报告人：赵之光（荷兰代尔夫特大学博士生）

 

时间： 11月7日  下午 15: 10-18:00 地点 北大理教417 

 

摘要：Correspondence and canonicity theory have a long history in modal logic, and they are referred to as the ''three pillars of wisdom supporting the edifice of modal logic" together with duality theory. The Sahlqvist theorem gives a syntactic definition of a class of modal formulas, the Sahlqvist class, each member of which defines an elementary (i.e. first-order definable) class of Kripke frames and is canonical. Recently, a uniform and modular theory which subsumes the above results and extends them to logics with a non-classical propositional base has emerged, and has been dubbed unified correspondence. It is built on duality-theoretic insights and uniformly exports the
state-of-the-art in Sahlqvist theory from normal modal logic to a wide range of logics. 

The present talk concerns a unified correspondence treatment of the Sahlqvist theory for possibility semantics, extending the results from Sahlqvist formulas to the strictly larger class of inductive formulas, and from the full possibility frames to filter-descriptive possibility frames. Specifically, we define the possibility semantics version of the algorithm ALBA, and an adapted interpretation of the expanded modal language used in the algorithm. We make some comparisons among different semantic settings in the design of the algorithms, and put possibility semantics into this broader picture.