Belief Contraction, Anti-Formulae and Resource Overdraft:Part II Deletion In Resource Unbounded Logics

Abstract

The operation of deletion plays an important role in many areas of applied logic. However, there are a number of logical difficulties relating to the removal of elements from a database. These difficulties are usually handled by executing the operation of deletion on the meta-level. In Gabbay et al. 2002, we argued that bringing the operation of deletion to the object level was a useful exercise and we analysed how this can be achieved in resource bounded logics such as linear logic. In this paper, we continue the investigation by analysing ways of effecting object level deletion for logics which do not have a resource bound on the number of times a formula can be used.