Dear all,
We will have our next LIRa session tomorrow, on Thursday, 23 February 16:30.
This will be a hybrid session. If you want to attend online, please use our recurring zoom link: https://uva-live.zoom.us/j/89230639823?pwd=YWJuSnJmTDhXcWhmd1ZkeG5zb0o5UT09 (Meeting ID: 892 3063 9823, Passcode: 421723)
You can find the details of the talk below.
Speaker: Søren Knudstorp (ILLC, University of Amsterdam)
Date and Time: Thursday, February 23rd 2023, 16:30-18:00
Venue: ILLC seminar room F1.15 in Science Park 107 and online.
Title: Modal Information Logics: Axiomatizations and Decidability
Abstract. In this talk, I will be presenting results from my Master of Logic thesis “Modal Information Logics”, supervised by Johan van Benthem and Nick Bezhanishvili.
The thesis studies formal properties of a family of so-called modal information logics (MILs) — modal logics first proposed in van Benthem (1996) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states.
Although MILs have been around for some time, not much is known: van Benthem (2017, 2019) pose two problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability.
The main results of the first part of the talk are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability. These results are then build upon to axiomatize and prove decidable the MILs attained by endowing the language with an ‘informational implication’—in doing so a link is also made to the work of Buszkowski (2021) on the Lambek Calculus.
Broadening the study, the basic MIL of suprema on join-semilattices is axiomatized with an infinite scheme. This constitutes the by far most substantive part of the thesis, hence we will only be lending an informal focus to accenting key ideas.
Finally, if time allows, we will comment on the connection between truthmaker semantics and MILs and extend the (compactness and) decidabilit results in Fine and Jago (2019), chiefly via defining and proving a truthmaker analogue of the FMP.
Hope to see you there!
The LIRa team