Inductive inference of logic programs based on algebraic semantics

In this paper we present a new inductive inference algorithm for a class of logic programs, called linear monadic logic programs. It has several unique features not found in Shapiro's Model Inference System. It has been proved that a set of trees is rational if and only if it is computed by a linear monadic logic program, and that the rational set of trees is recognized by a tree automaton. Based on these facts, we can reduce the problem of inductive inference of linear monadic logic programs to the problem of inductive inference of tree automata. Further several efficient inference algorithms for finite automata have been developed. We extend them to an inference algorithm for tree automata and use it to get an efficient inductive inference algorithm for linear monadic logic programs. The correctness, time complexity and several comparisons of our algorithm with Model Inference System are shown.