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Many popularly studied recursions in deductive databases can be compiled into one or a set of highly regular chain generating paths, each of which consists of one or a set of connected predicates. Previous studies on chain-based query evaluation in deductive databases take a chain generating path as an inseparable unit in the evaluation. However, some recursions, especially many functional recursions whose compiled chain consists of infinitely evaluable function(s), should be evaluated by chain-split evaluation, which splits a chain generating path into two portions in the evaluation: an immediately evaluable portion and a delayed-evaluation portion. In this paper, the necessity of chain-split evaluation is examined from the points of view of both efficiency and finite evaluation, and three chain-split evaluation techniques: magic sets, buffered evaluation, and partial evaluation are developed. Our study shows that chain-split evaluation is a primitive recursive query evaluation technique for different kinds of recursions, and it can be implemented efficiently in deductive databases by extensions to the existing recursive query evaluation methods.