Observer-invariance is regarded as a minimum requirement for an appropriate definition of time derivatives. We derive various derivatives systematically from spacetime setting, where observer-invariance special case covariance principle and covered by Ricci-calculus. The analysis considered tangential n -tensor fields on moving surfaces provides formulations which are applicable numerical compu...

Glivenko's theorem says that, in propositional logic, classical provability of a formula entails intuitionistic double negation that formula. We generalise from to an arbitrary nucleus, calculus inductively generated abstract consequence relation, and logic any set objects whatsoever. The resulting conservation comes with precise criteria for its validity, which allow us instantly include G\"od...

We give syntax and a PER-model semantics for a typed-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of sub-typing with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtyping systems. Single-ton types have applications in the use of type systems for speciication and progra...