In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.

Formalised proofs of Cut admissibility often rely on the invertibility of the rules of a sequent calculus. We will present some sufficient conditions for when a rule is invertible with respect to a calculus, which we illustrate with many examples. Appropriate definitions are given for rarely defined intuitive notions, such as a formula being principal for a rule. It must be noted we give purely...

INTRODUCTION ..................................................................................... 251 I. THE WAYBACK MACHINE AND THE ADMISSIBILITY OF SCREEN SHOTS AS EVIDENCE .................................................... 252 A. WayBack What?: How It Works ......................................... 252 B. Screen Shots as Evidence .................................................... 256 1....

This work uses temporal logic as a calculus for expressing integrity constraints that specify admissibility of dynamic database behaviour. Formulas are interpreted in state sequences representing dynamic behaviour. Our approach incorporates temporal quantification by 11 always 11 , 11 sometime 11 , and quantifiers bounded by intervals in state sequences. Moreover, dynamically changing domains o...