Topological Generalizations of Possible Worlds Semantics and Their Proof Systems

Explore topological generalizations of possible worlds semantics and their proof systems in this 32-minute lecture by Sara Negri. Delve into the framework of neighbourhood semantics and its applications to modal and conditional logics. Examine the transition from Kripke semantics to neighbourhood semantics, and discover how these concepts relate to modalities and conditionals. Investigate non-normal logics and the process of deriving sequent calculus rules from neighbourhood semantics. Learn about monotonic systems, structural properties of NS-sequent calculi, and improvements for non-monotonic systems. Analyze bi-neighbourhood semantics, including labelled calculus, soundness, completeness, and optimization techniques. Gain insights into ongoing research in this field, based on collaborative work with Nicola Olivetti, Marianna Girlando, and Tiziano Delmonte.

Syllabus

Intro
From Kripke (relational) to neighbourhood semantics
Neighbourhood Semantics (cont.)
The link between neighbourhood semantics and
Modalities and conditionals through neighbourhood semantics
Non-normal logics (classical modal logics)
From neighbourhood semantics to sequent calculus rules
From (classical modal) axioms to (NS) rules
Monotonic systems In some cases, instead of adding extra neighbourhood
Structural properties of NS-sequent calculi
Improvements for non-monotonic systems
Bi-neighbourhood semantics
A bi-neighbourhood labelled calculus-LSE (2)
Soundness and completeness
Optimization-TLSE (3)
Completeness and decidability
Summary