We consider Martin-Löf’s well-ordering type constructor in the context of an impredicative type theory. We show that the well-ordering types can represent various inductive types faithfully in the presence of the filling-up equality rules or η-rules. We also discuss various properties of the filling-up rules. ! " ! # $ % &" '( ) '* + '' + ,. '' " ''/0 % &..'1 " '2 34",5 6 ,5/0 7 % ! 0 " ! # &" ...

Behavioural type systems ensure more than the usual safety guarantees of static analysis. They are based on the idea of “types-as-processes”, providing dedicated type algebras for particular properties, ranging from protocol compatibility to race-freedom, lock-freedom, or even responsiveness. Two successful, although rather different, approaches, are session types and process types. The former ...

Semantic substitution errors (e.g., saying "arm" when "leg" is intended) are among the most common types of errors occurring during spontaneous speech. It has been shown that grammatical gender of German target nouns is preserved in the errors (E. Mane, 1999). In 3 experiments, the authors explored different accounts of the grammatical gender preservation effect in German. In all experiments, s...

We prove that, if a geodesic metric space has Markov type 2 with constant 1, then it is an Alexandrov space of nonnegative curvature. The same technique provides a lower bound of the Markov type 2 constant of a space containing a tripod or a branching point.

In this paper, we firstly review the neutrosophic set, and then construct two new concepts called neutrosophic implication of type 1 and of type 2 for neutrosophic sets. Furthermore, some of their basic properties and some results associated with the two neutrosophic implications are proven.

In this note first we define the notion of dual positive implicative hyper Kideal of type 4, where for simplicity is written by DPIHKI − T4. Then we give some related results. Finally we determine all of hyper K-algebras of order 3, which have D1 = {1}, D2 = {1, 2} or D3 = {0, 1} as a DPIHKI − T4.