Abstract. We describe a second-order type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated supp...
—Interactive theorem provers based on higher-order logic (HOL) traditionally follow the definitional approach, reducing high-level specifications to logical primitives. This al...
Dmitriy Traytel, Andrei Popescu, Jasmin Christian ...
We survey two basic techniques for showing that the monadic second-order theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (g...
A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the subs...