The Many Faces of Modal Logic

Dirk Pattinson (ANU)

Dirk Pattinson (ANU) will give present "The Many Faces of Modal Logic" at 11 in G14 Old Quad.

Abstract: Syntactically, all modal logics arise as extensions of propositional logics with additional operators. This view encompasses many logics that are structurally different and have been designed and studied for different purposes, such as (extensions of) the modal logic K, probabilistic and graded modal logics and various variants of conditional logic. The talk is centred around the question of whether (and how?) something similar also happens on the semantical level. The starting point is that the semantics of modal logics is defined in terms of possible worlds where each world comes with additional structure, such as relational successors for the modal logic K, or preference relations for logics of non-monotonic reasoning. We systematise this into a general notion of co-algebraic semantics and focus on the question of what properties can be investigated at this, more encompassing, level of generality, and shed light on the questions of completeness, decidability and complexity.