This paper deals with database updates. More precisely we focus on addition and deletion operations, when transition constraints are expressed on the database.
In the first section, we present an overview of works in the fields of belief revision, knowledge base and database updates. We claim that database update semantics is a formulas-based (or syntactical) one. Furthermore, we pay attention to the notion of transition constraints, introduced in the database domain many years ago in order to constrain state changes.
In the second section, we present the formalism we think necessary to express transition constraints and reason with them. It is a particular modal formalism which allows us to reason with the current state of the database and with its next state as well.
In Sections 3 and 4, we intend to characterize the database state that follows from an addition or a deletion, taking transition constraints into account. We give importance to a notion of minimal change which extends the classical notion of minimal change on finite bases. We show that, when no transition constraint is expressed, the semantics we give to the addition (resp.: deletion) is a maxichoice one. We also focus on another particular case of transition constraints which could allow us to computationally generate the next database state. Then we discuss the problem of extending these cases to the general one.