Finite Frames Fail

Finite Frames Fail

Many intermediate logics, even extremely well-behaved ones such as IPC, lack the finite model property for admissible rules. We give conditions under which this failure holds. We show that frames which validate all admissible rules necessarily satisfy a certain closure condition, and we prove ...

Intuitionistic Rules

Intuitionistic Rules

The totality of admissible rules is an invariant associated to a logic. In my dissertation, I explain how one can describe the admissible rules of a logic and I hint at several ways in which admissible rules provide one with information about a given logic. To be a bit more specific, I describ...

Admissibility and refutation

Admissibility and refutation

Refutation systems are formal systems for inferring the falsity of formulae. These systems can, in particular, be used to syntactically characterise logics. In this paper, we explore the close connection between refutation systems and admissible rules. We develop technical machinery to constru...