Dear all,
We will have our next LIRa session on Thursday, April 16th, 16:30-18.00. Our speaker is Yu Wei. You will receive the zoom link and a reminder of the guidelines for online sessions the day before the talk. After the talk, we will continue the discussion with (online) drinks, as usual. Please, find the details below.
Speaker: Yu Wei
Date and Time: Thursday, April 16th 2020, 16:30-18:00
(Note: the starting time is back to our normal slot of 16:30hrs)
Venue: online
Title: Quantifier-free Epistemic Term-Modal Logic with Assignments
Abstract. In standard epistemic logic, agent names are usually assumed
to be common knowledge implicitly, which is unreasonable for various
applications. Inspired by term-modal logic and assignment operators in
dynamic logic, Yanjing Wang & Jeremy Seligman (2018) introduced a
quantifier-free modal predicate logic where names can be non-rigid in
order to handle various de dicto /de re distinctions. Their main
technical result is a complete axiomatization over constant-domain S5
models.
However, it is more interesting to allow varying domains where the
existence of all agents is not commonly known, and also to include
function symbols as a natural generalization. Note that there are many
nontrivial questions about varying-domain models, like the
accessibility relations for the agents non-existent at a world, and
how to define an epistemic model in this setting. As we will see, with
properly defined varying-domain models in place, we can express the
meta-level notion “existence” and something just like Barcan
formula & Converse Barcan formula in our object language though
without any quantifiers. Additionally, varying-domain models provide
us with a wider perspective to distinguish two sorts of
constant-domain models, and prompt a systematic approach to give
axiomatizations over various Kripke and epistemic models.
As for the complexity, on one hand, we show the undecidability of all
the logics over varying-domain and two kinds of constant-domain
epistemic models. On the other hand, we can indeed find some decidable
fragments of this modal predicate logic with function symbols. This is
joint work with Yanjing Wang and Jeremy Seligman.
Reference
Wang, Y., Seligman, J. (2018). When names are not commonly known:
epistemic logic with assignments. arXiv preprint arXiv:1805.03852.
Hope to see you there!
The LIRa team