On the Inference of Natural Level Mappings: A Decade of Research Advances in Logic-Based Program Development

Reasoning about termination is a key issue in logic program development. One classic technique for proving termination is to construct a well-founded order on goals that decreases between successive goals in a derivation. In practise, this is achieved with the aid of a level mapping that maps atoms to natural numbers. This paper examines why it can be difficult to base termination proofs on natural level mappings that directly relate to the recursive structure of the program. The notions of bounded-recurrency and bounded-acceptability are introduced to alleviate these problems. These concepts are equivalent to the classic notions of recurrency and acceptability respectively, yet provide practical criteria for constructing termination proofs in terms of natural level mappings for definite logic programs. Moreover, the construction is entirely modular in that termination conditions are derived in a bottom-up fashion by considering, in turn, each the strongly connected components of the program.