We present some possible definitions for what it means for a type theory to be a conservative extension over another type theory. We do so by giving two type theories of natural numbers: T T (N) and T T (N, ×). T T (N) is ...

The analysis of time-dependent systems in a probabilistic setting has greatly benefited from the application of temporal logic. This thesis focuses on a specific probabilistic modal fixed point logic setup, which offers a ...

The concept of truth has been studied and used along the areas of philosophy, logic, and mathematics. Although is the same word (“truth”) it has been used in very different ways in each area. Logicians have studied truth ...

Intuitionistic propositional logic with 2nd order propositional quantifiers (IPL2) was introduced by Gabbay in 1974. Since then, a substantial body of work has been written about its semantics. However, there has not been ...