Title：Semantics for Varying-Domain First-Order Modal Logic

Speaker：Yuanzhe Yang (PKU)

Time: 2024/11/19 15:10-18:00

Location: Room 206, Building of Geometry (地学楼), Peking University

Abstract：

Varying-domain first-order Kripke model is a very natural generalization of ordinary Kripke model, in which each world is a distinct first-order structure, and the domains of such structures can be completely different. However, it is not easy to define a reasonable semantics on such structures. In this talk, we first review a number of different varying-domain semantics for first-order modal logic, including free logic, common-sense modality and indexed modality. Then, we introduce two new kinds of varying-domain semantics: the first is the semantics with a strict implication operator generalizing the common-sense modality, and the second is the semantics equipped with two kinds of variables (one local and the other global), and two assignment operators through which variables of different kinds can exchange their values. We will present expressivity and axiomatization results for these semantics.