there. In time, we will add more exciting content. Thanks to Damian Szmuc for getting this up and running! 2. Universität Regensburg is hosting a virtual workshop on August 27 and 28 that will be of interest to some of our members. The (quite provocative) title is *"If ifs and ands were pots and pans ..." Qualitative and quantitative approaches to reasoning and conditionals. *For more information visit this link <https://www.uni-regensburg.de/philosophie-kunst-geschichte-gesellschaft/theoretische-philosophie/workshops/2020/index.html> . Ok, now to talks. There are two, both on Thursday. First, at 16:00 GMT-3, Carlos Areces (UNC & CONICET) will talk about Henkin Completeness in Modal Logic with an application to semi-structured databases. Then, at 20:00 GMT-5, Guillermo Badia (UQ) will talk about wew proofs with old methods in inconsistent metamathematics. More details, including links to the talks, can be found below. Supergroup Talk: Speaker: Guillermo Badia Title: New proofs with old methods in inconsistent metamathematics: completeness, Löwenheim-Skolem and compactness theorems Time and Date: Thursday August 6th, 20:00 GMT-5 Link: <https://ksu.zoom.us/j/7613620942> https://unimelb.zoom.us/j/846890369?pwd=TktZYmlIUGlYOU9ZaXFJcCt0TFJFZz09 Abstract: In the meta-theory of classical first order logic, the Completeness, Löwenheim-Skolem and Compactness theorems stand out as the "Big Three" among the results of the subject. The best known proofs of these facts are due to Henkin and, although very transparent, they require a fair bit of classicality for their reasoning to go through. To circumvent this problem in the context of an inconsistent meta-theory it makes sense to look for alternative approaches. In this talk, we take a "low-tech" argument originally due to Löwenheim (but later perfected by Gödel in his PhD thesis) and reconstruct it in the context of a substructural meta-theory with the naive comprehension schema. In particular, we establish by non-classical means the Big Three in their original formulation involving material implication. Our object logic will be a non-contractive variant of the quantificational logic of paradox (LPQ) with the Church constant (falsum). This is joint work with Zach Weber and Patrick Girard. Talks by Member Groups: *Lógicos em Quarentena* Speaker: Carlos Areces (UNC & CONICET) Title: Henkin Completeness in Modal Logic (with an application to semi-structured databases) Time and Date: Thursday, August 6 16:00 GMT-3 Link: https://meet.google.com/eoq-uibs-atw Abstract: Saul Kripke published in 1959 a proof of completeness for first-order S5 modal logic [7] and in 1963 he extended the method to cover the propositional modal systems T, S4, S5, and B [8]. His method employed a generalization of Beth’s tableaux and completeness was established by showing how to derive a proof from a failed attempt to find a counter model. In 1966, Kaplan criticized Kripke’s proof in his review of Kripke’s article [6] and suggested a different and, arguably, more elegant approach based on an adaptation of Henkin’s model theoretic completeness proof for first-order logic [5]. (Actually, completeness proof for S5 following Henkin’s ideas had already been published in 1959 in an article by Bayart [2], and other proofs were published at about the same time of Kaplan’s by Makinson in 1966 [9] and Cresswell in 1967 [4].) Henkin’s proof of completeness for first-order logic used to important ideas: 1) that a consistent set of formulas can be extended to a maximally consistent set of formulas, and 2) that existential quantifiers can be witnessed using constants, which can then be used to form the domain of the model. The first of these two ideas is fundamental in modern completeness proofs for classical propositional modal logics which build a canonical model (satisfying all consistent formulas) that has as domain the (uncountable) set of all maximally consistent sets of formulas. The second idea (witnesses) seemed less useful in the propositional setting — till the arrival of hybrid modal logics [1]. One of the main characteristics of hybrid modal logics is the inclusion of nominals which are special propositional symbols that name particular states in the model. This “naming” is achieved by restricting the interpretation of nominals to be singleton sub- sets of the domain. Nominals can be used as witnesses for the modal existential oper- ators and, in this way, the completeness construction needs to build just a single maximal, witnessed consistent set of formulas from which a countable model is built (see, e.g., [3, Chap 7.3] and [10]). As a side-effect a particularly strong completeness result can be proved, that establishes that it is possible to give a complete axiomatic system for the basic hybrid logic, which remains complete under the extension with a particular family of axioms w.r.t. the corresponding class of models. Together with Raul Fervari, we have recently extended these results to provide general strong completeness results for an axiomatization of XPath, a query language for semi-structured databases. Other Notes and Announcements: - *The Logic Supergroup has a YouTube channel!* Recordings of almost all talks are available at https://www.youtube.com/channel/UCqOAS8SHP-5nGjYEE2FE6xw - 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 any of the organizers 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 logica-l+unsubscr...@dimap.ufrn.br. Para ver esta discussão na web, acesse https://groups.google.com/a/dimap.ufrn.br/d/msgid/logica-l/CAMTR992veE%2BCbuK9rtYDp%2BpFa%2BGrFj3%3DZeEko2CpEcryb%2BNz2w%40mail.gmail.com.
