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Beyond Skolem Chase: A Study of Finite Chase under Standard Chase Variant

The chase procedure is an indispensable tool for several database applications, where its termination guarantees decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination. It is known that the standard chase variant is more powerful in termination analysis provided a database is given. But all-instance termination analysis presents a challenge, since the critical database and similar techniques do not work. The interest of this paper is on the following question: How to devise a framework in which various known decidable classes of finite skolem chase can all be properly extended by the technique of standard chase? To address this question, we develop a novel technique to characterize the activeness of all possible cycles of a certain length in the standard chase procedure, which leads to the formulation of a parameterized class called k-SAFE(cycle), which guarantees all-instance, allpath termination, where the parameter takes a cycle function by which a concrete class of finite standard chase is instantiated. The approach applies to any class of finite skolem chase that is identified with a condition of acyclicity. More generally, we show how to extend the hierarchy of bounded rule sets under skolem chase without increasing the complexity of data and combined reasoning tasks.