Dear all,

We will have our next LIRa session on Thursday, 15 August 11:00.

To attend online, please use the zoom link below.

This will be a special joint session with the NihiL seminar. Please note that the speaker will be on location, and note the irregular time of the day.

Speaker: Yanjing Wang (Peking University)

Date and Time: Thursday, August 15th 2024, 11:00-12:30

Onsite venue: ILLC seminar room F1.15 in Science Park 107

Online: https://uva-live.zoom.us/j/87618965843

Title: Point-set Neighborhood Logic

Abstract. In this paper, we propose Point-set Neighborhood Logic (PSNL) to reason about neighborhood structures. The bimodal language of PSNL is defined via a mutual induction of point-formulas and set-formulas. We show that this simple language is equally expressive as the language of Instantial Neighborhood Logic (INL) proposed by van Benthem et al. (2017). As the main results, we first give two complete proof systems, one in Hilbert-style and one in Gentzen sequent-style, each featuring two intertwined K-like systems. The proof of strong completeness of the Hilbert-style system is based on a direct canonical model construction without relying on a normal form. Based on the sequent calculus, we establish constructively the uniform interpolation property of PSNL, from which that of INL follows.

(Joint work with Junhua Yu)

Hope to see you there!

The LIRa team