Belief Contraction, Anti-formulae and Resource Overdraft: Part I Deletion in Resource Bounded Logics

There are several areas in applied logic where deletion from databases is involved in one way or another: Belief contraction (as formulated in the AGM theory of revision and contraction) Triggers of the form ‘If condition then remove A’, which are extensively used in database management systems Resource considerations as in relevance and linear logics, where addition or removal of resource can affect provability Free logic and the like, where existence and non-existence of individuals affects quantification. All of these areas have certain logical difficulties relating to the removal of elements. These difficulties are normally overcome by working on the meta-level. This paper offers a comprehensive model in which the various forms of removal are treated on the object level, i.e., as connectives of the object language.