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.