Characterisations of Termination in Logic Programming

The procedural interpretation of logic programs and queries is parametric to the selection rule, i.e. the rule that determines which atom is selected in each resolution step. Termination of logic programs and queries depends critically on the selection rule. In this survey, we present a unified view and comparison of seven notions of universal termination considered in the literature, and the corresponding classes of programs. For each class, we focus on a sufficient, and in most cases even necessary, declarative characterisation for determining that a program is in that class. By unifying different formalisms and making appropriate assumptions, we are able to establish a formal hierarchy between the different classes and their respective declarative characterisations.