The Ramification and Qualification Problems in Temporal Databases Nikos Papadakis & Dimitris Plexousakis University of Crete and Institute of Computer Science,FORTH

Dynamics of Databases A database represents a changing world. Changes occur as the results of database transactions. An atomic database transaction can be considered as an action.  Changes in a database occur as the results of actions. Actions have direct and indirect effects which may affect the integrity constraints.  The database may not be consistent after the execution of an action. Two infamous problems arise: the ramification and the qualification problems.

Definitions All predicates and functions whose truth value changes from one world state to another, are called fluents. One possible evolution of the world is a sequence of actions and is represented by a first-order term, called a situation. A situation contains the truth-values of fluents. When an action occurs the database changes from one situation to the next.

The Ramification Problem

The Ramification problem - Solutions All indirect effects are caused by the presence of constraints. The ramification problem refers to the concise description of the indirect effects of an action in the presence of constraints. The most simple solution is the minimal change approach. The method suggests that, when an action occurs in a situation S, we try to find the consistent situation S’ which has the fewer changes from S. Categorizing fluents. The fluents are separated in two groups. One group contains the fluents which can change only as a direct effect of an action. The other group contains the fluents which can change as direct or indirect effect of an action.

The Ramification problem - Solutions Causal relationships. A causal relationship has the form Causal relationship capture the dependence that exists between the context of a database and the indirect effects of an action.

Temporal Databases All actions occur at a specific point time. Objects and relationships exist over time. The values of fluents are dependent on the time instant at which they are evaluated.

Temporal Databases – Ramification problem Example Assume that if a public employee commits a misdemeanor then for the next five months he is considered illegal. When a public employee is illegal, then he must be suspended for the entire time interval over which he is considered illegal. In temporal databases, we must determine the direct and indirect effects of an action not only in the resulting situation, but possibly for many future situations. The solutions to the ramification problem in conventional databases can not solve the problem in temporal databases because they determine the direct and indirect effects only for the next situation.

Correspondence between time – action - situation Situation axis Time axis Action axis The above weakness can be alleviated by constructing a correspondence between situations and actions with time.

Solution We define the predicate to mean that the action a executed at time t. We assume that all action are instantaneous. We define each fluent f(t) to mean that the fluent f is true for the next t time moments. We decrease the temporal variable t as time progresses.

Solution For each action we define one dynamic rule. For each fluent f we define two static rules. The dynamic rules execute only when an action occurs. The static rules executed every time that the fluent is false. The above rules solve the ramification problem since the dynamic rule capture all direct effects of each action whereas the static ones capture the indirect effects of each action in every state of the database.

Example Assume that if a public employee commits a misdemeanor then for the next five months he is considered illegal. When a public employee is illegal, then he must be suspended for the entire time interval over which he is considered illegal. The above rules solve the ramification problem since the dynamic rule capture the direct effect (illegal) of action misdemeanor whereas the static capture the indirect effect (suspended).

The Qualification Problem

An action is allowed to execute if and only if some preconditions hold. The problem of determining the context in which an action is allowed to execute is the qualification problem. Most important solutions are: - determine the preconditions for each action. - default solution.

Temporal databases – Qualification Problem Example Assume a public employee can receive promotion only if he has stayed in the same position for at least five years and is not under suspension. In temporal databases, the direct and indirect effects of an action can disqualify some other action not only in the resulting situation, but possibly for many future situations. The solutions to the qualification problem in conventional databases can not solve the problem in temporal databases because they determine if one action can or cannot execute only in the next situation.

Solution For each action a we determine a dynamic rule. Example Assume a public employee can receive promotion only if he has stayed in the same position for at least five years and is not under suspension

Conclusion We presented a solution for the ramification and qualification problems in temporal databases, when the action are instantaneous and the execution is sequential. In the future we examine the problems when two or more action execute concurrency and when the action can change our beliefs about the past. We examine the problems when the actions have duration. We investigate these problems in a modal logic framework.