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

[Graham Leigh]

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 .

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 Amsterdam, 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
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