First - Order Incremental

We consider the problem of repeatedly evaluating the same (computationally expensive) query to a database that is being updated between successive query requests. In this situation, it should be possible to use the di erence between successive database states and the answer to the query in one state to reduce the cost of evaluating the query in the next state. We use rst-order queries to compute the di erences, and call this process \ rst-order incremental query evaluation." After formalizing the notion of rst-order incremental query evaluation, we give an algorithm that constructs, for each regular chain query (including transitive closure as a special case), a nonrecursive program to compute the di erence between the answer after an update and the answer before the update. We then extend this result to weakly regular queries, which are regular chain programs augmented with conjunctive queries having the so-called cartesian-closed increment property, and to the case of unbounded-set insertions where the sets are binary cartesian products. Finally, we show that the class of weakly regular queries is decidable.