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)
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.
Wang, Y., Seligman, J. (2018). When names are not commonly known: epistemic logic with assignments. arXiv preprint arXiv:1805.03852.