9 am cstRe: Nordic Online Logic Seminar: next talk on January 24, by Johan van Benthem

[John Baldwin]

John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
60607


On Thu, Jan 6, 2022 at 3:26 PM Graham Leigh <graham.leigh at gu.se> wrote:

> The Nordic Online Logic Seminar (NOL Seminar) is organised monthly over
> Zoom, with expository talks on topics of interest for the broader logic
> community. The seminar is open for professional or aspiring logicians and
> logic aficionados worldwide.
>
> See the announcement for the next talk below. If you wish to receive the
> Zoom ID and password for it, as well as further announcements, please
> subscribe here: https://listserv.gu.se/sympa/subscribe/nordiclogic
> <https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Flistserv.gu.se%2Fsympa%2Fsubscribe%2Fnordiclogic&data=04%7C01%7Cjbaldwin%40groute.uic.edu%7C5d7b581aee45459e012b08d9d15b1694%7Ce202cd477a564baa99e3e3b71a7c77dd%7C0%7C0%7C637771012163730356%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C2000&sdata=3IwyJZaOGULxUtEHLSkHiuSZIjEtS3bb3xwzlRPeiQw%3D&reserved=0>
>  .
>
> Val Goranko and Graham Leigh
> NOL seminar organisers
>
> --------------------------------------
>  Nordic Online Logic Seminar
>
> Next talk: Monday, January 24, 16.00-17.30 CET (UTC+1), on Zoom (details
> are provided to the seminar subscribers)
>
> Title: *Interleaving Logic and Counting*
>
> Speaker: *Johan van Benthem**, **Professor of Logic* *at the **University*
>  *of **A**msterdam**, Stanford University**, **and Tsinghua University*
>
> Abstract:
> Reasoning with generalized quantifiers in natural language combines
> logical and arithmetical features, transcending divides between
> qualitative
> and quantitative. This practice blends with inference patterns in
> ‘grassroots
> mathematics’ such as pigeon-hole principles. Our topic is this cooperation
> of logic and counting on a par, studied with small systems and gradually
> moving upward. We start with monadic first-order logic with counting.
> We provide normal forms that allow for axiomatization, determine which
> arithmetical notions are definable, and conversely, discuss which logical
> notions and reasoning principles can be defined out of arithmetical ones.
> Next we study a series of strengthenings in the same style, including
> second-order versions, systems with multiple counting, and a new modal
> logic with counting. As a complement to our fragment approach, we also
> discuss another way of controlling complexity: changing the semantics
> of counting to reason about ‘mass’ or other aggregating notions than
> cardinalities. Finally, we return to the basic reasoning practices that lie
> embedded in natural language, confronting our formal systems with
> linguistic quantifier vocabulary, monotonicity reasoning, and procedural
> semantics via semantic automata. We conclude with some pointers to
> further entanglements of logic and counting in the metamathematics
> of formal systems, the philosophy of logic, and cognitive psychology.
> (Joint work with Thomas Icard)
>
> Paper available at:
> https://eprints.illc.uva.nl/id/eprint/1813/1/Logic.Counting.pdf
> <https://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Feprints.illc.uva.nl%2Fid%2Feprint%2F1813%2F1%2FLogic.Counting.pdf&data=04%7C01%7Cjbaldwin%40groute.uic.edu%7C5d7b581aee45459e012b08d9d15b1694%7Ce202cd477a564baa99e3e3b71a7c77dd%7C0%7C0%7C637771012163730356%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C2000&sdata=Ki72h3kxHuV3g3kKd2YrHQfkKS2RhY0NdOnf3AaJhYI%3D&reserved=0>
>
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