We give a simple order-theoretic construction of a Cartesian closed category of sequential functions. It is based on bistable biorders, which are sets with a partial order — the ...
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of...
Abstract. We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus ...
It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-...
Subtyping for inductive types in dependent type theories is studied in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types ar...